Henri Poincaré
description: French mathematician, physicist, engineer, and philosopher of science
114 results
Zen and the Art of Motorcycle Maintenance: An Inquiry Into Values
by Robert M. Pirsig · 1 Jan 1974
, the most eminent scientific man of his generation.” He was an astronomer, a physicist, a mathematician and philosopher all in one. His name was Jules Henri Poincaré. It always seemed incredible to me, and still does, I guess, that Phćdrus should have traveled along a line of thought that had never been
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
by Jordan Ellenberg · 14 May 2021 · 665pp · 159,350 words
built into the way we think about space, location, and motion. We can’t help being geometric. We have, in other words, intuition. The geometer Henri Poincaré, in a 1905 essay, identifies intuition and logic as the two indispensable pillars of mathematical thought. Every mathematician leans in one direction or the other
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are—only how many there are. Topology is like that but for shapes. In its modern form it comes to us from the French mathematician Henri Poincaré. Him again! It’s a name we’ll be hearing a lot, because Poincaré had a hand in an astonishingly broad range of geometric developments
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financial center of France. He began studying mathematics at the Sorbonne in the 1890s, taking great interest in the probability courses, which were taught by Henri Poincaré. Bachelier was not a typical student; an orphan, he had to work for his living, and hadn’t received the lycée training that had molded
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impossible. The language of differential equations was what Ross, Hudson, Kermack, and McKendrick used in their models. Ross had left St. Louis by the time Henri Poincaré delivered his lecture on the final day of the 1904 exposition, but had he seen it, he might have gotten a ten-year head start
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/. he esteemed his diagram: Bill Casselman, “On the Dissecting Table,” Plus Magazine, Dec. 1, 2000. https://plus.maths.org/content/dissecting-table. “You have doubtless”: Henri Poincaré, The Value of Science, trans. G. B. Halsted (New York: The Science Press, 1907), 23. at least one study: M. J. Nathan, et al., “Actions
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with Words: The Roles of Action and Pedagogical Language for Grounding Mathematical Proof,” Learning and Instruction 33 (2014): 182–93. when he needed: Jeremy Gray, Henri Poincaré: A Scientific Biography (Princeton: Princeton University Press, 2012), 26. Chapter 2: How Many Holes Does a Straw Have? a 1970 paper: David Lewis and Stephanie
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the middle, but definitely none who remove a hole from a fully baked no-holed pastry. “I recall above all”: Galina Weinstein, “A Biography of Henri Poincaré—2012 Centenary of the Death of Poincaré,” ArXiv preprint server, July 3, 2012, 6. Accessed at https://arxiv.org/pdf/1207.0759.pdf. the loss
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of Alsace: Jeremy Gray, Henri Poincaré: A Scientific Biography (Princeton: Princeton University Press, 2012), 18–19. In 1889 he won: June Barrow-Green, “Oscar II’s Prize Competition and the Error
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Sciences 48, no. 2 (1994): 107–31. precise habits: Weinstein, “A Biography of Henri Poincaré,” 20. the joke in Paris circles: Tobias Dantzig, Henri Poincaré: Critic of Crisis (New York: Charles Scribner’s Sons, 1954), 3. He was not only: Gray, Henri Poincaré, 67. “Geometry is the art”: “La Géométrie est l’art de bien raisonner
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sur des figures mal faites.” Henri Poincaré, “Analysis situs,” Journal de l’École Polytechnique ser. 2, no. 1 (1895): 2. “The circles he drew
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”: Dantzig, Henri Poincaré, 3. Noether’s innovation: To be fair to Poincaré, Leopold Vietoris, who was there at the
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exposition is mostly from D. R. Francis, The Universal Exposition of 1904, vol. 1 (St. Louis: Louisiana Purchase Exposition Company, 1913). “[T]here are symptoms”: Henri Poincaré, “The Present and the Future of Mathematical Physics,” trans. J. W. Young, Bulletin of the American Mathematical Society 37, no. 1 (Dec. 1999): 25. “victorious
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, says on p. 343 that Bachelier’s grades were quite good. Dreyfus was convicted: All material on Poincaré and the Dreyfus affair is from Gray, Henri Poincaré, 166–69. “[O]ne might fear”: Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” 348. Bachelier did end up: The
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from Parmanand Singh, “The So-Called Fibonacci Numbers in Ancient and Medieval India,” Historia Mathematica 12, no. 3 (1985): 229–44. “What did the ancients”: Henri Poincaré, “The Present and the Future of Mathematical Physics,” trans. J. W. Young, Bulletin of the American Mathematical Society 37, no. 1 (1999): 26. Chapter 11
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remarked, while visiting: Melvin Henriksen, “Reminiscences of Paul Erdös (1913–1996),” Humanistic Mathematics Network Journal 1, no. 15 (1997): 7. “he could not find words”: Henri Poincaré, The Value of Science, trans. George Bruce Halsted (New York: The Science Press, 1907), 138. in a movie with everyone: Brandon Griggs, “Kevin Bacon on
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Chorus of Voices: An Interview with Rita Dove,” Agni 54 (2001), 175. “you also realize”: “A Chorus of Voices,” 175. “What I have just said”: Henri Poincaré, “The Future of Mathematics” (1908), trans. F. Maitland, appearing in Science and Method (Mineola, NY: Dover Publications, 2003), 32. Perelman himself: Luke Harding, “Grigory Perelman
