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C茅dric Villani: looks like he stepped out of a Neil Gaiman novel (Image: Paolo Verzone / Agence VU / Camera Press)

Birth of a Theorem: A mathematical adventure by Fields medallist C茅dric Villani is an exhilarating but exhausting journey as he pours you into his mind

I MET C茅dric Villani when he visited London in 2011, a year after he had won the Fields medal, the prestigious mathematical prize awarded to researchers under the age of 40.

As we chatted, I was charmed by the French mathematician鈥檚 rapid-fire way of speaking, a staccato rhythm that jumped from topic to topic without pausing for breath.

Reading his new book, Birth of a Theorem, I instantly recognised that same rhythm. The book covers the few years leading up to his Fields medal win, giving a flavour of the frantic thought processes behind the work that ultimately won him the prize.

The book opens like a film noir, as Villani sits sprawling in his office with intellectual partner Cl茅ment Mouhot. The pair are wrestling with a tricky case 鈥� not a murder, but the intricate properties of the Boltzmann equation, a statistical description of how particles in a gas behave.

In a tumble of dialogue they bat about phrases like 鈥渕odulo minimal regularity bounds鈥� and 鈥淢oser-style iteration scheme鈥� 鈥� essentially incomprehensible to the average reader, but they sweep you along for the ride.

Initially, it鈥檚 a refreshing alternative to most pop-maths books, which understandably make every effort to hold your hand as they guide you through tricky concepts. Instead, Villani pours you inside his mind and swirls you around, leaving you with nothing to hold on to and breathlessly wondering what you鈥檒l encounter next.

聯Villani pours you inside his mind, leaving you nothing to hold on to, wondering what you鈥檒l encounter聰

Villani鈥檚 diary of trips around the world to lecture and research is interspersed with verbatim emails between himself and Mouhot as they attack the problem of Landau damping, a nuance of how waves propagate through a Boltzmann-described gas. It鈥檚 interesting to see them at work, even firing off emails on Christmas day, but the text is littered with TeX, a markup language mathematicians use for typesetting equations, which makes it a bit like reading the code of an arcane computer program.

Reams of dense equations pasted in from various academic papers aren鈥檛 much better, since it鈥檚 impossible to follow the logic at work without a fairly high level of mathematical training. I ended up just idly flicking through them, wondering if Villani had ever heard Stephen Hawking鈥檚 quip from the intro of A Brief History of Time about every equation halving a book鈥檚 sales.

Passages about Villani鈥檚 personal life, like missing French bread and cheese during a stay at Princeton University, are more relatable, but nothing out of the ordinary. Extensive lists of his favourite music and lengthy descriptions of his dreams are as interesting as they sound.

Then there are quotes from poems, song lyrics and Neil Gaiman stories which hint at the varied sources of mathematical inspiration, but it鈥檚 never quite clear how they connect with Villani鈥檚 thinking about his research 鈥� though with his giant cravat and ever-present spider brooch, Villani himself could have stepped out of a Gaiman novel.

When I met Villani, he told me how most journalists would ask him to do quick mental arithmetic, as if this was all a professional mathematician really did all day. I鈥檇 hoped to get a deeper understanding of his work from reading the book, but perhaps that was never the goal.

As a note from the translator says, the book is meant to be an 鈥渋mprecise recollection鈥�, 鈥渁 work of literary imagination鈥� and not 鈥渁 scientific treatise鈥�, and it delivers exactly on this promise. I felt like a passenger inside Villani鈥檚 head, bombarded by his every thought, both waking and unconscious. Unfortunately, I tired of the ride before I reached the end.

This article appeared in print under the headline 鈥淏oltzmann and brio鈥