Information Renaissance

Henri Poincaré--the Renaissance Man as French Scientist

So at the end of a hard academic term, my mind turns to someone I want to learn more about,
and to learn from--Henri Poincaré.

Here's a good introductory essay on him from the Wikipedia entry for Henri Poincaré where you get a sense of who he is and what he accomplished:

Jules Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [pwɛ̃kaˈʀe][1]) was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science. Poincaré is often described as a polymath, and in mathematics as 'The Last Universalist', since he excelled in all fields of the discipline as it existed during his lifetime.

As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is considered to be one of the founders of the field of topology.

Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form.

Here's an interesting account on his contributions and fields:

Poincaré made many contributions to different fields of applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology.

He was also a popularizer of mathematics and physics and wrote several books for the lay public.

And here's some information on how his mind worked,
along with his strengths and foibles:

Character

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.

The mathematician Darboux claimed he was un intuitif (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. He believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.

[edit] Toulouse' characterization

Poincaré's mental organization was not only interesting to Poincaré himself but also to Toulouse, a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled Henri Poincaré (1910). In it, he discussed Poincaré's regular schedule:

* 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.

* His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper.

* He was ambidextrous and nearsighted.

* 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 his lecturers were writing on the blackboard.

However, these abilities were somewhat balanced by his shortcomings:

* He was physically clumsy and artistically inept.

* He was always in a rush and disliked going back for changes or corrections.

* 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.

In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré was the type that started from basic principle each time. (O'Connor et al., 2002)

His method of thinking is well summarized as:

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. (He neglected details and jumped from idea to idea, the facts gathered from each idea would then come together and solve the problem.) (Belliver, 1956)

Here are the sources--some referenced above--from the General References on the Wikipedia for a point of departure for more research:

General References

* Bell, Eric Temple, 1986. Men of Mathematics (reissue edition). Touchstone Books. ISBN 0671628186.
* Belliver, André, 1956. Henri Poincaré ou la vocation souveraine. Paris: Gallimard.
* Bernstein, Peter L, 1996. "Against the Gods: A Remarkable Story of Risk". (p. 199-200). John Wiley & Sons.
* Boyer, B. Carl, 1968. A History of Mathematics: Henri Poincaré, John Wiley & Sons.
* Olivier Darrigol (2004): "The Mystery of the Einstein-Poincaré Connection". Isis: Vol.95, Issue 4; pg. 614, 14 pgs
* Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press. Contains among others:
* Grattan-Guinness, Ivor, 2000. The Search for Mathematical Roots 1870-1940. Princeton Uni. Press.
* Gray, Jeremy, 1986. Linear differential equations and group theory from Riemann to Poincaré, Birkhauser
* Kolak, Daniel, 2001. Lovers of Wisdom, 2nd ed. Wadsworth.
* Murzi, 1998. "Henri Poincaré".
* O'Connor, J. John, and Robertson, F. Edmund, 2002, "Jules Henri Poincaré". University of St. Andrews, Scotland.
* Peterson, Ivars, 1995. Newton's Clock: Chaos in the Solar System (reissue edition). W H Freeman & Co. ISBN 0716727242.
* Poincaré, Henri. 1894. "On the nature of mathematical reasoning," 972-81.
* ________. 1898. "On the foundations of geometry," 982-1011.
* ________. 1900. "Intuition and Logic in mathematics," 1012-20.
* ________. 1905-06. "Mathematics and Logic, I-III," 1021-70.
* ________. 1910. "On transfinite numbers," 1071-74.
* Sageret, Jules, 1911. Henri Poincaré. Paris: Mercure de France.
* Toulouse, E.,1910. Henri Poincaré. - (Source biography in French)

Posted by Jay Gillette at May 4, 2007 05:32 PM