1,592
个编辑
更改
跳到导航
跳到搜索
Moved page from wikipedia:en:Benoit Mandelbrot (history)
此词条暂由彩云小译翻译，翻译字数共1902，未经人工整理和审校，带来阅读不便，请见谅。
{{short description|French-American mathematician}}
{{See also|Mandelbrot set}}
{{Use dmy dates|date=February 2020}}
{{Infobox scientist
{{Infobox scientist
{信息盒科学家
| name = Benoit<span style="font-size:80%;font-weight:normal"><!-- The following syntax required to permit nested refs: -->{{#tag:ref|In his autobiography, Mandelbrot did not add a [[circumflex]] to the "i" (i.e. "î") in his first name, as is usual for [[Benoît|the French given name]]. He included "B" as a [[middle initial]]. His ''New York Times'' obituary stated that "he added the middle initial himself, though it does not stand for a middle name",<ref name="nyt_obit">{{cite news |url=https://www.nytimes.com/2010/10/17/us/17mandelbrot.html |title=Benoît Mandelbrot, Mathematician, Dies at 85 |last=Hoffman |first=Jascha |date=16 October 2010 |work=The New York Times |accessdate=16 October 2010}}</ref> an assertion that is supported by his obituary in ''The Guardian''.<ref name="guardian_obit">{{cite news |url=https://www.theguardian.com/science/2010/oct/17/benoit-mandelbrot-obituary |title=Benoît Mandelbrot obituary |last=Lesmoir-Gordon |first=Nigel |date=17 October 2010 |work=[[The Guardian]] | accessdate=17 October 2010 |location=London}}</ref>|group=n|name=Mandelbrot's_name}}</span> Mandelbrot
| name = Benoit<span style="font-size:80%;font-weight:normal"><!-- The following syntax required to permit nested refs: --></span> Mandelbrot
| name = Benoit < span o < > style = " font-size: 80% ; font-weight: normal" > < !-以下语法允许嵌套裁判: -- > </span > Mandelbrot
| image = Benoit Mandelbrot, TED 2010.jpg
| image = Benoit Mandelbrot, TED 2010.jpg
2010年 TED 本华·曼德博
| caption = Mandelbrot at a [[TED (conference)|TED conference]] in 2010 shortly before his death.
| caption = Mandelbrot at a TED conference in 2010 shortly before his death.
2010年，曼德尔布洛特去世前不久在 TED 大会上。
| birth_date = {{birth date|1924|11|20|df=y}}
| birth_date =
出生日期
| birth_place = [[Warsaw]], [[Second Polish Republic|Poland]]
| birth_place = Warsaw, Poland
出生地: 波兰华沙
| death_date = {{death date and age|2010|10|14|1924|11|20|df=y}}
| death_date =
死亡日期
| death_place = [[Cambridge, Massachusetts]], United States
| death_place = Cambridge, Massachusetts, United States
死亡地点: 美国马萨诸塞州剑桥
| nationality = {{hlist | Polish | French | American}}
| nationality =
国籍 =
| fields = {{hlist | [[Mathematics]] | [[Aerodynamics]]}}
| fields =
2012年10月22日 | 田野 =
| alma_mater = {{br list | [[École Polytechnique]] | {{nowrap|[[California Institute of Technology]]}} | [[University of Paris]]}}
| alma_mater = | University of Paris}}
巴黎大学
| doctoral_students = {{hlist |class=nowraplinks |list_style=line-height:1.25em | [[Laurent-Emmanuel Calvet|L-E. Calvet]] | [[Eugene Fama]] | [[Ken Musgrave]] | [[Murad Taqqu]] <!--Red link: | [[Daniel Zajdenweber]]-->}}
| doctoral_students =
博士生 =
| known_for = {{hlist |class=nowraplinks |list_style=line-height:1.25em | [[Mandelbrot set]] | [[Chaos theory]] | [[Fractal]]s | [[Zipf–Mandelbrot law]]}}
| known_for =
已知的
| influences = [[Johannes Kepler]], [[Paul Lévy (mathematician)|Paul Lévy]], [[Szolem Mandelbrojt]]
| influences = Johannes Kepler, Paul Lévy, Szolem Mandelbrojt
| influences = Johannes Kepler, Paul Lévy, Szolem Mandelbrojt
| influenced = [[Nassim Nicholas Taleb]]
| influenced = Nassim Nicholas Taleb
影响 = 纳西姆·尼可拉斯·塔雷伯
| spouse = {{longitem|Aliette Kagan<br />{{smaller|married 1955–2010 (his death)}}}}
| spouse = }}
| spouse = }
| work_institutions = {{hlist | [[Yale University]] | [[IBM]]}} {{longitem|[[Pacific Northwest National Laboratory]]}}
| work_institutions =
工作机构
| prizes = {{longitem|style=line-height:1.15em;white-space:nowrap |''[[Légion d'honneur]]''<br />{{smaller|(''Chevalier'' 1990{{dot}}''Officier'' 2006)}}}} {{Br list | 2003 [[Japan Prize]] | 1993 [[Wolf Prize]] | 1989 [[Harvey Prize]] | 1986 [[Franklin Medal]] | 1985 [[Barnard Medal for Meritorious Service to Science|Barnard Medal]]}}
| prizes = Officier 2006)}}}}
2006)}}}}}}
}}
}}
}}
'''Benoit B.'''<ref group="n" name="Mandelbrot's_name" /> '''Mandelbrot'''{{#tag:ref|Pronounced {{IPAc-en|ˈ|m|æ|n|d|əl|b|r|ɒ|t}} {{respell|MAN|dəl-brot}} in English.<ref>{{OED|Mandelbrot}}</ref> When speaking in French, Mandelbrot pronounced his name {{IPA-fr|bənwa mɑ̃dɛlbʁot|}}.<ref>Recording of the ceremony on 11 September 2006 at which Mandelbrot received the insignia for an Officer of the ''[[Legion of Honour|Légion d'honneur]]''.</ref>|group=n}} (20 November 1924 – 14 October 2010) was a Polish-born French and American [[mathematician]] and [[polymath]] with broad interests in the practical sciences, especially regarding what he labeled as "the art of [[Benoit Mandelbrot#Fractals and the .22theory of roughness.22|roughness]]" of physical phenomena and "the uncontrolled element in life".<ref>https://www.insidescience.org/news/remembering-father-fractals</ref><ref>[https://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness?language=en Benoit Mandelbrot: Fractals and the art of roughness]. ted.com (February 2010)</ref><ref>[[#Hudson|Hudson & Mandelbrot]], Prelude, page xviii</ref> He referred to himself as a "fractalist"<ref name=Mandelbrot/> and is recognized for his contribution to the field of [[fractal geometry]], which included coining the word "fractal", as well as developing a theory of "roughness and [[self-similarity]]" in nature.<ref name=nature>{{Cite journal
Benoit B. When speaking in French, Mandelbrot pronounced his name .|group=n}} (20 November 1924 – 14 October 2010) was a Polish-born French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist"
伯努瓦 b。在用法语说话时，曼德布洛特宣布了他的名字。| group = n }(1924年11月20日至2010年10月14日)是波兰出生的法国和美国数学家和博学家，对实用科学有着广泛的兴趣，特别是对他所称的物理现象的”粗糙艺术”和”生活中不受控制的元素”。他说自己是个“分裂主义者”
| last1 = Gomory | first1 = R.
| authorlink1 = Ralph E. Gomory
In 1936, while he was a child, Mandelbrot's family emigrated to France from Warsaw, Poland. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.
1936年，当曼德布洛特还是个孩子的时候，他的家人从波兰华沙移民到了法国。第二次世界大战结束后，曼德布洛特学习了数学，从巴黎和美国的大学毕业，并在加利福尼亚理工学院获得了航空学硕士学位。他的大部分职业生涯都在美国和法国度过，拥有法国和美国双重国籍。1958年，他在 IBM 开始了35年的职业生涯，在那里他成为了 IBM 研究员，并定期休假到哈佛大学教书。在哈佛大学，他发表了关于美国商品市场与棉花期货的研究成果之后，他开始教授经济学和应用科学。
| title = Benoît Mandelbrot (1924–2010)
| doi = 10.1038/468378a
Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the Mandelbrot set in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order".
由于可以访问 IBM 的计算机，曼德尔布洛特是第一个使用计算机图形学图形来创建和显示分形几何图形的人，这导致了他在1980年发现了曼德尔布洛特集合。他展示了如何从简单的规则中创造出视觉的复杂性。他说，通常被认为是“粗糙”、“混乱”或“混乱”的事物，如云或海岸线，实际上有一定程度的秩序。
| journal = Nature
| volume = 468
Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012.
在他职业生涯的最后阶段，他是耶鲁大学数学科学系的斯特林教席，也是耶鲁历史上获得终身教职的最年长的教授。曼德布洛特还在太平洋西北国家实验室、法国里尔北方的大学、高级研究所和法国国家科学研究中心担任过职务。在他的职业生涯中，他获得了超过15个荣誉博士学位，并在许多科学期刊上服务，同时还获得了许多奖项。他的自传《分析家: 科学怪人的回忆录》在他死后于2012年出版。
| issue = 7322
| pages = 378
| year = 2010
Mandelbrot was born in a Jewish family, in Warsaw during the Second Polish Republic. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." Later, the family's move to France, the war, and his acquaintance with his father's brother, the mathematician Szolem Mandelbrojt who had moved to Paris around 1920, further prevented a standard education.
曼德布洛特出生于第二波兰共和国时期的华沙的一个犹太家庭。他的父亲靠卖衣服为生，母亲是牙科医生。在他的头两个学年里，他的一位叔叔私下辅导他，他鄙视死记硬背: “我的大部分时间都花在下棋、看地图和学习如何睁开眼睛看我周围的一切。”后来，他们全家搬到了法国，战争爆发，他和父亲的兄弟，数学家 Szolem Mandelbrojt 相识，后者在1920年前后移居巴黎，这进一步阻碍了他接受标准教育。
| pmid = 21085164
|bibcode = 2010Natur.468..378G | s2cid = 4393964
The family emigrated from Poland to France in 1936, when he was 11. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies. Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:
1936年，当他11岁的时候，他们一家从波兰移民到法国。他写道: “我的父母作为经济和政治难民加入了 Szolem，这一事实挽救了我们的生命。”。曼德布洛特曾在巴黎的 Lycée Rolin 工作，直到二战爆发，他的家人搬到了法国的图勒。他在布里夫拉盖亚尔德的犹太教教士 David Feuerwerker 的帮助下继续学业。当时法国大部分地区都被纳粹占领，曼德布洛特回忆起这段时期:
}}</ref>
{{quote|Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why? In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York.
{引用 | 我们一直担心的是，一个足够坚定的敌人可能会向某个权威举报我们，我们将会被送去送死。来自巴黎的密友吉娜 · 莫汉格就遇到了这种情况，她是附近一个县城的内科医生。仅仅是为了消除竞争，另一个医生谴责她... 我们逃过了这个命运。谁知道为什么呢？1958年，这对夫妇移居美国，在那里曼德尔布洛特加入了位于约克敦海茨的 IBM 汤玛士·Ｊ·华生研究中心的研究人员。
In 1936, while he was a child, Mandelbrot's family emigrated to France from [[Warsaw]], Poland. After [[World War II]] ended, Mandelbrot studied mathematics, graduating from universities in Paris and the United States and receiving a master's degree in [[aeronautics]] from the [[California Institute of Technology]]. He spent most of his career in both the United States and France, having [[Multiple citizenship|dual]] [[French nationality law|French]] and [[United States nationality law#Dual citizenship|American]] citizenship. In 1958, he began a 35-year career at [[IBM]], where he became an [[IBM Fellow]], and periodically took leaves of absence to teach at [[Harvard University]]. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.
