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第1,025行： − + + + − + − Poincaré's mental organisation was not only interesting to Poincaré himself but also to Édouard Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled ''Henri Poincaré'' (1910).<ref>[http://name.umdl.umich.edu/AAS9989.0001.001 Toulouse, Édouard, 1910. ''Henri Poincaré'', E. Flammarion, Paris]</ref><ref name="google">{{cite book|title=Henri Poincare|author=Toulouse, E.|date=2013|publisher=MPublishing|isbn=9781418165062|url=https://books.google.com/books?id=mpjWPQAACAAJ|accessdate=10 October 2014}}</ref> In it, he discussed Poincaré's regular schedule:+ + 第1,040行：
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==Character==
==Character性格==
[[File:Henri Poincaré by H Manuel.jpg|thumb|right|Photographic portrait of H. Poincaré by Henri Manuel]]
[[File:Henri Poincaré by H Manuel.jpg|thumb|right|Photographic portrait of H. Poincaré by Henri Manuel]]
Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.
Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.
庞加莱的工作习惯被比作蜜蜂从一朵花飞到另一朵花。庞加莱对他的思维方式很感兴趣；他研究了自己的习惯，并于1908年在巴黎普通心理学研究所发表了一篇关于他的观察结果的演讲。他把自己的思维方式与他如何取得几个发现联系在一起。
His method of thinking is well summarised as:
His method of thinking is well summarised as:
他的思维方式可以很好地概括为:
他的思维方式可以很好地概括为:
The mathematician Darboux claimed he was ''un intuitif'' (an intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic.<ref>{{cite book |title=Encounter|volume = 12|author= Congress for Cultural Freedom|url=https://books.google.com/books?id=4-QLAQAAIAAJ&q=Poincaré+disliked+logic|year=1959|publisher=Martin Secker & Warburg.}}</ref> (Despite this opinion, [[Jacques Hadamard]] wrote that Poincaré's research demonstrated marvelous clarity<ref>J. Hadamard. L'oeuvre de H. Poincaré. Acta Mathematica, 38 (1921), p. 208</ref> and Poincaré himself wrote that he <!-- TODO: Add Poincaré's opinion on rigorousness, see http://www.forgottenbooks.org/readbook/American_Journal_of_Mathematics_1890_v12_1000084889#233 — Each time I can I'm absolute rigour --> believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.)
The mathematician Darboux claimed he was ''un intuitif'' (an intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic.<ref>{{cite book |title=Encounter|volume = 12|author= Congress for Cultural Freedom|url=https://books.google.com/books?id=4-QLAQAAIAAJ&q=Poincaré+disliked+logic|year=1959|publisher=Martin Secker & Warburg.}}</ref> (Despite this opinion, [[Jacques Hadamard]] wrote that Poincaré's research demonstrated marvelous clarity<ref>J. Hadamard. L'oeuvre de H. Poincaré. Acta Mathematica, 38 (1921), p. 208</ref> and Poincaré himself wrote that he <!-- TODO: Add Poincaré's opinion on rigorousness, see http://www.forgottenbooks.org/readbook/American_Journal_of_Mathematics_1890_v12_1000084889#233 — Each time I can I'm absolute rigour --> believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.)
数学家达布克斯声称他是“不直觉的”（直觉的），认为这一点可以从他经常通过视觉表现来工作的事实中得到证明。他不在乎严谨，也不喜欢逻辑。<ref>{{cite book |title=Encounter|volume = 12|author= Congress for Cultural Freedom|url=https://books.google.com/books?id=4-QLAQAAIAAJ&q=Poincaré+disliked+logic|year=1959|publisher=Martin Secker & Warburg.}}</ref> （尽管如此，[[Jacques Hadamard]]写道，庞加莱的研究显示出惊人的清晰性。<ref>J. Hadamard. L'oeuvre de H. Poincaré. Acta Mathematica, 38 (1921), p. 208</ref>庞加莱自己也写道他<！--TODO:加上庞加莱对严谨的看法，参见http://www.forgottenbooks.org/readbook/American_Journal_of_Mathematics_1890_v12_1000084889#233 —每次我能做到的时候，我都是绝对严谨的-->相信逻辑不是一种发明的方式，而是一种构建思想的方式，逻辑限制了思想。）
===Toulouse's characterisation图卢兹的特征化===
===Toulouse's characterisation===
Poincaré's mental organisation was not only interesting to Poincaré himself but also to Édouard Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled ''Henri Poincaré'' (1910).<ref>[http://name.umdl.umich.edu/AAS9989.0001.001 Toulouse, Édouard, 1910. ''Henri Poincaré'', E. Flammarion, Paris]</ref><ref name="google">{{cite book|title=Henri Poincare|author=Toulouse, E.|date=2013|publisher=MPublishing|isbn=9781418165062|url=https://books.google.com/books?id=mpjWPQAACAAJ|accessdate=10 October 2014}}</ref> In it, he discussed Poincaré's regular schedule:
庞加莱的心理组织不仅令庞加莱本人感兴趣，而且巴黎高等研究院心理学实验室的心理学家埃杜阿尔德·图卢兹也感兴趣。图卢兹写了一本书，名叫《亨利·庞加莱》（1910年）<ref>[http://name.umdl.umich.edu/AAS9989.0001.001 Toulouse, Édouard, 1910. ''Henri Poincaré'', E. Flammarion, Paris]</ref><ref name="google">{{cite book|title=Henri Poincare|author=Toulouse, E.|date=2013|publisher=MPublishing|isbn=9781418165062|url=https://books.google.com/books?id=mpjWPQAACAAJ|accessdate=10 October 2014}}</ref>在其中，他讨论了庞加莱的常规日程安排：
* He worked during the same times each day in short periods of time. He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.
