Mathematician:Jules Henri Poincaré

Mathematician

French mathematician and philosopher.

Often referred to as "The last universalist", as he was the last one able to master the whole of mathematics at the time. (Since then the field has grown too large.)

Introduced the field of special relativity.

Nationality

French

History

• Born: 29 April 1854
• Died: 7 July 1912

Theorems and Definitions

• Poincaré Duality
• Poincaré Group, also known as a Fundamental Group
• Poincaré Half-Plane Model
• Poincaré Map
• Poincaré Metric
• Poincaré Plane
• Poincaré Symmetry

• Euler-Poincaré Characteristic (with Leonhard Paul Euler)
• Hilbert-Poincaré Series (with David Hilbert)
• Neumann-Poincaré Operator (with Carl Gottfried Neumann) (also known as Poincaré-Neumann Operator)
• Poincaré-Steklov Operator (with Vladimir Andreevich Steklov)

• Poincaré Conjecture (now proven)
• Poincaré Duality Theorem
• Poincaré's Last Geometric Theorem
• Poincaré's Lemma
• Poincaré Recurrence Theorem

• Poincaré-Bendixson Theorem (with Ivar Otto Bendixson)
• Poincaré-Birkhoff-Witt Theorem (with George David Birkhoff and Ernst Witt)
• Poincaré-Hopf Theorem (with Heinz Hopf)
• Poincaré-Lindstedt Method (also known as the Lindstedt-Poincaré Method) (with Anders Lindstedt)

Results named for Jules Henri Poincaré can be found here.

Definitions of concepts named for Jules Henri Poincaré can be found here.

Publications

• 1892–99: Les Méthodes nouvelles de la mécanique céleste ("New Methods in Celestial Mechanics") (3 volumes)
• 1894: On the nature of mathematical reasoning
• 1895: Analysis situs
• 1896: Calcul des Probabilités
• 1898: On the foundations of geometry
• 1899: Complément à l'Analysis Situs (Rend. Circ. Mat. Palermo Vol. 13: pp. 285 – 343)
• 1900: Intuition and Logic in mathematics
• 1900: Sur les groupes continus
• 1902: Science and Hypothesis
• 1905: The Value of Science
• 1905–06: Mathematics and Logic, I–III
• 1905–10: Lessons of Celestial Mechanics
• 1908: Science and Method
• 1910: On transfinite numbers
• 1912: Sur un théorème de géométrie (in which is presented what is now known as Poincaré's Last Geometric Theorem)

Notable Quotes

Though the source be obscure, still the stream flows on.

People have been shocked by this formula, and yet it is as good as life for life's sake, if life is but misery.

What we call objective reality is, in the last analysis, what is common to many thinking beings and could be common to all.

Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of beauty which strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp.

-- Quoted in 1972: George F. Simmons: Differential Equations

On resolving the paradoxes of set theory:

Whatever the remedy adopted, we can promise ourselves the joy of a doctor called to witness an interesting pathological case.

-- Quoted in 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics

It is by logic we prove. It is by intuition we discover.

-- Quoted in 2021: Jay Cummings: Proofs

Also known as

Usually known as Henri Poincaré.

Sources

• John J. O'Connor and Edmund F. Robertson: "Jules Henri Poincaré": MacTutor History of Mathematics archive

• 1937: Eric Temple Bell: Men of Mathematics: Chapter $\text{XXVIII}$
• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): Preface
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Poincaré, Jules Henri (1854-1912)
• 1991: David Wells: Curious and Interesting Geometry ... (previous) ... (next): A Chronological List Of Mathematicians
• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Introduction
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Poincaré, Jules Henri (1854-1912)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Poincaré, Jules Henri (1854-1912)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Poincaré, (Jules) Henri (1854-1912)
• 2021: Jay Cummings: Proofs ... (previous) ... (next): Chapter $1$: $1.1$ Chessboard Problems