In his early work, he found that the price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.
在他的早期工作中，他发现金融市场的价格变化并不遵循正态分布，而是具有无限方差的 l é vy 稳定分布。例如，他发现，棉花价格遵循一个 l é vy 稳定分布，参数 α 等于1.7，而不是像正态分布一样遵循2。“稳定”分布具有这样的性质: 一个随机变量的多个实例的和服从相同的分布，但具有更大的尺度参数。
Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the [[Mandelbrot set]] in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order".<ref name="Wolfram" /> His math and geometry-centered research career included contributions to such fields as [[statistical physics]], [[meteorology]], [[hydrology]], [[geomorphology]], [[anatomy]], [[taxonomy (biology)|taxonomy]], [[neurology]], [[linguistics]], [[information technology]], [[computer graphics]], [[economics]], [[geology]], [[medicine]], [[physical cosmology]], [[engineering]], [[chaos theory]], [[econophysics]], [[metallurgy]] and the [[social science]]s.<ref>list includes specific sciences mentioned in [[#Hudson|Hudson & Mandelbrot]], the Prelude, p. xvi, and p. 26</ref>
Toward the end of his career, he was [[Sterling Professor]] of Mathematical Sciences at [[Yale University]], where he was the oldest professor in Yale's history to receive tenure.<ref>{{cite web |author=Steve Olson | url=http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html |title=The Genius of the Unpredictable |publisher=Yale Alumni Magazine |date=November–December 2004 |accessdate=22 July 2014| author-link=Steve Olson (writer) }}</ref> Mandelbrot also held positions at the [[Pacific Northwest National Laboratory]], [[Université Lille Nord de France]], [[Institute for Advanced Study]] and [[Centre National de la Recherche Scientifique]]. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, ''The Fractalist: Memoir of a Scientific Maverick'', was published posthumously in 2012.
As a visiting professor at Harvard University, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in 1979. In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".
作为哈佛大学的客座教授，Mandelbrot 开始研究被称为 Julia 集的分形，它们在复平面的某些变换下是不变的。在加斯顿 · 朱莉娅和皮埃尔 · 法图之前工作的基础上，曼德尔布洛特使用计算机绘制了朱莉娅集合的图像。在研究这些 Julia 集的拓扑结构时，他研究了他在1979年提出的 Mandelbrot 集。1982年，曼德布洛特在《自然的分形几何》一书中扩展和更新了他的观点。这一有影响力的工作带来了分形进入主流的专业和流行数学，以及沉默批评家，谁曾驳回分形作为“程序人工制品”。
== Early years ==
Mandelbrot speaking about the [[Mandelbrot set, during his acceptance speech for the Légion d'honneur in 2006]]
曼德布洛特谈到了[2006年他在法国荣誉军团勋章的获奖感言中谈到了曼德布洛特集合]
Mandelbrot was born in a [[Jews|Jewish]] family, in [[Warsaw]] during the [[Second Polish Republic]]. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."<ref name="wolf">{{cite journal |last=Mandelbrot |first=Benoît |title=The Wolf Prizes for Physics, ''A Maverick's Apprenticeship''|publisher=Imperial College Press |year=2002 |url=http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf}}</ref> Later, the family's move to France, the [[World War II|war]], and his acquaintance with his father's brother, the mathematician [[Szolem Mandelbrojt]] who had moved to Paris around 1920, further prevented a standard education.
In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension. According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before". Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":
1975年，曼德布洛特创造了分形这个术语来描述这些结构，并首次发表了他的观点，后来被翻译成分形: 形式、机会和维度。计算机科学家、物理学家斯蒂芬•沃尔夫拉姆(Stephen Wolfram)表示，这本书对曼德布洛特来说是一个“突破” ，在此之前，他通常会“将相当简单的数学应用到以前几乎没有认真研究过数学的领域”。沃尔夫勒姆补充说，由于这项新研究的结果，他不再是一个“流浪的科学家” ，后来称他为“分形之父” :
The family emigrated from Poland to France in 1936, when he was 11. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.<ref name=Mandelbrot />{{rp|17}}<ref name="bbc_obit">{{cite news|url=https://www.bbc.co.uk/news/world-europe-11560101|title=BBC News – 'Fractal' mathematician Benoît Mandelbrot dies aged 85|date=17 October 2010|work=[[BBC Online]] | accessdate=17 October 2010}}</ref> Mandelbrot attended the Lycée Rolin in Paris until the start of [[World War II]], when his family moved to [[Tulle]], France. He was helped by [[Rabbi]] [[David Feuerwerker]], the Rabbi of [[Brive-la-Gaillarde]], to continue his studies.<ref name=Mandelbrot/>{{rp|62–63}}<ref>Hemenway P. (2005) ''Divine proportion: Phi in art, nature and science''. Psychology Press. {{isbn|0-415-34495-6}}</ref> Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:
{{quote|Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.
{引用 | Mandelbrot 最终做了一项伟大的科学工作，确定了一个更强大、更基本的观点ーー简而言之，有一些被他称为“分形”的 Unicode几何图形列表，在所有尺度上都是同样“粗糙”的。无论你看起来多么近，它们都不会变得更简单，就像你脚下看到的岩石海岸线的部分看起来就像你从太空中看到的那样参差不齐。
{{quote|Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?<ref name=Mandelbrot />{{rp|49}}}}
A Mandelbrot set
一个曼德布洛特集合
In 1944, Mandelbrot returned to Paris, studied at the [[Lycée du Parc]] in [[Lyon]], and in 1945 to 1947 attended the [[École Polytechnique]], where he studied under [[Gaston Julia]] and [[Paul Lévy (mathematician)|Paul Lévy]]. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics.<ref name="guardian_obit" /> Returning to France, he obtained his [[Doctor of Philosophy|PhD degree]] in Mathematical Sciences at the [[University of Paris]] in 1952.<ref name="wolf" />
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
然而，曼德布洛特从未觉得自己正在发明一种新思想。他在与科学作家亚瑟·查理斯·克拉克的一部纪录片中描述了自己的感受:
==Research career==
From 1949 to 1958, Mandelbrot was a staff member at the [[Centre National de la Recherche Scientifique]]. During this time he spent a year at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]], where he was sponsored by [[John von Neumann]]. In 1955 he married Aliette Kagan and moved to [[Geneva, Switzerland]] (to collaborate with [[Jean Piaget]] at the International Centre for Genetic Epistemology) and later to the [[Université Lille Nord de France]].<ref name="people">{{Cite journal|last=Barcellos|first=Anthony|title=Mathematical People, ''Interview of B. B. Mandelbrot''|publisher=Birkhaüser|year=1984|url=http://users.math.yale.edu/~bbm3/web_pdfs/inHisOwnWords.pdf}}</ref> In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the [[International Business Machines|IBM]] [[Thomas J. Watson Research Center]] in [[Yorktown Heights, New York]].<ref name="people" /> He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow [[Emeritus]].<ref name="wolf" />
According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence<blockquote>the name Mandelbrot, and the word "mandala"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas. He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
根据克拉克的说法，“曼德尔布罗特集合确实是整个数学史上最惊人的发现之一。谁能想到这么简单的一个方程竟然能产生无限复杂的图像? ”克拉克还注意到了一个“奇怪的巧合”——曼德尔布洛特的名字，以及“曼荼罗”——意为宗教象征——我确信这纯粹是巧合，但事实上曼德尔布洛特集似乎包含了大量的曼荼罗。他加入了耶鲁大学数学系，并在1999年获得了他的第一个终身职位，那时他75岁。在他2005年退休的时候，他是数学科学的斯特林教席。
<!-- Deleted image removed: [[File:Mandelbrot-IBM.jpg|thumb|left|Mandelbrot working at IBM]] -->
From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as [[information theory]], economics, and [[fluid dynamics]].
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.}}
曼德布洛特创立了有史以来第一个“粗糙理论” ，他看到了山脉、海岸线和河流盆地形状的“粗糙” ，看到了植物、血管和肺的结构，看到了星系的聚集。他个人的追求是创造一些数学公式来衡量这些物体在自然界中的整体“粗糙度”
===Randomness in financial markets===
In his paper titled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses self-similar curves that have Hausdorff dimension that are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.
在他题为《英国海岸有多长？统计自相似性和分维数1967年发表在《科学》杂志上，曼德尔布洛特讨论了自相似曲线，这些曲线都有豪斯多夫维数，是分形的例子，尽管曼德尔布洛特在论文中没有使用这个术语，因为他直到1975年才造出这个术语。这篇论文是曼德布洛特关于分形主题的首批出版物之一。
Mandelbrot saw [[financial market]]s as an example of "wild randomness", characterized by concentration and long range dependence. He developed several original approaches for modelling financial fluctuations.<ref>{{cite book |author= Rama Cont |chapter= Mandelbrot, Benoit |journal= Encyclopedia of Quantitative Finance |publisher= Wiley |date= 19 April 2010 |doi= 10.1002/9780470061602.eqf01006 |isbn = 9780470057568|author-link= Rama Cont }}</ref>
In his early work, he found that the price changes in [[financial market]]s did not follow a [[Gaussian distribution]], but rather [[Paul Lévy (mathematician)|Lévy]] [[stable distributions]] having infinite [[variance]]. He found, for example, that cotton prices followed a Lévy stable distribution with parameter ''α'' equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger [[scale parameter]].<ref>{{cite web |url=https://www.newscientist.com/article/mg15420784.700-flight-over-wall-st.html |title=''New Scientist'', 19 April 1997 |publisher=Newscientist.com |date=19 April 1997 |accessdate=17 October 2010}}</ref>
Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured." and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.
曼德布洛特强调用分形作为现实和有用的模型来描述现实世界中的许多“粗糙”现象。他的结论是: “真实的粗糙度通常是分形的，可以测量。”还是个特立独行的人。他非正式和充满激情的写作风格和他对视觉和几何直觉的强调(通过大量插图的支持)使得《自然的分形几何学》对非专业人士来说易于理解。这本书激发了人们对分形的广泛兴趣，并促成了混沌理论和其他领域的科学和数学。
===Developing "fractal geometry" and the Mandelbrot set===
Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.
曼德布洛特也将他的想法应用于宇宙学。1974年，他对奥尔伯斯悖论(“黑暗的夜空”之谜)提出了新的解释，证明了分形理论的结果是解决这一悖论的充分而非必要的方法。他假设，如果宇宙中的恒星是分散分布的(例如，康托尔尘埃) ，就没有必要依靠大爆炸理论来解释这一悖论。他的模型不能排除宇宙大爆炸的可能性，但是即使宇宙大爆炸没有发生，也可以考虑到黑暗的天空。
As a visiting professor at [[Harvard University]], Mandelbrot began to study fractals called [[Julia set]]s that were invariant under certain transformations of the [[complex plane]]. Building on previous work by [[Gaston Julia]] and [[Pierre Fatou]], Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the [[Mandelbrot set]] which was introduced by him in 1979. In 1982, Mandelbrot expanded and updated his ideas in ''[[The Fractal Geometry of Nature]]''.<ref>[https://books.google.com/books?id=xJ4qiEBNP4gC&printsec=frontcover ''The Fractal Geometry of Nature''], by Benoît Mandelbrot; W H Freeman & Co, 1982; {{isbn|0-7167-1186-9}}</ref> This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "[[Artifact (observational)|program artifacts]]".