* He worked during the same times each day in short periods of time. He undertook mathematical research for four hours a day, between 10 a.m. and noon then again from 5 p.m. to 7 p.m.. He would read articles in journals later in the evening.
*他每天在同一时间短时间内工作。他每天进行四个小时的数学研究，从上午10点到中午，然后再从下午5点到晚上7点。。晚上晚些时候他会在杂志上读文章。
Poincaré was dismayed by Georg Cantor's theory of transfinite numbers, and referred to it as a "disease" from which mathematics would eventually be cured.
Poincaré was dismayed by Georg Cantor's theory of transfinite numbers, and referred to it as a "disease" from which mathematics would eventually be cured.
* His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.
* His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.
*他通常的工作习惯是在脑子里彻底解决一个问题，然后把完成的问题写在纸上。
Poincaré said, "There is no actual infinite; the Cantorians have forgotten this, and that is why they have fallen into contradiction."
Poincaré said, "There is no actual infinite; the Cantorians have forgotten this, and that is why they have fallen into contradiction."
* He was ambidextrous and nearsighted.
* He was ambidextrous and nearsighted.
*他两手灵巧，近视。
* His ability to visualise what he heard proved particularly useful when he attended lectures, since his eyesight was so poor that he could not see properly what the lecturer wrote on the blackboard.
* His ability to visualise what he heard proved particularly useful when he attended lectures, since his eyesight was so poor that he could not see properly what the lecturer wrote on the blackboard.
*当他去听课时，他对所听到的东西进行视觉化的能力被证明是特别有用的，因为他的视力很差，他不能正确地看到讲课者在黑板上写的东西。
* He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.
* He never spent a long time on a problem since he believed that the subconscious would continue working on the problem while he consciously worked on another problem.
这些能力在某种程度上被他的缺点所抵消：
*他身体笨拙，艺术上拙劣。
*他总是匆匆忙忙的，不喜欢回去修改或更正。
*他从来没有在一个问题上花很长时间，因为他相信潜意识会在他有意识地处理另一个问题时继续工作。
In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al., 2002).
In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al., 2002).
此外，图卢兹指出，大多数数学家都是从已经确立的原则出发，而庞加莱每次都是从基本原理出发（O'Connor et al.，2002）。
His method of thinking is well summarised as:
His method of thinking is well summarised as:
他的思维方法概括如下：
{{quote|text=''Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire.'' (Accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory.)|sign=Belliver (1956)}}
{{quote|text=''Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire.'' (Accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory.)|sign=Belliver (1956)}}
{{quote|text=“他习惯于忽略细节，只看山顶，以惊人的速度从一个瞬间到另一个瞬间，发现的事实围绕着他们的中心聚集在一起，并自动地被归入他的记忆中。”|sign=Belliver (1956)}}
Named after him
Named after him
以他的名字命名
以他的名字命名
===Attitude towards transfinite numbers===
===Attitude towards transfinite numbers对超限数的态度===
Poincaré was dismayed by [[Georg Cantor]]'s theory of [[transfinite number]]s, and referred to it as a "disease" from which mathematics would eventually be cured.<ref name="daub266">Dauben 1979, p. 266.</ref>
Poincaré was dismayed by [[Georg Cantor]]'s theory of [[transfinite number]]s, and referred to it as a "disease" from which mathematics would eventually be cured.<ref name="daub266">Dauben 1979, p. 266.</ref>
庞加莱对[[Georg Cantor]]的[[超限数]]理论感到沮丧，并将其称为数学最终将被治愈的“疾病”。<ref name="daub266">Dauben 1979, p. 266.</ref>
Poincaré said, "There is no actual infinite; the Cantorians have forgotten this, and that is why they have fallen into contradiction."<ref>{{citation
Poincaré said, "There is no actual infinite; the Cantorians have forgotten this, and that is why they have fallen into contradiction."<ref>{{citation
庞加莱说：“没有真正的无限；坎托利亚人忘记了这一点，这就是他们陷入矛盾的原因。”<ref>{{citation
|title=From Frege to Gödel: a source book in mathematical logic, 1879–1931
|title=From Frege to Gödel: a source book in mathematical logic, 1879–1931
庞加莱在巴黎 Société de Psychologie 之前的著名演讲(出版为《科学与假说》、《科学的价值》和《科学与方法》)被雅克·阿达马引用为创造力和发明由两个心理阶段组成，第一阶段是对问题可能解决方案的随机组合，随后是批判性评价。
庞加莱在巴黎 Société de Psychologie 之前的著名演讲(出版为《科学与假说》、《科学的价值》和《科学与方法》)被雅克·阿达马引用为创造力和发明由两个心理阶段组成，第一阶段是对问题可能解决方案的随机组合，随后是批判性评价。
==Honours==
==Honours==