Poincare: An accessible biography

This is a review of Henri Poincare: A Scientific Biography, written by Jeremy Gray and published by Princeton University Press (592 pages).

Poincare was a great mathematician and physicist. He invented the theory of automorphic functions and the field of algebraic topology, and made distinguished contributions to partial differential equations, celestial mechanics (chaos), special relativity (Lorentz and Poincare groups), number theory, and the famous conjecture in geometric topology named after him and eventually proved by Grigori Perlman. The book also describes Poincare's work on distortionless telephony and his crucial role as a consultant in the Dreyfus case (conducted by Monsieur Bertillon, immortalized by Conan Doyle in The Hound of the Baskervilles).

The introduction declares that the book only addresses Poincare's contributions to mathematics, physics and philosophy. That it does, and in doing so covers large swathes of nineteenth century science, scores of other scientists, and many profound issues of our existence which occupied Poincare: What is the relationship between rigor and understanding? What do the laws of mathematics and physics tell us about the universe? What does science say about ethics?

The book is mainly a scientific biography. It provides a minimum of personal detail and confines itself to Poincare's public life. Even so, the book reveals his intimate scientific and philosophical thoughts (e.g. he held that the principles of physics were human inventions; and that rigor in mathematics is necessary but not sufficient. Poincare's intuitionist approach led him to oppose Hilbert's program of axiomatizing mathematics).

Nonetheless, there are some sections, which deal with occasions on which Poincare allowed himself to be psychologically analyzed, where we learn about his stances on religion, politics, women's rights, and patriotism; about his sleeping and eating habits; his ambidexterity; his custom of thinking all the time. From other places in the book we learn that he was not a prodigy - he published his first results in his mid-twenties; that he never took notes at university, but remembered the details of every course; that he never worked in the evenings, as he found it hard to switch off; that he liked music, especially Wagner; that his cousin Raymond became the Prime Minister as well as President of France; that his brother-in-law Boutroux was the prominent philosopher of the day.

Poincare had no close collaborators or adherent students. However, he interacted with a large number of scientists. Among them: Bertrand Russell (with whom he had protracted arguments), Boltzmann, Darboux, Einstein (whom he met only once), Hermite (who came from the same region of France as Poincare, and was a crucial mentor), Hertz, Hilbert, Klein, Langevin (with whom he traveled to the US), Lie, Lorentz, Minkowski, Mittag-Leffler (who played a crucial role as founder-editor of the Acta Mathematica in publishing Poincare), for example.

Poincare was nominated many times for the physics Nobel, but never successfully. The absence of any single spectacular contribution to physics seems to have been the hurdle to his being awarded. He was an ardent popularizer of science.

Summary

The book reads smoothly and up to its midpoint may be read even by a popular audience. At this stage, the discussions become technical and focus on his mathematical and physical contributions. Still, a non-expert in math such as myself was able to follow to quite an extent. The text is well researched and reveals a wealth of detail on European mathematical and physics culture during the middle and end of the nineteenth century. A person with a bachelor's degree in a STEM discipline should be able to read the book with profit.