Mandelbrot's awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006.
曼德布洛特获得的奖项包括1993年的沃尔夫物理奖、2000年欧洲地球物理学会的刘易斯 · 弗莱 · 理查森奖、2003年的日本奖以及2006年的美国数学学会爱因斯坦讲师奖。
[[File:Mandelbrot p1130876.jpg|thumb|right|Mandelbrot speaking about the [[Mandelbrot set]], during his acceptance speech for the [[Légion d'honneur]] in 2006]]
The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Chevalier in France's Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises.
小行星27500 Mandelbrot 以他的名字命名。1990年11月，他被授予法国法国荣誉军团勋章骑士称号。2005年12月，曼德尔布洛特被任命为太平洋西北国家实验室的巴特尔研究员。2006年1月，曼德尔布洛特被提升为法国荣誉军团勋章安全委员会官员。在2010年5月的毕业典礼上，曼德尔布洛特获得了约翰·霍普金斯大学的荣誉学位。
In 1975, Mandelbrot coined the term ''[[fractal]]'' to describe these structures and first published his ideas, and later translated, ''Fractals: Form, Chance and Dimension''.<ref>''Fractals: Form, Chance and Dimension'', by Benoît Mandelbrot; W H Freeman and Co, 1977; {{isbn|0-7167-0473-0}}</ref> According to computer scientist and physicist [[Stephen Wolfram]], the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".<ref name=Wolfram>Wolfram, Stephen. [https://www.wsj.com/articles/SB10001424127887324439804578107271772910506 "The Father of Fractals"], ''Wall Street Journal'', 22 November 2012</ref> Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":
A partial list of awards received by Mandelbrot:
曼德布洛特获得的部分奖项:
{{quote|Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.<ref name=Wolfram />}}
Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesco broccoli are two examples from nature."<ref name=Wolfram /> He points out an unexpected conclusion:
{{quote|One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.<ref name=Wolfram />}}
Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphic computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s [[psychedelic art]] with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist [[Johannes Kepler]], who calculated and described the orbits of the planets.<ref>Ivry, Benjamin. [http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all "Benoit Mandelbrot Influenced Art and Mathematics"], ''Forward'', 17 November 2012</ref>
[[File:Newton-lplane-Mandelbrot.jpg|thumb|A Mandelbrot set]]
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
{{quote|Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.<ref name=Clarke>[https://www.youtube.com/watch?v=Lk6QU94xAb8 "Arthur C Clarke – Fractals – The Colors Of Infinity"], video interviews, 54 min.</ref>}}
According to Clarke, "the [[Mandelbrot set]] is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally ''infinite'' complexity?" Clarke also notes an "odd coincidence<blockquote>the name Mandelbrot, and the word "[[mandala]]"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.<ref name=Clarke /></blockquote>
Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division.<ref name="wos44">{{cite web|url=http://www.webofstories.com/play/10483|title=Web of Stories • Benoît Mandelbrot • IBM: background and policies|last=Mandelbrot|first=Benoît|author2=Bernard Sapoval|author3=Daniel Zajdenweber|date=May 1998|publisher=[[Web of Stories]] | accessdate=17 October 2010}}</ref> He joined the Department of Mathematics at [[Yale]], and obtained his first [[tenure]]d post in 1999, at the age of 75.<ref name="Tenner">{{cite news|url=https://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/|title=Benoît Mandelbrot the Maverick, 1924–2010|last=Tenner|first=Edward|date=16 October 2010|work=[[The Atlantic]] | accessdate=16 October 2010}}</ref> At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
===Fractals and the "theory of roughness"===
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, [[coastline]]s and [[river basin]]s; the structures of plants, [[blood vessel]]s and [[lung]]s; the clustering of [[galaxy|galaxies]]. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.<ref name=Mandelbrot />{{rp|xi}} He began by asking himself various kinds of questions related to nature:
{{quote|Can [[geometry]] deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?<ref name=Mandelbrot>Mandelbrot, Benoit (2012). ''The Fractalist: Memoir of a Scientific Maverick'', Pantheon Books. {{isbn|978-0-307-38991-6}}.</ref>{{rp|xii}}}}
In his paper titled [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]] published in [[Science (journal)|''Science'']] in 1967 Mandelbrot discusses [[self-similarity|self-similar]] curves that have [[Hausdorff dimension]] that are examples of ''fractals'', although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.<ref>"Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?": Benoit Mandelbrot (1967). "[https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw Benoît Mandelbrot, Novel Mathematician, Dies at 85]", ''The New York Times''.</ref><ref name="Mandelbrot_Science_1967">{{cite journal| title=How long is the coast of Britain? Statistical self-similarity and fractional dimension | journal=Science | date=5 May 1967 | author=Mandelbrot, Benoit B. | pages=636–638 | volume=156 | issue=3775 |doi=10.1126/science.156.3775.636 | pmid=17837158|url=http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf | bibcode=1967Sci...156..636M | s2cid=15662830 }}</ref>
Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured."<ref name=Mandelbrot />{{rp|296}} Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented in ''[[The Fractal Geometry of Nature]]'' had been previously described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new:
{{quote|The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty.<ref name=Mandelbrot />{{rp|292}}}}
Fractals are also found in human pursuits, such as music, painting, architecture, and [[stock market]] prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional [[Euclidean geometry]]: <blockquote>Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.<br /> —Mandelbrot, in his introduction to ''[[The Fractal Geometry of Nature]]''</blockquote>
[[File:Mandel zoom 08 satellite antenna.jpg|thumb|right|Section of a Mandelbrot set]]
Mandelbrot has been called an artist, and a visionary<ref name="RLD">{{cite web|author=Devaney, Robert L.|authorlink= Robert L. Devaney |title="Mandelbrot's Vision for Mathematics" in ''Proceedings of Symposia in Pure Mathematics''. Volume 72.1 |publisher=American Mathematical Society |year=2004 |url=http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |access-date=5 January 2007 |url-status=dead |archive-url=https://web.archive.org/web/20061209093734/http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |archive-date=9 December 2006 }}</ref> and a maverick.<ref>{{cite web|url=https://www.pbs.org/wgbh/nova/fractals/mandelbrot.html|title=A Radical Mind|last=Jersey|first=Bill|date=24 April 2005|work=Hunting the Hidden Dimension|publisher=NOVA/ PBS|accessdate=20 August 2009}}</ref> His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made ''The Fractal Geometry of Nature'' accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.
Mandelbrot died from pancreatic cancer at the age of 85 in a hospice in Cambridge, Massachusetts on 14 October 2010. Reacting to news of his death, mathematician Heinz-Otto Peitgen said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years." Nicolas Sarkozy, President of France at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".
2010年10月14日，曼德尔布洛特在马萨诸塞州剑桥的一家临终关怀胰腺癌去世，享年85岁。数学家海因茨-奥托 · 佩特根在听到他去世的消息后说: “如果我们谈论数学内部的影响，以及在科学中的应用，他是过去50年来最重要的人物之一。”曼德布洛特去世时的法国总统尼古拉•萨科齐(Nicolas Sarkozy)表示，曼德布洛特“拥有强大的、独创的头脑，从不回避创新和打破先入为主的观念[ ... ... 他是工作，完全在主流研究之外发展起来，导致了现代信息理论的产生。”曼德布洛特在《经济学人》上发表的讣告指出，他是“学术之外的名人” ，并称赞他是“分形几何之父”。
Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of [[Olbers' paradox]] (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a [[Necessity and sufficiency|sufficient, but not necessary]], resolution of the paradox. He postulated that if the [[star]]s in the universe were fractally distributed (for example, like [[Cantor dust]]), it would not be necessary to rely on the [[Big Bang]] theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.<ref>''Galaxy Map Hints at Fractal Universe'', by Amanda Gefter; New Scientist; 25 June 2008</ref>
Best-selling essayist-author Nassim Nicholas Taleb has remarked that Mandelbrot's book The (Mis)Behavior of Markets is in his opinion "The deepest and most realistic finance book ever published".
最畅销的散文作家兼作家纳西姆·尼可拉斯·塔雷伯 · 曼德布洛特评论说，曼德布洛特的著作《市场的(错误)行为》是他认为“有史以来最深刻、最现实的金融著作”。
==Awards and honors==
Mandelbrot's awards include the [[Wolf Prize]] for Physics in 1993, the [[Lewis Fry Richardson]] Prize of the [[European Geophysical Society]] in 2000, the [[Japan Prize]] in 2003,<ref name=jp>[http://www.japanprize.jp/en/laureates_by_year2000.html Laureates of the Japan Prize]. japanprize.jp</ref> and the Einstein Lectureship of the [[American Mathematical Society]] in 2006.