From eternity to here: the quest for the ultimate theory of time
by Sean M. Carroll · 15 Jan 2010 · 634pp · 185,116 words
of the curvature of spacetime, was due almost exclusively to Einstein.) One of the major contributors to special relativity was the French mathematician and physicist Henri Poincaré. While Einstein was the one who took the final bold leap into asserting that the “time” as measured by any moving observer was as good
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of Life spins, and history repeats itself. But soon after Nietzsche imagined his demon, the idea of eternal recurrence popped up in physics. In 1890 Henri Poincaré proved an intriguing mathematical theorem, showing that certain physical systems would necessarily return to any particular configuration infinitely often, if you just waited long enough
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of their mutual gravitational pull. (For two bodies it’s easy, and Newton had solved it: Planets move in ellipses.) This problem was tackled by Henri Poincaré, who in his early thirties was already recognized as one of the world’s leading mathematicians. He did not solve it, but submitted an essay
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ingenious that he was awarded the prize, and his paper was prepared for publication in Mittag-Leffler’s new journal, Acta Mathematica.169 Figure 52: Henri Poincaré, pioneer of topology, relativity, and chaos theory, and later president of the Bureau of Longitude. But there was a slight problem: Poincaré had made a
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of special relativity, it was legitimately a collaborative effort involving the work of a number of physicists and mathematicians, including George FitzGerald, Hendrik Lorentz, and Henri Poincaré. It was eventually Hermann Minkowski who took Einstein’s final theory and showed that it could be understood in terms of a four-dimensional spacetime
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, Max Planck area Planck energy Planck length Planck mass Planck’s constant Planck time planetary motion pocket universes. See also baby universes Podolsky, Boris Poincaré, Henri Poincaré recurrence theorem Poincaré transformations Popper, Karl popular culture position possibilism potential energy predestination. See also Future Hypothesis prediction and Boltzmann brains and classical mechanics and
The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling
by Adam Kucharski · 23 Feb 2016 · 360pp · 85,321 words
it into a successful prediction. After all, isn’t roulette supposed to be random? THERE ARE TWO WAYS to deal with randomness in roulette, and Henri Poincaré was interested in both of them. It was one of his many interests: in the early twentieth century, pretty much anything that involved mathematics had
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have become the most important object of human knowledge.” Cards and casinos since have inspired many other scientific ideas. We have seen how roulette helped Henri Poincaré develop the early ideas of chaos theory and allowed Karl Pearson to test his new statistical techniques. We also met Stanislaw Ulam, whose card games
The Scientist as Rebel
by Freeman Dyson · 1 Jan 2006 · 332pp · 109,213 words
Newton (Pantheon, 2003). 4. Oxford University Press, 1974. 18 CLOCKWORK SCIENCE TODAY THE NAME of Albert Einstein is known to almost everybody, the name of Henri Poincaré to almost nobody. A hundred years ago the opposite was true. Then, Einstein was a newly appointed technical expert, third class, examining patent applications in
Chaos: Making a New Science
by James Gleick · 18 Oct 2011 · 396pp · 112,748 words
field. In the 1960s, though, he left topology for untried territory. He began studying dynamical systems. Both subjects, topology and dynamical systems, went back to Henri Poincaré, who saw them as two sides of one coin. Poincaré, at the turn of the century, had been the last great mathematician to bring a
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PROVED CATASTROPHIC Of all the classical physicists and mathematicians who thought about dynamical systems, the one who best understood the possibility of chaos was Jules Henri Poincaré. Poincaré remarked in Science and Method: “A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and
Infinite Ascent: A Short History of Mathematics
by David Berlinski · 2 Jan 2005 · 158pp · 49,168 words
’s parallel postulate unobtrusively recedes. Lines through a point parallel to a given line? There are lots of them. Writing some thirty years after Lobachevsky, Henri Poincaré provided a far more intuitive model of hyperbolic geometry, one known now as the Poincaré disk. Up to a certain point, the disk is what
When Einstein Walked With Gödel: Excursions to the Edge of Thought
by Jim Holt · 14 May 2018 · 436pp · 127,642 words
up on the idea of an academic career, telling a friend that “the whole comedy has become boring.” He had recently read a book by Henri Poincaré, a French mathematician of enormous reputation, that identified three fundamental unsolved problems in science. The first concerned the “photoelectric effect”: How did ultraviolet light knock
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century. It was David Hilbert—a “supergiant,” in Harris’s estimation—who originated “formalism,” which views higher mathematics as a game played with formal symbols. Henri Poincaré (another “supergiant”), Hermann Weyl, and L.E.J. Brouwer were behind “intuitionism,” according to which numbers and other mathematical objects are mind-dependent constructions. Bertrand
