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شرح حال ژول آنری-هانری پوانکاره(1270 - 1330 هـ = 1854 - 1912 م)
intuition in mathematical discovery
For two weeks I tried to prove that no function could exist analogous to those I have since called the Fuchsian functions: I was then totally ignorant ...
به مدت دو هفته سعی کردم ثابت کنم که هیچ تابعی نمی تواند مشابه آنهایی باشد که من از آن به بعد توابع فوکسی نامیده ام: در آن زمان کاملاً نادان بودم ...
The phrase "Henri Poincaré theta-Fuchsian bus" refers to an anecdote where Henri Poincaré had a spontaneous mathematical breakthrough about theta-Fuchsian functions while stepping onto an omnibus (a type of bus) in Coutances. This is a famous story illustrating how creative insights can arrive suddenly, often after periods of focused work followed by a relaxed state or distraction, with the "subliminal self" connecting seemingly unrelated ideas
عبارت «اتوبوس تتا-فوشیان هنری پوانکاره» به حکایتی اشاره دارد که در آن هنری پوانکاره هنگام قدم گذاشتن بر روی یک اومنیبوس (نوعی اتوبوس) در کوتانس، به طور خودجوش به یک کشف ریاضی در مورد توابع تتا-فوشیان دست یافت. این داستان مشهوری است که نشان می‌دهد چگونه بینش‌های خلاقانه می‌توانند به طور ناگهانی، اغلب پس از دوره‌های کار متمرکز و به دنبال آن حالت آرامش یا حواس‌پرتی، با «خود ناخودآگاه» که ایده‌های به ظاهر نامرتبط را به هم متصل می‌کند، به وجود آیند.
The "Henri Poincaré theta-Fuchsian bus" is a reference to his own account of a moment of spontaneous mathematical discovery, where his subconscious mind connected new ideas about Fuchsian functions with non-Euclidean geometry as he stepped onto a bus. It serves as a well-known example of creative cognitive processes in action
«اتوبوس تتا-فوشیان هنری پوانکاره» اشاره‌ای به روایت خودش از لحظه‌ای از کشف خودجوش ریاضی است، جایی که ذهن ناخودآگاه او هنگام ورود به اتوبوس، ایده‌های جدیدی در مورد توابع فوشیان را با هندسه نااقلیدسی مرتبط کرد. این به عنوان نمونه‌ای شناخته شده از فرآیندهای شناختی خلاقانه در عمل عمل می‌کند.
خلاصه هوش مصنوعی
The phrase "Henri Poincaré theta-Fuchsian bus" refers to an anecdote where Henri Poincaré had a spontaneous mathematical breakthrough about theta-Fuchsian functions while stepping onto an omnibus (a type of bus) in Coutances. This is a famous story illustrating how creative insights can arrive suddenly, often after periods of focused work followed by a relaxed state or distraction, with the "subliminal self" connecting seemingly unrelated ideas.
The Story Explained
1. The Breakthrough:
Poincaré was stepping onto the omnibus when the idea struck him that the transformations he had used to define Fuchsian functions were identical with those of non-Euclidean geometry.
2. The "Aha!" Moment:
This idea came to him with the characteristics of brevity, suddenness, and immediate certainty, without any prior thought paving the way for it.
3. The "Subliminal Self":
Poincaré later reflected on his creative process, postulating that such insights arise from the "subliminal self" – a part of the mind that continues to work on a problem even when conscious attention is elsewhere.
4. Theta-Fuchsian Functions:
While the specific term "theta-Fuchsian functions" might not be in the direct quote, the breakthrough involved Fuchsian functions and the idea of transformations, often discussed in relation to theta functions and automorphic forms.
In Summary
The "Henri Poincaré theta-Fuchsian bus" is a reference to his own account of a moment of spontaneous mathematical discovery, where his subconscious mind connected new ideas about Fuchsian functions with non-Euclidean geometry as he stepped onto a bus. It serves as a well-known example of creative cognitive processes in action.
Poincaré on Fuchsian groups - Harvard Mathematics Department
The indicidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some plac...
Harvard University
How a Little Boredom in Your Life Can Help You Do Big Things
۷ آبان ۱۳۹۷ — Channel Your Subliminal Self One day Henri Poincaré, the 19th-century French mathematician, was stepping onto a bus and...
Inc.com
Open Research Online Poincaré and the idea of a group oro.open ...
Fuchsian functions. Poincaré then wrote to Fuchs, and it became ... theta functions, and introduced ... J.J. Gray, Henri Poincaré:
CiteSeerX
نمایش همه
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خلاصه هوش مصنوعی
"Henri Poincaré omnibus" refers to a famous anecdote by the mathematician Henri Poincaré, where while boarding an omnibus in Coutances, he had a sudden realization about the nature of the mathematical problem he was working on, an experience that mirrored the intuition of Archimedes during his "Eureka!" moment.
The Story
Poincaré was traveling to Coutances when he entered an omnibus, and as he stepped onto the vehicle, he had a flash of insight about the mathematical questions he was pondering.
This moment of sudden understanding or intuition came to him at the precise moment he stepped onto the omnibus.
Significance
The anecdote highlights Poincaré's view of the importance of intuition in mathematical discovery.
It is often compared to Archimedes' "Eureka!" moment, as both represent sudden, profound insights that occur at seemingly ordinary times.
خلاصه هوش مصنوعی
"هنری پوانکاره همه چیز را کشف کرد" به حکایتی معروف از ریاضیدان، هنری پوانکاره، اشاره دارد که در آن هنگام سوار شدن به یک اتوبوس در کوتانس، ناگهان متوجه ماهیت مسئله ریاضی که روی آن کار می‌کرد، شد، تجربه‌ای که شهود ارشمیدس را در لحظه "یافتم!" منعکس می‌کرد.
داستان
پوانکاره در حال سفر به کوتانس بود که وارد یک اتوبوس شد و هنگامی که سوار وسیله نقلیه شد، جرقه‌ای از بینش در مورد سوالات ریاضی که در مورد آنها فکر می‌کرد، به او دست داد.
این لحظه درک یا شهود ناگهانی دقیقاً در همان لحظه‌ای که سوار اتوبوس شد، به او رسید.
اهمیت
این حکایت، دیدگاه پوانکاره در مورد اهمیت شهود در کشف ریاضی را برجسته می‌کند.
این اغلب با لحظه "یافتم!" ارشمیدس مقایسه می‌شود، زیرا هر دو نمایانگر بینش‌های ناگهانی و عمیقی هستند که در زمان‌های به ظاهر عادی رخ می‌دهند.
خلاصه هوش مصنوعی
The quote "For two weeks I tried to prove that no function" comes from Henri Poincaré, a French mathematician, who stated that he spent this time trying to prove that no function could exist that was analogous to what he later called Fuchsian functions. He was attempting to prove the non-existence of these functions before a sudden breakthrough led him
to their discovery.
Details from the Quote:
Author:
Henri Poincaré
Topic:
The non-existence of certain functions, which he would later name "Fuchsian functions".
Context:
Poincaré was initially trying to prove that these types of functions could not exist.
Outcome:
After two weeks of unsuccessful attempts, he had a breakthrough while thinking about his coffee, which led him to the discovery of these functions.
Significance:
This moment was a significant part of his intellectual journey and is tied to the history of mathematics, particularly in the development of automorphic forms.
Henri Poincaré and the Disc Model of non-Euclidean Geometry
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Henri Poincaré - Wikipedia
In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid ...
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Springer Undergraduate Mathematics Series
... For two weeks I tried to prove that no function could exist analogous to those I have since called the Fuchsian functions: I w...
pyrkov-professor.ru
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