The small asteroid [[27500 Mandelbrot]] was named in his honor. In November 1990, he was made a Chevalier in France's [[Legion of Honour]]. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the [[Pacific Northwest National Laboratory]].<ref>{{cite web|url=http://www.pnl.gov/news/release.asp?id=141 |title=PNNL press release: Mandelbrot joins Pacific Northwest National Laboratory |publisher=Pnl.gov |date=16 February 2006 |accessdate=17 October 2010}}</ref> Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006.<ref>{{cite web|url=http://www.legifrance.gouv.fr/WAspad/UnTexteDeJorf?numjo=PREX0508911D |title=''Légion d'honneur'' announcement of promotion of Mandelbrot to ''officier'' |language=fr |publisher=Legifrance.gouv.fr |accessdate=17 October 2010}}</ref> An honorary degree from [[Johns Hopkins University]] was bestowed on Mandelbrot in the May 2010 commencement exercises.<ref>{{cite web|url=http://gazette.jhu.edu/2010/06/07/six-granted-honorary-degrees-society-of-scholars-inductees-recognized-2/ |title=Six granted honorary degrees, Society of Scholars inductees recognized |publisher=Gazette.jhu.edu |date=7 June 2010 |accessdate=17 October 2010}}</ref>
{|
{|
A partial list of awards received by Mandelbrot:<ref name="Vita">{{cite web | author=Mandelbrot, Benoit B. | title=Vita and Awards (Word document) | date=2 February 2006 | url=https://web.archive.org/web/20070601000000*/http://math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc | accessdate=6 January 2007}} Retrieved from Internet Archive 15 December 2013.</ref>
|- style="vertical-align:top"
|-style = “ vertical-align: top”
{{div col|colwidth=25em}}
| style="padding-right:2em"|
“ padding-right: 2em”
* 2004 Best Business Book of the Year Award
* AMS Einstein Lectureship
* Barnard Medal
* Caltech Service
* [[Casimir Funk]] Natural Sciences Award
* [[Charles Proteus Steinmetz]] Medal
* Fellow, American Geophysical Union
* [[Fellow of the American Statistical Association]]<ref>[http://www.amstat.org/awards/fellowslist.cfm View/Search Fellows of the ASA], accessed 20 August 2016.</ref>
* [[Fellow of the American Physical Society]] (1987) <ref> {{cite web|url=https://www.aps.org/programs/honors/fellowships/archive-all.cfm?initial=&year=1987&unit_id=&institution=|title=APS Fellow Archive|publisher=APS|accessdate= 24 September 2020}} </ref>
|
|
* [[The Franklin Institute Awards|Franklin Medal]]
* [[Harvey Prize]] (1989)
* Honda Prize
* Humboldt Preis
* IBM Fellowship
* Japan Prize (2003)
* [[John Scott Award]]
* Légion d'honneur ([[Legion of Honour]])
|}
|}
* Lewis Fry Richardson Medal
* Medaglia della Presidenza della Repubblica Italiana
* Médaille de Vermeil de la Ville de Paris
* Nevada Prize
* Member of the [[Norwegian Academy of Science and Letters]].<ref>{{cite web|url=http://www.dnva.no/c26849/artikkel/vis.html?tid=40116|title=Gruppe 1: Matematiske fag|publisher=[[Norwegian Academy of Science and Letters]] | language=Norwegian|accessdate=7 October 2010}}</ref>
* Science for Art
* Sven Berggren-Priset
* Władysław Orlicz Prize
* [[Wolf Foundation Prize]] for Physics (1993)
{{div col end}}
== Legacy ==
Mandelbrot died from [[pancreatic cancer]] at the age of 85 in a [[hospice]] in [[Cambridge, Massachusetts]] on 14 October 2010.<ref name="nyt_obit" /><ref>{{cite news |title=Benoît Mandelbrot, fractals pioneer, dies |url=http://www.upi.com/Science_News/2010/10/16/Benoit-Mandelbrot-fractals-pioneer-dies/UPI-11551287266964/ |accessdate=17 October 2010 |newspaper=United Press International |date=16 October 2010}}</ref> Reacting to news of his death, mathematician [[Heinz-Otto Peitgen]] said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years."<ref name="nyt_obit" />
[[Chris Anderson (entrepreneur)|Chris Anderson]], [[TED (conference)|TED conference]] curator, described Mandelbrot as "an icon who changed how we see the world".<ref>{{cite news |url=https://montrealgazette.com/technology/Mandelbrot+father+fractal+geometry+dies/3682961/story.html |title=Mandelbrot, father of fractal geometry, dies |work=[[The Gazette (Montreal)|The Gazette]] |access-date=16 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101019233754/http://www.montrealgazette.com/technology/Mandelbrot%2Bfather%2Bfractal%2Bgeometry%2Bdies/3682961/story.html |archive-date=19 October 2010 }}</ref> [[Nicolas Sarkozy]], [[President of France]] at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory."<ref>{{cite news |url=http://www.lefigaro.fr/flash-actu/2010/10/16/97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php |title=Sarkozy rend hommage à Mandelbrot |language=French |trans-title=Sarkozy pays homage to Mandelbrot |work=[[Le Figaro]] | accessdate=17 October 2010}}</ref> Mandelbrot's obituary in ''The Economist'' points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".<ref>[http://www.economist.com/node/17305197 Benoît Mandelbrot's obituary]. ''The Economist'' (21 October 2010)</ref>
Best-selling essayist-author [[Nassim Nicholas Taleb]] has remarked that Mandelbrot's book ''The (Mis)Behavior of Markets'' is in his opinion "The deepest and most realistic finance book ever published".<ref name=nature/>
==Bibliography==
===in English===
*Fractals: Form, Chance and Dimension, 1977, 2020
* [[The Fractal Geometry of Nature]], 1982
* Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E, 1997 by Benoit B. Mandelbrot and R.E. Gomory
* Fractales, hasard et finance, 1959-1997, 1 November 1998
* Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976) (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot
* Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot) 14 December 2001 by Benoit Mandelbrot and F.J. Damerau
* Fractals and Chaos: The Mandelbrot Set and Beyond, 9 January 2004
* The Misbehavior of Markets: A Fractal View of Financial Turbulence, 2006 by Benoit Mandelbrot and Richard L. Hudson
* The Fractalist: Memoir of a Scientific Maverick, 2014
===In French===
* La forme d'une vie. Mémoires (1924-2010) by Benoît Mandelbrot (Author), Johan-Frédérik Hel Guedj (Translator)
==References in popular culture==
* In 2004, the American singer-songwriter [[Jonathan Coulton]] wrote "Mandelbrot Set". Formerly, it contained the lines "Mandelbrot's in heaven / at least he will be when he's dead / right now he's still alive and teaching math at Yale". Live performances after Mandelbrot's passing in 2010 feature only the first line and a brief rock instrumental.
* In 2007, the author [[Laura Ruby]] published "The Chaos King," which includes a character named Mandelbrot and discussion of chaos theory.
* In 2017, [[Zach Weinersmith]]' webcomic, [[Saturday Morning Breakfast Cereal]], portrayed Mandelbrot.<ref>{{Cite web | url=http://www.smbc-comics.com/comic/mandelbrot | title=Saturday Morning Breakfast Cereal – Mandelbrot}}</ref>
* In 2017, Liz Ziemska published a novella, Mandelbrot The Magnificent, a fictional account of how Mandelbrot saved his family during WWII
== See also ==
{{External media |align=right | width=210px |headerimage=[[File:Mandelbrot p1130861.jpg|210px]] | video1=[http://www.webofstories.com/play/benoit.mandelbrot/1;jsessionid=E8EB8E149375B3987E49D5E4F02FCB57 Family background and early education], (4:11) Benoit Mandelbrot interview, Part 1 of 144, [[Web of Stories]]<ref name="wos1">{{cite web |url=http://www.webofstories.com/play/9596 |title=Web of Stories – Benoît Mandelbrot – Family background and early education |last=Mandelbrot |first=Benoît |author2=Bernard Sapoval |author3=Daniel Zajdenweber |date=May 1998 |publisher=[[Web of Stories]] | accessdate=19 October 2010}}</ref>}}
{|
|- style="vertical-align:top"
| style="padding-right:2em"|
* "[[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|How Long is the Coast of Britain?]]"
* [[Louis Bachelier]]
* [[Zipf–Mandelbrot law]]
* [[Seven states of randomness]]
* [[Skewness risk]]
Category:1924 births
类别: 1924出生
* [[Kurtosis risk]]
Category:2010 deaths
分类: 2010年死亡人数
* [[Fractal dimension]]
Category:20th-century American mathematicians
范畴: 20世纪美国数学家
* [[Lacunarity]]
Category:21st-century French mathematicians
范畴: 21世纪法国数学家
|
Category:20th-century American economists
类别: 20世纪美国经济学家
* [[Self-similarity]]
Category:21st-century American economists
类别: 21世纪美国经济学家
* [[Self-affinity]]
Category:Alexander von Humboldt Fellows
类别: 亚历山大·冯·洪堡研究员
* [[Hurst exponent]]
Category:California Institute of Technology alumni
类别: 加州理工学院校友
* [[Fractional Brownian motion]]
Category:Chaos theorists
范畴: 混沌理论家
* [[Multifractal system]]
Category:Deaths from cancer in Massachusetts
分类: 马萨诸塞州癌症死亡人数
* [[1/f noise]]
Category:Deaths from pancreatic cancer
分类: 死于胰腺癌
* [[Mandelbrot Competition]]
Category:École Polytechnique alumni
类别: 巴黎综合理工学院校友
|}
Category:Fellows of the American Geophysical Union
类别: 美国地球物理联盟研究员
Category:Fellows of the American Statistical Association
类别: 美国统计协会研究员
== Notes ==
Category:Fellows of the Econometric Society
类别: 经济计量学会研究员
{{Reflist|group=n|colwidth=50em}}
Category:Fellows of the American Physical Society
类别: 美国物理学会会员
Category:French emigrants to the United States
类别: 移居美国的法国移民
== References ==
Category:French scientists
分类: 法国科学家
{{Reflist|25em}}
Category:Harvard University people
类别: 哈佛大学的人
Category:IBM employees
类别: IBM 员工
==Bibliography==
Category:IBM Fellows
类别: IBM Fellows
* {{cite book |ref=Hudson|last1=Hudson |first1=Richard L. |last2=Mandelbrot |first2=Benoît B. |title=The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward |url=https://archive.org/details/misbehaviorofmar00beno|url-access=registration|year=2004 |publisher=Basic Books |location=New York |isbn=978-0-465-04355-2}}
Category:IBM Research computer scientists
类别: IBM 研究计算机科学家
Category:Institute for Advanced Study visiting scholars
类别: 高级研究所访问学者
== Further reading ==
Category:Jewish French scientists
类别: 犹太法国科学家
* Mandelbrot, Benoit B. (2010). [https://www.amazon.com/Fractalist-Memoir-Scientific-Maverick/dp/030738991X ''The Fractalist, Memoir of a Scientific Maverick.''] New York: [http://www.randomhouse.com/highschool/catalog/display.pperl?isbn=9780307389916&view=email_prep Vintage Books], Division of Random House. {{isbn|978-0-307-38991-6}}
Category:Members of the Norwegian Academy of Science and Letters
类别: 挪威科学与文学学会成员
* {{cite book |last1=Mandelbrot |first1=Benoît B. |title=The Fractal Geometry of Nature | year=1983 |publisher=W.H. Freeman |location=San Francisco |isbn=978-0-7167-1186-5|title-link=The Fractal Geometry of Nature }}
Category:Members of the United States National Academy of Sciences
类别: 美国国家科学院院士
* [[Heinz-Otto Peitgen]], [[Hartmut Jürgens]], [[Dietmar Saupe]] and Cornelia Zahlten: ''Fractals: An Animated Discussion'' (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. {{isbn|0-7167-2213-5}} (re-published by Films for the Humanities & Sciences, {{isbn|978-0-7365-0520-8}})
Category:Officiers of the Légion d'honneur
类别: 美国法国荣誉军团勋章协会官员
* Mandelbrot, Benoit B. (1997) ''Fractals and Scaling in Finance: Discontinuity, Concentration, Risk'', Springer.
Category:Polish emigrants to France
类别: 移居法国的波兰移民
* {{cite journal |last=Mandelbrot |first=Benoît |date=February 1999 |title=A Multifractal Walk down Wall Street |journal=[[Scientific American]] | bibcode=1999SciAm.280b..70M |volume=280 |page=70 |doi=10.1038/scientificamerican0299-70 |issue=2}}
Category:Polish emigrants to the United States
类别: 移居美国的波兰移民
* Mandelbrot, Benoit B., ''Gaussian Self-Affinity and Fractals'', Springer: 2002.
Category:Polish Jews
分类: 波兰犹太人
* {{cite news |url=http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html |title=A focus on the exceptions that prove the rule |last1=Mandelbrot |first1=Benoît |first2=Nassim |last2=Taleb |date=23 March 2006 |work=[[Financial Times]] |access-date=17 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101023201028/http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html |archive-date=23 October 2010 }}
Category:University of Paris alumni
类别: 巴黎大学校友
* [https://www.pbs.org/wgbh/nova/fractals/ "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature"], ''[[Nova (American TV series)|NOVA]]'', WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.
Category:Wolf Prize in Physics laureates
类别: 沃尔夫物理学奖获得者
* {{cite book |last1=Frame |first1=Michael |last2=Cohen |first2=Nathan |title=Benoit Mandelbrot: A Life in Many Dimensions |year=2015 |publisher=World Scientific Publishing Company |location=Singapore |isbn=978-981-4366-06-9 }}
Category:Yale University faculty
类别: 耶鲁学院
* Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des Sciences de Paris, 249, 613–615.
Category:Yale Sterling Professors
分类: 耶鲁斯特林教授
* Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106.
Category:20th-century French mathematicians
范畴: 20世纪法国数学家
* Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543.
