Henri Poincaré: A Scientific Biography,

Jeremy
Gray
,
Princeton U. Press
, 2013. $35.00 (608 pp.). ISBN 978-0-691-15271-4

Henri Poincaré: Impatient Genius,

Ferdinand
Verhulst
,
Springer
, 2012. $49.95 (271 pp.). ISBN 978-1-4614-2406-2

Writing a comprehensive biography of Jules Henri Poincaré is a most difficult task. Two books that tackle the subject are Henri Poincaré: A Scientific Biography by Jeremy Gray and Henri Poincaré: Impatient Genius by Ferdinand Verhulst. Gray is a professor of the history of mathematics at the Open University based in the UK; Verhulst is a professor of mathematics at the University of Utrecht in the Netherlands. He notes in his preface—and I agree—that it is impossible to do justice to Poincaré in one monograph.

The “last of the universalists” is what Eric Bell called Poincaré in the 1937 history, Men of Mathematics. But Poincaré was not only one of the greatest mathematicians; he was a polymath. He contributed fundamental insights to mathematics, physics, astronomy, and philosophy. Poincaré was an essayist who made deep incursions into the psychology of creativity; he was fascinated by how ideas emerged and believed that the unconscious played a central role. He was also an influential intellectual. His book La science et l’hypothèse (Science and Hypothesis, 1904) was required reading for any cultured person, especially in France. Some of his books are still in print after 100 years.

What’s more, Poincaré was a member of the European establishment, a symbol of European culture and tradition. Twice, in 1886 and in 1900, he was president of the Mathematical Society of France. He was elected to the French Academy for his literary achievements. He became director of that preeminent French literary academy, and he also served as president of France’s Academy of Sciences—an unmatched combination. At one point he held five professorships, and he collected honorary degrees from the universities of Oxford and Cambridge, among others.

How can one book possibly do justice to a life full of such diverse excellence? Perhaps by answering two questions: What can we learn about Poincaré as a person, and how can we learn some of the technical details of what he did? The biographies by Gray and Verhulst attempt to tackle both. In that regard, the books are similar. They are also similar in that their first parts deal generally with Poincaré’s life, and then they address his technical work. But in their detailed construction and their focus, they are somewhat different.

As to the first question, Poincaré had a shining public persona, but it is hard to get insights into his personal life. Both books cover his work habits, which we know about because he told us in some of his writings and also because he consented to psychological examinations. He had no confidants, and he had perhaps three students in total; Louis Bachelier, seen now as the founder of financial mathematics, is the most famous.

As to the second question, both books cover a broad range of topics, including rotating fluid masses and a special emphasis on the three-body problem, a fascinating story with myriad political nuances. In general, both bios can be read at two technical levels: curious “amateur scientist” at one, technically proficient mathematician, physicist, or philosophy of science enthusiast at the other.

Stylistically I found Gray’s chapters to be more like essays that can be read independently of each other. At roughly 600 pages, Scientific Biography gets more into the complexity of the man, whereas Impatient Genius, nearly 60% shorter, has genealogical trees, mini-bios of relevant people, and anecdotes, and it presents examples in a somewhat distracting chapter-within-a-chapter construction.

Each book brings a viewpoint. In Gray’s book, Poincaré is “a man with a coherent view about the nature of knowledge,” the rare creative person who both trusts his intuition and can speak intelligently about it. In Verhulst’s, the theme is impatience. We are told that Poincaré was uninterested in correcting proofs, that he worked quickly, and that his manuscripts had hardly a line crossed out. Based on his schedule, however, he did not look like a man in a rush: He worked from 10 in the morning to 12 noon and from 5 to 7 in the evening. His mind was surely always on—he wrote on how ideas came to him in periods of idleness—but he made a point of saying he disconnected himself completely while on holidays.

Poincaré’s name has carried to our time. Both books get into what is now known as the Poincaré–Birkhoff theorem, a special case conjectured by Poincaré in 1912 from consideration of the three-body problem; George Birkhoff proved it in 1913. That one was easy. But the so-called Poincaré conjecture, also mentioned in both books, was for a long time one of the most important open questions in topology. It was finally proved by Grigori Perelman in 2003, roughly a century after Poincaré proposed it. Poincaré was recognized for contributions to the three-body problem and to our understanding of the stability of the solar system, work that was improperly recognized in his lifetime for its broader implications. Yet, his “failure to solve the [three-body] problem”—connected to the identification of homoclinic intersections—is why he is considered the father of chaos.

Although creativity is often associated with art, Poincaré was not artistic, at least in the conventional sense. On the entrance examination for the École Polytechnique, he scored a zero in drawing. I found it amazing that someone who developed the qualitative theory of differential equations and other concepts that are typically explained or aided by pictures could not draw.

There are more connections with art and aesthetics worth mentioning. Poincaré’s thinking was especially close to a surrealist’s. Psychologist Édouard Toulouse wrote that Poincaré’s thought “was spontaneous, little conscious, more like dreaming than rational, seeming most suited to works of pure imagination.” It is well documented that Poincaré’s Science and Hypothesis inspired Pablo Picasso and Marcel Duchamp, two of the most influential 20th-century artists.

The aesthetics connection is with elegant writing. Poincaré’s obituary in Nature said that “passion for scientific truth did not suffice for him, he loved literary beauty… . He knew that the French language is itself a country, and, against every perilous invasion, this soldier of sound speech stood firmly at the frontier.” Coming from an English publication, that was high praise indeed.

Julio M. Ottino is the Distinguished Robert R. McCormick Institute Professor and the Walter P. Murphy Professor of chemical and biological engineering at Northwestern University in Evanston, Illinois. His research includes theoretical and experimental connections among chaos, fluid mixing, and granular dynamics.