Henri Poincaré
description: French mathematician, physicist, engineer, and philosopher of science
113 results
Alex's Adventures in Numberland
by Alex Bellos · 3 Apr 2011 · 437pp · 132,041 words
error. The more data we have, the closer the jagged landscape of outcomes will fit the curve. In the late nineteenth century the French mathematician Henri Poincaré knew that the distribution of an outcome that is subject to random measurement error will approximate the bell curve. Poincaré, in fact, conducted the same
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was a mean of somewhere around 400g, and a more or less symmetrical spread between 380 and 420g. If I had been as indefatigable as Henri Poincaré, I would have continued the experiment for a year and had 365 (give or take days of bakery closure) weights to compare. With more data
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is never so simple. The normal distribution is a theoretical ideal, and one cannot assume that all results will conform to it. I wondered about Henri Poincaré. When he measured his bread did he eliminate bias due to the Parisian weather, or the time of day of his measurements? Perhaps he had
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properties he was describing. The challenge of visualizing the hlic plane galvanized many mathematicians in the final decades of the nineteenth century. One attempt, by Henri Poincaré, caught the imagination of M.C. Escher, whose famous Circle Limit series of woodcuts was inspired by the Frenchman’s ‘disc model’ of a hyperbolic
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equally ‘real’ as flat or spherical surfaces. Every surface has its own geometry, and we need to choose the one that best applies, or, as Henri Poincaré once said: ‘One geomtry cannot be more true than another; it can only be more convenient.’ Euclidean geometry, for example, is the most appropriate for
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in which infinity could have more than one size. Cantor’s ideas were so unorthodox that they initially provoked ridicule from many of his peers. Henri Poincaré, for example, described his work as ‘a malady, a perverse illness from which some day mathematics would be cured’, while Leopold Kronecker, Cantor’s former
Surfaces and Essences
by Douglas Hofstadter and Emmanuel Sander · 10 Sep 2012 · 1,079pp · 321,718 words
that one can cite — great scientific discoveries resulting from sudden inspirations of people who found undreamt-of links between seemingly unrelated domains. Thus the mathematician Henri Poincaré wrote, “One day… the idea came to me very concisely, very suddenly, and with great certainty, that the transformations of indeterminate ternary quadratic forms were
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from physical tools: as opposed to being just an external device, a concept becomes an integral part of the person who acquires it. The mathematician Henri Poincaré is said to have stated, “When a dog eats the flesh of a goose, it turns into the flesh of a dog.” He was referring
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young physicist today? What would Alexander Pushkin bring to today’s poetry? What would Shakespeare or Dante write if they were alive today? What would Henri Poincaré give to mathematics, and Sigmund Freud to cognitive science? What analogies would they discover lurking implicitly in today’s concepts? What depths could they perceive
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building nor burials — just a listing of names of a number of important individuals. Accordingly, Albert Einstein is clearly in the pantheon of physicists, and Henri Poincaré, though not buried in the Panthéon in Paris, certainly figures very high in the pantheon of mathematicians. Various sacred sites and books serve to keep
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. And yet this is just a prejudice, no more valid for mathematics than for any other human activity. Anecdotes as Antidotes The great French mathematician Henri Poincaré devoted much thought to the nature of scientific creativity. In a commentary on mathematicians, he wrote: Could anyone think… that they have always marched forward
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of phenomena where even the other top scientists of his era had seen only unrelated things. In this regard, it is interesting to read what Henri Poincaré, whom we cited earlier concerning the way mathematicians are guided by analogies, had to say about Einstein. In a letter of reference for the young
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limited to the carrying-out of menial tasks. You quoted a mathematician talking about analogy, so now let me quote another mathematician talking about categorization. Henri Poincaré described mathematics as “the art of giving the same name to different things”. That is, it’s the art of discovering unusual and subtle new
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), p. 108. Page 112A certain fox from Normandy… La Fontaine (1668), Book III, p. 11. Page 132When a dog eats the flesh of a goose… Henri Poincaré, as quoted by Roger Apéri in Dieudonné, Loi, and Thom (1982), pp. 58–72. Page 133There Is No Word… Tony Hoagland, Poetry Magazine, July–August
The Physics of Wall Street: A Brief History of Predicting the Unpredictable
by James Owen Weatherall · 2 Jan 2013 · 338pp · 106,936 words
the best minds of the day, and he began to work on a dissertation — the one Samuelson later discovered, on speculation in financial markets — with Henri Poincaré, perhaps the most famous mathematician and physicist in France at the time. Poincaré was an ideal person to mentor Bachelier. He had made substantial contributions
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York: Oxford University Press. — — — . 2001. “Naturalism: Friends and Foes.” Philosophical Perspectives 15: 37–67. — — — . 2007. Second Philosophy. New York: Oxford University Press. Mahwin, Jean. 2005. “Henri Poincaré. A Life in the Service of Science.” Notices of the AMS 52 (9): 1036–44. Malaney, Pia. 1996. “The Index Number Problem: A Differential Geometric
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
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
The Misbehavior of Markets: A Fractal View of Financial Turbulence
by Benoit Mandelbrot and Richard L. Hudson · 7 Mar 2006 · 364pp · 101,286 words
Bachelier and His Legacy IN MARCH 1900, the academic equivalent of a trial by fire was convened at the University of Paris. The judges included Henri Poincaré, one of the most celebrated mathematicians of all time. He was a genius whose restless energy had led him across virtually every field of mathematical
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
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
What We Cannot Know: Explorations at the Edge of Knowledge
by Marcus Du Sautoy · 18 May 2016
decide nothing here. There is an infinite chaos which separated us.’ THE FATE OF THE SOLAR SYSTEM If Newton is my hero, then French mathematician Henri Poincaré should be the villain in my drive to predict the future. And yet I can hardly blame him for uncovering one of the most devastating
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of a resurgence of French mathematics. Gaston Darboux, the permanent secretary of the French Academy of Sciences, declared: From that moment on the name of Henri Poincaré became known to the public, who then became accustomed to regarding our colleague no longer as a mathematician of particular promise but as a great
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. 2 If nature were not beautiful it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Henri Poincaré I wasted a lot of time at university playing billiards in our student common room. I could have pretended that it was all part of
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
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