Category:21st-century American mathematicians
范畴: 21世纪美国数学家
<noinclude>
<small>This page was moved from [[wikipedia:en:Benoit Mandelbrot]]. Its edit history can be viewed at [[曼德布洛特/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{short description|French-American mathematician}}
{{See also|Mandelbrot set}}
{{Use dmy dates|date=February 2020}}
{{Infobox scientist
{{Infobox scientist
{信息盒科学家
| name = Benoit<span style="font-size:80%;font-weight:normal"><!-- The following syntax required to permit nested refs: -->{{#tag:ref|In his autobiography, Mandelbrot did not add a [[circumflex]] to the "i" (i.e. "î") in his first name, as is usual for [[Benoît|the French given name]]. He included "B" as a [[middle initial]]. His ''New York Times'' obituary stated that "he added the middle initial himself, though it does not stand for a middle name",<ref name="nyt_obit">{{cite news |url=https://www.nytimes.com/2010/10/17/us/17mandelbrot.html |title=Benoît Mandelbrot, Mathematician, Dies at 85 |last=Hoffman |first=Jascha |date=16 October 2010 |work=The New York Times |accessdate=16 October 2010}}</ref> an assertion that is supported by his obituary in ''The Guardian''.<ref name="guardian_obit">{{cite news |url=https://www.theguardian.com/science/2010/oct/17/benoit-mandelbrot-obituary |title=Benoît Mandelbrot obituary |last=Lesmoir-Gordon |first=Nigel |date=17 October 2010 |work=[[The Guardian]] | accessdate=17 October 2010 |location=London}}</ref>|group=n|name=Mandelbrot's_name}}</span> Mandelbrot
| name = Benoit<span style="font-size:80%;font-weight:normal"><!-- The following syntax required to permit nested refs: --></span> Mandelbrot
| name = Benoit < span o < > style = " font-size: 80% ; font-weight: normal" > < !-以下语法允许嵌套裁判: -- > </span > Mandelbrot
| image = Benoit Mandelbrot, TED 2010.jpg
| image = Benoit Mandelbrot, TED 2010.jpg
2010年 TED 本华·曼德博
| caption = Mandelbrot at a [[TED (conference)|TED conference]] in 2010 shortly before his death.
| caption = Mandelbrot at a TED conference in 2010 shortly before his death.
2010年，曼德尔布洛特去世前不久在 TED 大会上。
| birth_date = {{birth date|1924|11|20|df=y}}
| birth_date =
出生日期
| birth_place = [[Warsaw]], [[Second Polish Republic|Poland]]
| birth_place = Warsaw, Poland
出生地: 波兰华沙
| death_date = {{death date and age|2010|10|14|1924|11|20|df=y}}
| death_date =
死亡日期
| death_place = [[Cambridge, Massachusetts]], United States
| death_place = Cambridge, Massachusetts, United States
死亡地点: 美国马萨诸塞州剑桥
| nationality = {{hlist | Polish | French | American}}
| nationality =
国籍 =
| fields = {{hlist | [[Mathematics]] | [[Aerodynamics]]}}
| fields =
2012年10月22日 | 田野 =
| alma_mater = {{br list | [[École Polytechnique]] | {{nowrap|[[California Institute of Technology]]}} | [[University of Paris]]}}
| alma_mater = | University of Paris}}
巴黎大学
| doctoral_students = {{hlist |class=nowraplinks |list_style=line-height:1.25em | [[Laurent-Emmanuel Calvet|L-E. Calvet]] | [[Eugene Fama]] | [[Ken Musgrave]] | [[Murad Taqqu]] <!--Red link: | [[Daniel Zajdenweber]]-->}}
| doctoral_students =
博士生 =
| known_for = {{hlist |class=nowraplinks |list_style=line-height:1.25em | [[Mandelbrot set]] | [[Chaos theory]] | [[Fractal]]s | [[Zipf–Mandelbrot law]]}}
| known_for =
已知的
| influences = [[Johannes Kepler]], [[Paul Lévy (mathematician)|Paul Lévy]], [[Szolem Mandelbrojt]]
| influences = Johannes Kepler, Paul Lévy, Szolem Mandelbrojt
| influences = Johannes Kepler, Paul Lévy, Szolem Mandelbrojt
| influenced = [[Nassim Nicholas Taleb]]
| influenced = Nassim Nicholas Taleb
影响 = 纳西姆·尼可拉斯·塔雷伯
| spouse = {{longitem|Aliette Kagan<br />{{smaller|married 1955–2010 (his death)}}}}
| spouse = }}
| spouse = }
| work_institutions = {{hlist | [[Yale University]] | [[IBM]]}} {{longitem|[[Pacific Northwest National Laboratory]]}}
| work_institutions =
工作机构
| prizes = {{longitem|style=line-height:1.15em;white-space:nowrap |''[[Légion d'honneur]]''<br />{{smaller|(''Chevalier'' 1990{{dot}}''Officier'' 2006)}}}} {{Br list | 2003 [[Japan Prize]] | 1993 [[Wolf Prize]] | 1989 [[Harvey Prize]] | 1986 [[Franklin Medal]] | 1985 [[Barnard Medal for Meritorious Service to Science|Barnard Medal]]}}
| prizes = Officier 2006)}}}}
2006)}}}}}}
}}
}}
}}
'''Benoit B.'''<ref group="n" name="Mandelbrot's_name" /> '''Mandelbrot'''{{#tag:ref|Pronounced {{IPAc-en|ˈ|m|æ|n|d|əl|b|r|ɒ|t}} {{respell|MAN|dəl-brot}} in English.<ref>{{OED|Mandelbrot}}</ref> When speaking in French, Mandelbrot pronounced his name {{IPA-fr|bənwa mɑ̃dɛlbʁot|}}.<ref>Recording of the ceremony on 11 September 2006 at which Mandelbrot received the insignia for an Officer of the ''[[Legion of Honour|Légion d'honneur]]''.</ref>|group=n}} (20 November 1924 – 14 October 2010) was a Polish-born French and American [[mathematician]] and [[polymath]] with broad interests in the practical sciences, especially regarding what he labeled as "the art of [[Benoit Mandelbrot#Fractals and the .22theory of roughness.22|roughness]]" of physical phenomena and "the uncontrolled element in life".<ref>https://www.insidescience.org/news/remembering-father-fractals</ref><ref>[https://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness?language=en Benoit Mandelbrot: Fractals and the art of roughness]. ted.com (February 2010)</ref><ref>[[#Hudson|Hudson & Mandelbrot]], Prelude, page xviii</ref> He referred to himself as a "fractalist"<ref name=Mandelbrot/> and is recognized for his contribution to the field of [[fractal geometry]], which included coining the word "fractal", as well as developing a theory of "roughness and [[self-similarity]]" in nature.<ref name=nature>{{Cite journal
Benoit B. When speaking in French, Mandelbrot pronounced his name .|group=n}} (20 November 1924 – 14 October 2010) was a Polish-born French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist"
伯努瓦 b。在用法语说话时，曼德布洛特宣布了他的名字。| group = n }(1924年11月20日至2010年10月14日)是波兰出生的法国和美国数学家和博学家，对实用科学有着广泛的兴趣，特别是对他所称的物理现象的”粗糙艺术”和”生活中不受控制的元素”。他说自己是个“分裂主义者”
| last1 = Gomory | first1 = R.
| authorlink1 = Ralph E. Gomory
In 1936, while he was a child, Mandelbrot's family emigrated to France from Warsaw, Poland. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.
1936年，当曼德布洛特还是个孩子的时候，他的家人从波兰华沙移民到了法国。第二次世界大战结束后，曼德布洛特学习了数学，从巴黎和美国的大学毕业，并在加利福尼亚理工学院获得了航空学硕士学位。他的大部分职业生涯都在美国和法国度过，拥有法国和美国双重国籍。1958年，他在 IBM 开始了35年的职业生涯，在那里他成为了 IBM 研究员，并定期休假到哈佛大学教书。在哈佛大学，他发表了关于美国商品市场与棉花期货的研究成果之后，他开始教授经济学和应用科学。
| title = Benoît Mandelbrot (1924–2010)
| doi = 10.1038/468378a
Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the Mandelbrot set in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order".
由于可以访问 IBM 的计算机，曼德尔布洛特是第一个使用计算机图形学图形来创建和显示分形几何图形的人，这导致了他在1980年发现了曼德尔布洛特集合。他展示了如何从简单的规则中创造出视觉的复杂性。他说，通常被认为是“粗糙”、“混乱”或“混乱”的事物，如云或海岸线，实际上有一定程度的秩序。
| journal = Nature
| volume = 468
Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012.
在他职业生涯的最后阶段，他是耶鲁大学数学科学系的斯特林教席，也是耶鲁历史上获得终身教职的最年长的教授。曼德布洛特还在太平洋西北国家实验室、法国里尔北方的大学、高级研究所和法国国家科学研究中心担任过职务。在他的职业生涯中，他获得了超过15个荣誉博士学位，并在许多科学期刊上服务，同时还获得了许多奖项。他的自传《分析家: 科学怪人的回忆录》在他死后于2012年出版。
| issue = 7322
| pages = 378
| year = 2010
Mandelbrot was born in a Jewish family, in Warsaw during the Second Polish Republic. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." Later, the family's move to France, the war, and his acquaintance with his father's brother, the mathematician Szolem Mandelbrojt who had moved to Paris around 1920, further prevented a standard education.
曼德布洛特出生于第二波兰共和国时期的华沙的一个犹太家庭。他的父亲靠卖衣服为生，母亲是牙科医生。在他的头两个学年里，他的一位叔叔私下辅导他，他鄙视死记硬背: “我的大部分时间都花在下棋、看地图和学习如何睁开眼睛看我周围的一切。”后来，他们全家搬到了法国，战争爆发，他和父亲的兄弟，数学家 Szolem Mandelbrojt 相识，后者在1920年前后移居巴黎，这进一步阻碍了他接受标准教育。
| pmid = 21085164
|bibcode = 2010Natur.468..378G | s2cid = 4393964
The family emigrated from Poland to France in 1936, when he was 11. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies. Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:
1936年，当他11岁的时候，他们一家从波兰移民到法国。他写道: “我的父母作为经济和政治难民加入了 Szolem，这一事实挽救了我们的生命。”。曼德布洛特曾在巴黎的 Lycée Rolin 工作，直到二战爆发，他的家人搬到了法国的图勒。他在布里夫拉盖亚尔德的犹太教教士 David Feuerwerker 的帮助下继续学业。当时法国大部分地区都被纳粹占领，曼德布洛特回忆起这段时期:
}}</ref>
{{quote|Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why? In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York.
{引用 | 我们一直担心的是，一个足够坚定的敌人可能会向某个权威举报我们，我们将会被送去送死。来自巴黎的密友吉娜 · 莫汉格就遇到了这种情况，她是附近一个县城的内科医生。仅仅是为了消除竞争，另一个医生谴责她... 我们逃过了这个命运。谁知道为什么呢？1958年，这对夫妇移居美国，在那里曼德尔布洛特加入了位于约克敦海茨的 IBM 汤玛士·Ｊ·华生研究中心的研究人员。
In 1936, while he was a child, Mandelbrot's family emigrated to France from [[Warsaw]], Poland. After [[World War II]] ended, Mandelbrot studied mathematics, graduating from universities in Paris and the United States and receiving a master's degree in [[aeronautics]] from the [[California Institute of Technology]]. He spent most of his career in both the United States and France, having [[Multiple citizenship|dual]] [[French nationality law|French]] and [[United States nationality law#Dual citizenship|American]] citizenship. In 1958, he began a 35-year career at [[IBM]], where he became an [[IBM Fellow]], and periodically took leaves of absence to teach at [[Harvard University]]. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.