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are too benighted to realize it? “A person who devoted his life to it might perhaps eventually be able to picture the fourth dimension,” wrote Henri Poincaré in the late nineteenth century. He made the task seem rather daunting, but maybe that is because, as a mathematician of peerless spatial intuition himself
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in the collection of New York’s Metropolitan Museum of Art. Thanks to the efforts of Abbott and Hinton, and to the popular writings of Henri Poincaré in France, the “fourth dimension” had become a household expression by the early twentieth century. It cropped up in the works of authors like Alfred
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mine.” In some cases, the reaction to Cantor’s theory broke along national lines. French mathematicians, on the whole, were wary of its metaphysical aura. Henri Poincaré (who rivaled Germany’s Hilbert as the greatest mathematician of the era) observed that higher infinities “have a whiff of form without matter, which is
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in their genre. Could this immersion have something to do with stocking the memory? As an instructive case of creative genius, consider the French mathematician Henri Poincaré, who died in 1912. Poincaré’s genius was distinctive in that it embraced nearly the whole of mathematics, from pure (number theory) to applied (celestial
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energy—all, fortunately, interconvertible. With Einstein’s theory of relativity, even matter came to be viewed as “frozen” energy. Sooner than give up energy conservation, Henri Poincaré once observed, we would invent new forms of energy to save it. Thanks to Emma Noether’s profoundly beautiful discovery, we know why: the timelessness
E=mc2: A Biography of the World's Most Famous Equation
by David Bodanis · 25 May 2009 · 349pp · 27,507 words
for interviews. Einstein wasn’t one of them. In time a few scientists did begin to hear of his work, and then jealousy set in. Henri Poincaré was one of the glories of Third Republic France, and, along with David Hilbert in Germany, one of the greatest mathematicians in the world. As
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death by the guillotine. “If I were King,” du Châtelet once wrote, “. . . women would be worth more, and men would gain something new to emulate.” henri poincaré lived for seven years after Einstein’s 1905 publications, still unreconciled to the fact that outside of France he wasn’t recognized as a founder
The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
by Justin Fox · 29 May 2009 · 461pp · 128,421 words
is thanks to chance—that is to say, thanks to our ignorance, that we can arrive at conclusions,” wrote the great French mathematician and physicist Henri Poincaré in 1908.3 The greatest tool for building knowledge upon such ignorance was what was called the Gaussian distribution (after German stargazer and mathematician Carl
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is not simply a tale of ignored genius. There was a major limitation to Bachelier’s work, of which he was well aware. His teacher, Henri Poincaré, made sure of that. While he celebrated the use of the bell curve in the physical sciences, Poincaré thought caution needed to be exercised in
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clearly into the future was crucial to making equilibrium economics work. It was also crucially problematic. “You regard men as infinitely selfish and infinitely farsighted,” Henri Poincaré wrote to mathematical economist Léon Walras in 1901. Infinite selfishness “may perhaps be admitted in a first approximation,” Poincaré allowed. But the assumption of infinite
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prices often leap or fall distances bigger than a penny. Then there was the really big issue, one already noted by both Irving Fisher and Henri Poincaré: Human behavior isn’t truly random. Men—and thus investors—at times act like sheep. Macaulay knew firsthand about investor behavior. His father was the
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envisioned such a market, too, but he had been unwilling to look more than an “instant” into its future. Over any longer period, his professor Henri Poincaré had surely warned him, the tendency of men to behave like ocean-jumping sheep stood in the way of rational theories of market behavior. Merton
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book by James Surowiecki, but the wording is misleading. Crowds—and markets—possess many useful traits. Wisdom is not one of them. It is as Henri Poincaré wrote a century ago: When men are brought together, they no longer decide by chance and independently of each other, but react upon one another
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crash were dismissed by Wall Street (and by Irving Fisher). Louis Bachelier French mathematician whose 1900 dissertation, written under the supervision of the great scientist Henri Poincaré, established that short-term financial market movements should be random. He used mathematical tools that presaged Albert Einstein’s work to describe this randomness. Fischer
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Press Books, 1956). These two books are the source of all Fisher biographical information in this book, except as otherwise noted. 3. Henri Poincaré, The Value of Science: Essential Writings of Henri Poincaré (New York: The Modern Library, 2001), 402. 4. Louis Bachelier, “Theory of Speculation,” in The Random Character of Stock Prices, trans
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What We Cannot Know: Explorations at the Edge of Knowledge
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The Fractalist
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