BIRTH OF A THEOREM
A Mathematical Adventure
Cedric Villani
Translated by Malcolm De Bevoise
Random House India
260 pages; Rs 699
Why do pure mathematicians spend years contemplating intractable abstractions? This book offers a fascinating window into the thought processes of one mathematician, who is among the most unusual thinkers of our time.
Cedric Villani, Directeur, Institut Henri Poincare, has won the Fermat Prize, the Poincare Prize and the Fields Medal, which is the most prestigious of awards for a pure mathematician. Birth of a Theorem is about the highs and heartbreaks experienced while writing and rewriting the theorem that led to the Fields.
The theorem offers "proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation". In brief, it describes entropy processes in plasmas and hot gases. Mr Villani co-authored this with his student Clement Mouhot between 2008 and 2009. He moved between Lyon, Princeton and Paris, as he worked on it. Mr Mouhot was elsewhere, so most of the work was done by email across time zones.
One caveat: The paper, "On Landau Damping", is 180-odd pages in length. At least 20-odd pages of that, and another 10-odd pages of other formulae, are embedded in this book. These sections are typeset differently. A wonderful disclaimer says "The technical material, though not actually irrelevant is, in any case, inessential to the story". So, don't be intimidated. Treat the maths like calligraphy in a vaguely familiar language, and read past it.
The book is not about mathematics. It is about the inner life of one mathematician. Mr Villani's ability to describe the violent, very real emotions that abstractions can evoke is what illuminates this book. Mr Villani (he exhorts himself "Work, Cedric, Work!") lives, breathes and literally dreams maths. His moods swing from the euphoric to the despairing.
Mathematical results are couched in the language of logic. But the process of generating results is more akin to an act of artistic creation. Higher maths involves thinking around corners and trying all sorts of tricks. Nobody normally details the missteps, errors and flaws that occur on the way to writing a rigorously logical paper. Here, the inspirations and frustrations, the road blocks and reboots are drawn in dramatic detail.
At one stage, Mr Villani tells himself, "You are a father, Cedric, ritual suicide is not an option." We learn that Mr Mouhot was also about to quit and he had drafted an email saying "All is lost", before discovering a new line of thought. Withal, Mr Villani also describes the absolute joy when breakthroughs occurs and "a voice in the head" tells him what to do.
He has a transcendental enthusiasm for life in general. He is widely read and listens to a very wide range of music. He is fluent in Italian, English (spoken in a fluid Gallic accent), and gets by in Japanese. There are liberal quotes from favourite poets, an extract from Neil Gaiman, and a tribute to manga genius, Tezuka Osamu. He loves "the (musical) tigresses who give you goose bumps" like Danielle Messia, Catherine Ribeiro, Patti Smith. He thinks his search for new music is analogous to his search for new mathematical ideas.
There are lovely pen-portraits of mathematicians and scientists, (including a few obits of friends) accompanied by Claude Gondard's sketches. There is a poignant tribute to John Nash, his mathematical hero. When Mr Villani meets Nash in Princeton, Nash is mildly alarmed at Mr Villani's attire. Mr Villanni is too diffident to introduce himself.
Mr Villani is somewhat eccentric in his personal habits and he has been described as "the Lady Gaga of mathematics". He hitches rides from strangers and swims naked in the sea. He is usually clad in a three-piece suit with loud velvet cravats, a fob watch and large spider-brooches. He sleeps in 10-minute snatches on his office floor.
There is a hilarious description of breaking into his own common room at 2 am because he has run out of tea. There are lamentations about the unavailability of decent cheese and baguettes in New Jersey. There are funny glimpses of intersections between personal and professional lives. He narrates the made-up stories he tells his kids, and he jots down his dreams. While his wife (a biologist) is on a field-trip, he must interrupt work at 4 am to change his son who has just wet the bed.
The competitive nature underneath the veneer of the sophisticated flaneur comes through when he writes about his hungry focus on the Fields Medal. The Fields is awarded every four years to four mathematicians, who must be under 40 on January 1 of that year. He will be 41 by 2014 and ineligible. "Landau Damping" must produce a big result. When he receives the Fields, in Hyderabad, at the hands of Pratibha Patil, he settles down to celebrate with a cup of masala chai.
Ignore the mathematics (unless you have done post-doctorial research in this specific area). Read the book for its vignettes describing the meetings of many beautiful minds (some of which belong to dead people). Read it for its wonderful exposition of the character of a genius, who would by any standards, qualify as a "character".