In his early work, he found that the price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.
在他的早期工作中，他发现金融市场的价格变化并不遵循正态分布，而是具有无限方差的 l é vy 稳定分布。例如，他发现，棉花价格遵循一个 l é vy 稳定分布，参数 α 等于1.7，而不是像正态分布一样遵循2。“稳定”分布具有这样的性质: 一个随机变量的多个实例的和服从相同的分布，但具有更大的尺度参数。
Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the [[Mandelbrot set]] in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order".<ref name="Wolfram" /> His math and geometry-centered research career included contributions to such fields as [[statistical physics]], [[meteorology]], [[hydrology]], [[geomorphology]], [[anatomy]], [[taxonomy (biology)|taxonomy]], [[neurology]], [[linguistics]], [[information technology]], [[computer graphics]], [[economics]], [[geology]], [[medicine]], [[physical cosmology]], [[engineering]], [[chaos theory]], [[econophysics]], [[metallurgy]] and the [[social science]]s.<ref>list includes specific sciences mentioned in [[#Hudson|Hudson & Mandelbrot]], the Prelude, p. xvi, and p. 26</ref>
Toward the end of his career, he was [[Sterling Professor]] of Mathematical Sciences at [[Yale University]], where he was the oldest professor in Yale's history to receive tenure.<ref>{{cite web |author=Steve Olson | url=http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html |title=The Genius of the Unpredictable |publisher=Yale Alumni Magazine |date=November–December 2004 |accessdate=22 July 2014| author-link=Steve Olson (writer) }}</ref> Mandelbrot also held positions at the [[Pacific Northwest National Laboratory]], [[Université Lille Nord de France]], [[Institute for Advanced Study]] and [[Centre National de la Recherche Scientifique]]. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, ''The Fractalist: Memoir of a Scientific Maverick'', was published posthumously in 2012.
As a visiting professor at Harvard University, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in 1979. In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".
作为哈佛大学的客座教授，Mandelbrot 开始研究被称为 Julia 集的分形，它们在复平面的某些变换下是不变的。在加斯顿 · 朱莉娅和皮埃尔 · 法图之前工作的基础上，曼德尔布洛特使用计算机绘制了朱莉娅集合的图像。在研究这些 Julia 集的拓扑结构时，他研究了他在1979年提出的 Mandelbrot 集。1982年，曼德布洛特在《自然的分形几何》一书中扩展和更新了他的观点。这一有影响力的工作带来了分形进入主流的专业和流行数学，以及沉默批评家，谁曾驳回分形作为“程序人工制品”。
== Early years ==
Mandelbrot speaking about the [[Mandelbrot set, during his acceptance speech for the Légion d'honneur in 2006]]
曼德布洛特谈到了[2006年他在法国荣誉军团勋章的获奖感言中谈到了曼德布洛特集合]
Mandelbrot was born in a [[Jews|Jewish]] family, in [[Warsaw]] during the [[Second Polish Republic]]. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."<ref name="wolf">{{cite journal |last=Mandelbrot |first=Benoît |title=The Wolf Prizes for Physics, ''A Maverick's Apprenticeship''|publisher=Imperial College Press |year=2002 |url=http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf}}</ref> Later, the family's move to France, the [[World War II|war]], and his acquaintance with his father's brother, the mathematician [[Szolem Mandelbrojt]] who had moved to Paris around 1920, further prevented a standard education.
In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension. According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before". Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":
1975年，曼德布洛特创造了分形这个术语来描述这些结构，并首次发表了他的观点，后来被翻译成分形: 形式、机会和维度。计算机科学家、物理学家斯蒂芬•沃尔夫拉姆(Stephen Wolfram)表示，这本书对曼德布洛特来说是一个“突破” ，在此之前，他通常会“将相当简单的数学应用到以前几乎没有认真研究过数学的领域”。沃尔夫勒姆补充说，由于这项新研究的结果，他不再是一个“流浪的科学家” ，后来称他为“分形之父” :
The family emigrated from Poland to France in 1936, when he was 11. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.<ref name=Mandelbrot />{{rp|17}}<ref name="bbc_obit">{{cite news|url=https://www.bbc.co.uk/news/world-europe-11560101|title=BBC News – 'Fractal' mathematician Benoît Mandelbrot dies aged 85|date=17 October 2010|work=[[BBC Online]] | accessdate=17 October 2010}}</ref> Mandelbrot attended the Lycée Rolin in Paris until the start of [[World War II]], when his family moved to [[Tulle]], France. He was helped by [[Rabbi]] [[David Feuerwerker]], the Rabbi of [[Brive-la-Gaillarde]], to continue his studies.<ref name=Mandelbrot/>{{rp|62–63}}<ref>Hemenway P. (2005) ''Divine proportion: Phi in art, nature and science''. Psychology Press. {{isbn|0-415-34495-6}}</ref> Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period:
{{quote|Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.
{引用 | Mandelbrot 最终做了一项伟大的科学工作，确定了一个更强大、更基本的观点ーー简而言之，有一些被他称为“分形”的 Unicode几何图形列表，在所有尺度上都是同样“粗糙”的。无论你看起来多么近，它们都不会变得更简单，就像你脚下看到的岩石海岸线的部分看起来就像你从太空中看到的那样参差不齐。
{{quote|Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?<ref name=Mandelbrot />{{rp|49}}}}
A Mandelbrot set
一个曼德布洛特集合
In 1944, Mandelbrot returned to Paris, studied at the [[Lycée du Parc]] in [[Lyon]], and in 1945 to 1947 attended the [[École Polytechnique]], where he studied under [[Gaston Julia]] and [[Paul Lévy (mathematician)|Paul Lévy]]. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics.<ref name="guardian_obit" /> Returning to France, he obtained his [[Doctor of Philosophy|PhD degree]] in Mathematical Sciences at the [[University of Paris]] in 1952.<ref name="wolf" />
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
然而，曼德布洛特从未觉得自己正在发明一种新思想。他在与科学作家亚瑟·查理斯·克拉克的一部纪录片中描述了自己的感受:
==Research career==
From 1949 to 1958, Mandelbrot was a staff member at the [[Centre National de la Recherche Scientifique]]. During this time he spent a year at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]], where he was sponsored by [[John von Neumann]]. In 1955 he married Aliette Kagan and moved to [[Geneva, Switzerland]] (to collaborate with [[Jean Piaget]] at the International Centre for Genetic Epistemology) and later to the [[Université Lille Nord de France]].<ref name="people">{{Cite journal|last=Barcellos|first=Anthony|title=Mathematical People, ''Interview of B. B. Mandelbrot''|publisher=Birkhaüser|year=1984|url=http://users.math.yale.edu/~bbm3/web_pdfs/inHisOwnWords.pdf}}</ref> In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the [[International Business Machines|IBM]] [[Thomas J. Watson Research Center]] in [[Yorktown Heights, New York]].<ref name="people" /> He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow [[Emeritus]].<ref name="wolf" />
According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence<blockquote>the name Mandelbrot, and the word "mandala"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas. He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
根据克拉克的说法，“曼德尔布罗特集合确实是整个数学史上最惊人的发现之一。谁能想到这么简单的一个方程竟然能产生无限复杂的图像? ”克拉克还注意到了一个“奇怪的巧合”——曼德尔布洛特的名字，以及“曼荼罗”——意为宗教象征——我确信这纯粹是巧合，但事实上曼德尔布洛特集似乎包含了大量的曼荼罗。他加入了耶鲁大学数学系，并在1999年获得了他的第一个终身职位，那时他75岁。在他2005年退休的时候，他是数学科学的斯特林教席。
<!-- Deleted image removed: [[File:Mandelbrot-IBM.jpg|thumb|left|Mandelbrot working at IBM]] -->
From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as [[information theory]], economics, and [[fluid dynamics]].
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.}}
曼德布洛特创立了有史以来第一个“粗糙理论” ，他看到了山脉、海岸线和河流盆地形状的“粗糙” ，看到了植物、血管和肺的结构，看到了星系的聚集。他个人的追求是创造一些数学公式来衡量这些物体在自然界中的整体“粗糙度”
===Randomness in financial markets===
In his paper titled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses self-similar curves that have Hausdorff dimension that are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.
在他题为《英国海岸有多长？统计自相似性和分维数1967年发表在《科学》杂志上，曼德尔布洛特讨论了自相似曲线，这些曲线都有豪斯多夫维数，是分形的例子，尽管曼德尔布洛特在论文中没有使用这个术语，因为他直到1975年才造出这个术语。这篇论文是曼德布洛特关于分形主题的首批出版物之一。
Mandelbrot saw [[financial market]]s as an example of "wild randomness", characterized by concentration and long range dependence. He developed several original approaches for modelling financial fluctuations.<ref>{{cite book |author= Rama Cont |chapter= Mandelbrot, Benoit |journal= Encyclopedia of Quantitative Finance |publisher= Wiley |date= 19 April 2010 |doi= 10.1002/9780470061602.eqf01006 |isbn = 9780470057568|author-link= Rama Cont }}</ref>
In his early work, he found that the price changes in [[financial market]]s did not follow a [[Gaussian distribution]], but rather [[Paul Lévy (mathematician)|Lévy]] [[stable distributions]] having infinite [[variance]]. He found, for example, that cotton prices followed a Lévy stable distribution with parameter ''α'' equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger [[scale parameter]].<ref>{{cite web |url=https://www.newscientist.com/article/mg15420784.700-flight-over-wall-st.html |title=''New Scientist'', 19 April 1997 |publisher=Newscientist.com |date=19 April 1997 |accessdate=17 October 2010}}</ref>
Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured." and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.
曼德布洛特强调用分形作为现实和有用的模型来描述现实世界中的许多“粗糙”现象。他的结论是: “真实的粗糙度通常是分形的，可以测量。”还是个特立独行的人。他非正式和充满激情的写作风格和他对视觉和几何直觉的强调(通过大量插图的支持)使得《自然的分形几何学》对非专业人士来说易于理解。这本书激发了人们对分形的广泛兴趣，并促成了混沌理论和其他领域的科学和数学。
===Developing "fractal geometry" and the Mandelbrot set===
Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.
曼德布洛特也将他的想法应用于宇宙学。1974年，他对奥尔伯斯悖论(“黑暗的夜空”之谜)提出了新的解释，证明了分形理论的结果是解决这一悖论的充分而非必要的方法。他假设，如果宇宙中的恒星是分散分布的(例如，康托尔尘埃) ，就没有必要依靠大爆炸理论来解释这一悖论。他的模型不能排除宇宙大爆炸的可能性，但是即使宇宙大爆炸没有发生，也可以考虑到黑暗的天空。
As a visiting professor at [[Harvard University]], Mandelbrot began to study fractals called [[Julia set]]s that were invariant under certain transformations of the [[complex plane]]. Building on previous work by [[Gaston Julia]] and [[Pierre Fatou]], Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the [[Mandelbrot set]] which was introduced by him in 1979. In 1982, Mandelbrot expanded and updated his ideas in ''[[The Fractal Geometry of Nature]]''.<ref>[https://books.google.com/books?id=xJ4qiEBNP4gC&printsec=frontcover ''The Fractal Geometry of Nature''], by Benoît Mandelbrot; W H Freeman & Co, 1982; {{isbn|0-7167-1186-9}}</ref> This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "[[Artifact (observational)|program artifacts]]".
Mandelbrot's awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006.
曼德布洛特获得的奖项包括1993年的沃尔夫物理奖、2000年欧洲地球物理学会的刘易斯 · 弗莱 · 理查森奖、2003年的日本奖以及2006年的美国数学学会爱因斯坦讲师奖。
[[File:Mandelbrot p1130876.jpg|thumb|right|Mandelbrot speaking about the [[Mandelbrot set]], during his acceptance speech for the [[Légion d'honneur]] in 2006]]
The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Chevalier in France's Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises.
小行星27500 Mandelbrot 以他的名字命名。1990年11月，他被授予法国法国荣誉军团勋章骑士称号。2005年12月，曼德尔布洛特被任命为太平洋西北国家实验室的巴特尔研究员。2006年1月，曼德尔布洛特被提升为法国荣誉军团勋章安全委员会官员。在2010年5月的毕业典礼上，曼德尔布洛特获得了约翰·霍普金斯大学的荣誉学位。
In 1975, Mandelbrot coined the term ''[[fractal]]'' to describe these structures and first published his ideas, and later translated, ''Fractals: Form, Chance and Dimension''.<ref>''Fractals: Form, Chance and Dimension'', by Benoît Mandelbrot; W H Freeman and Co, 1977; {{isbn|0-7167-0473-0}}</ref> According to computer scientist and physicist [[Stephen Wolfram]], the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".<ref name=Wolfram>Wolfram, Stephen. [https://www.wsj.com/articles/SB10001424127887324439804578107271772910506 "The Father of Fractals"], ''Wall Street Journal'', 22 November 2012</ref> Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":
A partial list of awards received by Mandelbrot:
曼德布洛特获得的部分奖项:
{{quote|Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.<ref name=Wolfram />}}
Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesco broccoli are two examples from nature."<ref name=Wolfram /> He points out an unexpected conclusion:
{{quote|One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.<ref name=Wolfram />}}
Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphic computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s [[psychedelic art]] with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist [[Johannes Kepler]], who calculated and described the orbits of the planets.<ref>Ivry, Benjamin. [http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all "Benoit Mandelbrot Influenced Art and Mathematics"], ''Forward'', 17 November 2012</ref>
[[File:Newton-lplane-Mandelbrot.jpg|thumb|A Mandelbrot set]]
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
{{quote|Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.<ref name=Clarke>[https://www.youtube.com/watch?v=Lk6QU94xAb8 "Arthur C Clarke – Fractals – The Colors Of Infinity"], video interviews, 54 min.</ref>}}
According to Clarke, "the [[Mandelbrot set]] is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally ''infinite'' complexity?" Clarke also notes an "odd coincidence<blockquote>the name Mandelbrot, and the word "[[mandala]]"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.<ref name=Clarke /></blockquote>
Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division.<ref name="wos44">{{cite web|url=http://www.webofstories.com/play/10483|title=Web of Stories • Benoît Mandelbrot • IBM: background and policies|last=Mandelbrot|first=Benoît|author2=Bernard Sapoval|author3=Daniel Zajdenweber|date=May 1998|publisher=[[Web of Stories]] | accessdate=17 October 2010}}</ref> He joined the Department of Mathematics at [[Yale]], and obtained his first [[tenure]]d post in 1999, at the age of 75.<ref name="Tenner">{{cite news|url=https://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/|title=Benoît Mandelbrot the Maverick, 1924–2010|last=Tenner|first=Edward|date=16 October 2010|work=[[The Atlantic]] | accessdate=16 October 2010}}</ref> At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
===Fractals and the "theory of roughness"===
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, [[coastline]]s and [[river basin]]s; the structures of plants, [[blood vessel]]s and [[lung]]s; the clustering of [[galaxy|galaxies]]. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.<ref name=Mandelbrot />{{rp|xi}} He began by asking himself various kinds of questions related to nature:
{{quote|Can [[geometry]] deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?<ref name=Mandelbrot>Mandelbrot, Benoit (2012). ''The Fractalist: Memoir of a Scientific Maverick'', Pantheon Books. {{isbn|978-0-307-38991-6}}.</ref>{{rp|xii}}}}
In his paper titled [[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]] published in [[Science (journal)|''Science'']] in 1967 Mandelbrot discusses [[self-similarity|self-similar]] curves that have [[Hausdorff dimension]] that are examples of ''fractals'', although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.<ref>"Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?": Benoit Mandelbrot (1967). "[https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw Benoît Mandelbrot, Novel Mathematician, Dies at 85]", ''The New York Times''.</ref><ref name="Mandelbrot_Science_1967">{{cite journal| title=How long is the coast of Britain? Statistical self-similarity and fractional dimension | journal=Science | date=5 May 1967 | author=Mandelbrot, Benoit B. | pages=636–638 | volume=156 | issue=3775 |doi=10.1126/science.156.3775.636 | pmid=17837158|url=http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf | bibcode=1967Sci...156..636M | s2cid=15662830 }}</ref>
Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured."<ref name=Mandelbrot />{{rp|296}} Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented in ''[[The Fractal Geometry of Nature]]'' had been previously described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new:
{{quote|The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty.<ref name=Mandelbrot />{{rp|292}}}}
Fractals are also found in human pursuits, such as music, painting, architecture, and [[stock market]] prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional [[Euclidean geometry]]: <blockquote>Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.<br /> —Mandelbrot, in his introduction to ''[[The Fractal Geometry of Nature]]''</blockquote>
[[File:Mandel zoom 08 satellite antenna.jpg|thumb|right|Section of a Mandelbrot set]]
Mandelbrot has been called an artist, and a visionary<ref name="RLD">{{cite web|author=Devaney, Robert L.|authorlink= Robert L. Devaney |title="Mandelbrot's Vision for Mathematics" in ''Proceedings of Symposia in Pure Mathematics''. Volume 72.1 |publisher=American Mathematical Society |year=2004 |url=http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |access-date=5 January 2007 |url-status=dead |archive-url=https://web.archive.org/web/20061209093734/http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |archive-date=9 December 2006 }}</ref> and a maverick.<ref>{{cite web|url=https://www.pbs.org/wgbh/nova/fractals/mandelbrot.html|title=A Radical Mind|last=Jersey|first=Bill|date=24 April 2005|work=Hunting the Hidden Dimension|publisher=NOVA/ PBS|accessdate=20 August 2009}}</ref> His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made ''The Fractal Geometry of Nature'' accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.
Mandelbrot died from pancreatic cancer at the age of 85 in a hospice in Cambridge, Massachusetts on 14 October 2010. Reacting to news of his death, mathematician Heinz-Otto Peitgen said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years." Nicolas Sarkozy, President of France at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".
2010年10月14日，曼德尔布洛特在马萨诸塞州剑桥的一家临终关怀胰腺癌去世，享年85岁。数学家海因茨-奥托 · 佩特根在听到他去世的消息后说: “如果我们谈论数学内部的影响，以及在科学中的应用，他是过去50年来最重要的人物之一。”曼德布洛特去世时的法国总统尼古拉•萨科齐(Nicolas Sarkozy)表示，曼德布洛特“拥有强大的、独创的头脑，从不回避创新和打破先入为主的观念[ ... ... 他是工作，完全在主流研究之外发展起来，导致了现代信息理论的产生。”曼德布洛特在《经济学人》上发表的讣告指出，他是“学术之外的名人” ，并称赞他是“分形几何之父”。
Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of [[Olbers' paradox]] (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a [[Necessity and sufficiency|sufficient, but not necessary]], resolution of the paradox. He postulated that if the [[star]]s in the universe were fractally distributed (for example, like [[Cantor dust]]), it would not be necessary to rely on the [[Big Bang]] theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.<ref>''Galaxy Map Hints at Fractal Universe'', by Amanda Gefter; New Scientist; 25 June 2008</ref>
Best-selling essayist-author Nassim Nicholas Taleb has remarked that Mandelbrot's book The (Mis)Behavior of Markets is in his opinion "The deepest and most realistic finance book ever published".
最畅销的散文作家兼作家纳西姆·尼可拉斯·塔雷伯 · 曼德布洛特评论说，曼德布洛特的著作《市场的(错误)行为》是他认为“有史以来最深刻、最现实的金融著作”。
==Awards and honors==
Mandelbrot's awards include the [[Wolf Prize]] for Physics in 1993, the [[Lewis Fry Richardson]] Prize of the [[European Geophysical Society]] in 2000, the [[Japan Prize]] in 2003,<ref name=jp>[http://www.japanprize.jp/en/laureates_by_year2000.html Laureates of the Japan Prize]. japanprize.jp</ref> and the Einstein Lectureship of the [[American Mathematical Society]] in 2006.
The small asteroid [[27500 Mandelbrot]] was named in his honor. In November 1990, he was made a Chevalier in France's [[Legion of Honour]]. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the [[Pacific Northwest National Laboratory]].<ref>{{cite web|url=http://www.pnl.gov/news/release.asp?id=141 |title=PNNL press release: Mandelbrot joins Pacific Northwest National Laboratory |publisher=Pnl.gov |date=16 February 2006 |accessdate=17 October 2010}}</ref> Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006.<ref>{{cite web|url=http://www.legifrance.gouv.fr/WAspad/UnTexteDeJorf?numjo=PREX0508911D |title=''Légion d'honneur'' announcement of promotion of Mandelbrot to ''officier'' |language=fr |publisher=Legifrance.gouv.fr |accessdate=17 October 2010}}</ref> An honorary degree from [[Johns Hopkins University]] was bestowed on Mandelbrot in the May 2010 commencement exercises.<ref>{{cite web|url=http://gazette.jhu.edu/2010/06/07/six-granted-honorary-degrees-society-of-scholars-inductees-recognized-2/ |title=Six granted honorary degrees, Society of Scholars inductees recognized |publisher=Gazette.jhu.edu |date=7 June 2010 |accessdate=17 October 2010}}</ref>
{|
{|
A partial list of awards received by Mandelbrot:<ref name="Vita">{{cite web | author=Mandelbrot, Benoit B. | title=Vita and Awards (Word document) | date=2 February 2006 | url=https://web.archive.org/web/20070601000000*/http://math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc | accessdate=6 January 2007}} Retrieved from Internet Archive 15 December 2013.</ref>
|- style="vertical-align:top"
|-style = “ vertical-align: top”
{{div col|colwidth=25em}}
| style="padding-right:2em"|
“ padding-right: 2em”
* 2004 Best Business Book of the Year Award
* AMS Einstein Lectureship
* Barnard Medal
* Caltech Service
* [[Casimir Funk]] Natural Sciences Award
* [[Charles Proteus Steinmetz]] Medal
* Fellow, American Geophysical Union
* [[Fellow of the American Statistical Association]]<ref>[http://www.amstat.org/awards/fellowslist.cfm View/Search Fellows of the ASA], accessed 20 August 2016.</ref>
* [[Fellow of the American Physical Society]] (1987) <ref> {{cite web|url=https://www.aps.org/programs/honors/fellowships/archive-all.cfm?initial=&year=1987&unit_id=&institution=|title=APS Fellow Archive|publisher=APS|accessdate= 24 September 2020}} </ref>
|
|
* [[The Franklin Institute Awards|Franklin Medal]]
* [[Harvey Prize]] (1989)
* Honda Prize
* Humboldt Preis
* IBM Fellowship
* Japan Prize (2003)
* [[John Scott Award]]
* Légion d'honneur ([[Legion of Honour]])
|}
|}
* Lewis Fry Richardson Medal
* Medaglia della Presidenza della Repubblica Italiana
* Médaille de Vermeil de la Ville de Paris
* Nevada Prize
* Member of the [[Norwegian Academy of Science and Letters]].<ref>{{cite web|url=http://www.dnva.no/c26849/artikkel/vis.html?tid=40116|title=Gruppe 1: Matematiske fag|publisher=[[Norwegian Academy of Science and Letters]] | language=Norwegian|accessdate=7 October 2010}}</ref>
* Science for Art
* Sven Berggren-Priset
* Władysław Orlicz Prize
* [[Wolf Foundation Prize]] for Physics (1993)
{{div col end}}
== Legacy ==
Mandelbrot died from [[pancreatic cancer]] at the age of 85 in a [[hospice]] in [[Cambridge, Massachusetts]] on 14 October 2010.<ref name="nyt_obit" /><ref>{{cite news |title=Benoît Mandelbrot, fractals pioneer, dies |url=http://www.upi.com/Science_News/2010/10/16/Benoit-Mandelbrot-fractals-pioneer-dies/UPI-11551287266964/ |accessdate=17 October 2010 |newspaper=United Press International |date=16 October 2010}}</ref> Reacting to news of his death, mathematician [[Heinz-Otto Peitgen]] said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years."<ref name="nyt_obit" />
[[Chris Anderson (entrepreneur)|Chris Anderson]], [[TED (conference)|TED conference]] curator, described Mandelbrot as "an icon who changed how we see the world".<ref>{{cite news |url=https://montrealgazette.com/technology/Mandelbrot+father+fractal+geometry+dies/3682961/story.html |title=Mandelbrot, father of fractal geometry, dies |work=[[The Gazette (Montreal)|The Gazette]] |access-date=16 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101019233754/http://www.montrealgazette.com/technology/Mandelbrot%2Bfather%2Bfractal%2Bgeometry%2Bdies/3682961/story.html |archive-date=19 October 2010 }}</ref> [[Nicolas Sarkozy]], [[President of France]] at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory."<ref>{{cite news |url=http://www.lefigaro.fr/flash-actu/2010/10/16/97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php |title=Sarkozy rend hommage à Mandelbrot |language=French |trans-title=Sarkozy pays homage to Mandelbrot |work=[[Le Figaro]] | accessdate=17 October 2010}}</ref> Mandelbrot's obituary in ''The Economist'' points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".<ref>[http://www.economist.com/node/17305197 Benoît Mandelbrot's obituary]. ''The Economist'' (21 October 2010)</ref>
Best-selling essayist-author [[Nassim Nicholas Taleb]] has remarked that Mandelbrot's book ''The (Mis)Behavior of Markets'' is in his opinion "The deepest and most realistic finance book ever published".<ref name=nature/>
==Bibliography==
===in English===
*Fractals: Form, Chance and Dimension, 1977, 2020
* [[The Fractal Geometry of Nature]], 1982
* Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E, 1997 by Benoit B. Mandelbrot and R.E. Gomory
* Fractales, hasard et finance, 1959-1997, 1 November 1998
* Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976) (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot
* Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot) 14 December 2001 by Benoit Mandelbrot and F.J. Damerau
* Fractals and Chaos: The Mandelbrot Set and Beyond, 9 January 2004
* The Misbehavior of Markets: A Fractal View of Financial Turbulence, 2006 by Benoit Mandelbrot and Richard L. Hudson
* The Fractalist: Memoir of a Scientific Maverick, 2014
===In French===
* La forme d'une vie. Mémoires (1924-2010) by Benoît Mandelbrot (Author), Johan-Frédérik Hel Guedj (Translator)
==References in popular culture==
* In 2004, the American singer-songwriter [[Jonathan Coulton]] wrote "Mandelbrot Set". Formerly, it contained the lines "Mandelbrot's in heaven / at least he will be when he's dead / right now he's still alive and teaching math at Yale". Live performances after Mandelbrot's passing in 2010 feature only the first line and a brief rock instrumental.
* In 2007, the author [[Laura Ruby]] published "The Chaos King," which includes a character named Mandelbrot and discussion of chaos theory.
* In 2017, [[Zach Weinersmith]]' webcomic, [[Saturday Morning Breakfast Cereal]], portrayed Mandelbrot.<ref>{{Cite web | url=http://www.smbc-comics.com/comic/mandelbrot | title=Saturday Morning Breakfast Cereal – Mandelbrot}}</ref>
* In 2017, Liz Ziemska published a novella, Mandelbrot The Magnificent, a fictional account of how Mandelbrot saved his family during WWII
== See also ==
{{External media |align=right | width=210px |headerimage=[[File:Mandelbrot p1130861.jpg|210px]] | video1=[http://www.webofstories.com/play/benoit.mandelbrot/1;jsessionid=E8EB8E149375B3987E49D5E4F02FCB57 Family background and early education], (4:11) Benoit Mandelbrot interview, Part 1 of 144, [[Web of Stories]]<ref name="wos1">{{cite web |url=http://www.webofstories.com/play/9596 |title=Web of Stories – Benoît Mandelbrot – Family background and early education |last=Mandelbrot |first=Benoît |author2=Bernard Sapoval |author3=Daniel Zajdenweber |date=May 1998 |publisher=[[Web of Stories]] | accessdate=19 October 2010}}</ref>}}
{|
|- style="vertical-align:top"
| style="padding-right:2em"|
* "[[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|How Long is the Coast of Britain?]]"
* [[Louis Bachelier]]
* [[Zipf–Mandelbrot law]]
* [[Seven states of randomness]]
* [[Skewness risk]]
Category:1924 births
类别: 1924出生
* [[Kurtosis risk]]
Category:2010 deaths
分类: 2010年死亡人数
* [[Fractal dimension]]
Category:20th-century American mathematicians
范畴: 20世纪美国数学家
* [[Lacunarity]]
Category:21st-century French mathematicians
范畴: 21世纪法国数学家
|
Category:20th-century American economists
类别: 20世纪美国经济学家
* [[Self-similarity]]
Category:21st-century American economists
类别: 21世纪美国经济学家
* [[Self-affinity]]
Category:Alexander von Humboldt Fellows
类别: 亚历山大·冯·洪堡研究员
* [[Hurst exponent]]
Category:California Institute of Technology alumni
类别: 加州理工学院校友
* [[Fractional Brownian motion]]
Category:Chaos theorists
范畴: 混沌理论家
* [[Multifractal system]]
Category:Deaths from cancer in Massachusetts
分类: 马萨诸塞州癌症死亡人数
* [[1/f noise]]
Category:Deaths from pancreatic cancer
分类: 死于胰腺癌
* [[Mandelbrot Competition]]
Category:École Polytechnique alumni
类别: 巴黎综合理工学院校友
|}
Category:Fellows of the American Geophysical Union
类别: 美国地球物理联盟研究员
Category:Fellows of the American Statistical Association
类别: 美国统计协会研究员
== Notes ==
Category:Fellows of the Econometric Society
类别: 经济计量学会研究员
{{Reflist|group=n|colwidth=50em}}
Category:Fellows of the American Physical Society
类别: 美国物理学会会员
Category:French emigrants to the United States
类别: 移居美国的法国移民
== References ==
Category:French scientists
分类: 法国科学家
{{Reflist|25em}}
Category:Harvard University people
类别: 哈佛大学的人
Category:IBM employees
类别: IBM 员工
==Bibliography==
Category:IBM Fellows
类别: IBM Fellows
* {{cite book |ref=Hudson|last1=Hudson |first1=Richard L. |last2=Mandelbrot |first2=Benoît B. |title=The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward |url=https://archive.org/details/misbehaviorofmar00beno|url-access=registration|year=2004 |publisher=Basic Books |location=New York |isbn=978-0-465-04355-2}}
Category:IBM Research computer scientists
类别: IBM 研究计算机科学家
Category:Institute for Advanced Study visiting scholars
类别: 高级研究所访问学者
== Further reading ==
Category:Jewish French scientists
类别: 犹太法国科学家
* Mandelbrot, Benoit B. (2010). [https://www.amazon.com/Fractalist-Memoir-Scientific-Maverick/dp/030738991X ''The Fractalist, Memoir of a Scientific Maverick.''] New York: [http://www.randomhouse.com/highschool/catalog/display.pperl?isbn=9780307389916&view=email_prep Vintage Books], Division of Random House. {{isbn|978-0-307-38991-6}}
Category:Members of the Norwegian Academy of Science and Letters
类别: 挪威科学与文学学会成员
* {{cite book |last1=Mandelbrot |first1=Benoît B. |title=The Fractal Geometry of Nature | year=1983 |publisher=W.H. Freeman |location=San Francisco |isbn=978-0-7167-1186-5|title-link=The Fractal Geometry of Nature }}
Category:Members of the United States National Academy of Sciences
类别: 美国国家科学院院士
* [[Heinz-Otto Peitgen]], [[Hartmut Jürgens]], [[Dietmar Saupe]] and Cornelia Zahlten: ''Fractals: An Animated Discussion'' (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. {{isbn|0-7167-2213-5}} (re-published by Films for the Humanities & Sciences, {{isbn|978-0-7365-0520-8}})
Category:Officiers of the Légion d'honneur
类别: 美国法国荣誉军团勋章协会官员
* Mandelbrot, Benoit B. (1997) ''Fractals and Scaling in Finance: Discontinuity, Concentration, Risk'', Springer.
Category:Polish emigrants to France
类别: 移居法国的波兰移民
* {{cite journal |last=Mandelbrot |first=Benoît |date=February 1999 |title=A Multifractal Walk down Wall Street |journal=[[Scientific American]] | bibcode=1999SciAm.280b..70M |volume=280 |page=70 |doi=10.1038/scientificamerican0299-70 |issue=2}}
Category:Polish emigrants to the United States
类别: 移居美国的波兰移民
* Mandelbrot, Benoit B., ''Gaussian Self-Affinity and Fractals'', Springer: 2002.
Category:Polish Jews
分类: 波兰犹太人
* {{cite news |url=http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html |title=A focus on the exceptions that prove the rule |last1=Mandelbrot |first1=Benoît |first2=Nassim |last2=Taleb |date=23 March 2006 |work=[[Financial Times]] |access-date=17 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20101023201028/http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html |archive-date=23 October 2010 }}
Category:University of Paris alumni
类别: 巴黎大学校友
* [https://www.pbs.org/wgbh/nova/fractals/ "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature"], ''[[Nova (American TV series)|NOVA]]'', WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.
Category:Wolf Prize in Physics laureates
类别: 沃尔夫物理学奖获得者
* {{cite book |last1=Frame |first1=Michael |last2=Cohen |first2=Nathan |title=Benoit Mandelbrot: A Life in Many Dimensions |year=2015 |publisher=World Scientific Publishing Company |location=Singapore |isbn=978-981-4366-06-9 }}
Category:Yale University faculty
类别: 耶鲁学院
* Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des Sciences de Paris, 249, 613–615.
Category:Yale Sterling Professors
分类: 耶鲁斯特林教授
* Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106.
Category:20th-century French mathematicians
范畴: 20世纪法国数学家
* Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543.
Category:21st-century American mathematicians
范畴: 21世纪美国数学家
<noinclude>
<small>This page was moved from [[wikipedia:en:Benoit Mandelbrot]]. Its edit history can be viewed at [[曼德布洛特/edithistory]]</small></noinclude>
[[Category:待整理页面]]