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Chasing a Conjecture: Inside the Mind of a Mathematician
A conjecture is like an unfulfilled fantasy in the world of pure mathematics where the most fantastic things happen routinely.
Proving a conjecture is like trying to make a fantasy come true, and it can consume a mathematician for years, just as the effort to produce a great work of fiction, music or art can take over the life of its creator.
This unusual, beguiling memoir is about such a journey. It begins with a child growing up in Mumbai, fascinated by mathematics, and ends with a man, just turned 40, winning a prestigious prize for proving, with a fellow-traveller, one of the most important conjectures in number theory – the branch of mathematics that studies whole numbers.
In this compelling account, Khare illuminates a quest that might seem impossibly esoteric to the outsider, but seen through his eyes, becomes palpably real and human. At its core, this is a book about the creative process; the mysterious ways by which ideas arise in the mind and take flight, amid many false starts and obstacles. While this undoubtedly requires solitude, a lot of the action also takes place in a delightfully collaborative atmosphere, across continents, which Khare evokes vividly.
Paraphrasing a famous mathematician, Khare says, ‘It is the person and not the method who solves a mathematical problem.’ So, appropriately, this book is also about a person, most poignantly about a man navigating the push and pull of creative ambition while trying to fulfil personal commitments such as wanting to be with his ill mother in Mumbai.
Proving a conjecture is like trying to make a fantasy come true, and it can consume a mathematician for years, just as the effort to produce a great work of fiction, music or art can take over the life of its creator.
This unusual, beguiling memoir is about such a journey. It begins with a child growing up in Mumbai, fascinated by mathematics, and ends with a man, just turned 40, winning a prestigious prize for proving, with a fellow-traveller, one of the most important conjectures in number theory – the branch of mathematics that studies whole numbers.
In this compelling account, Khare illuminates a quest that might seem impossibly esoteric to the outsider, but seen through his eyes, becomes palpably real and human. At its core, this is a book about the creative process; the mysterious ways by which ideas arise in the mind and take flight, amid many false starts and obstacles. While this undoubtedly requires solitude, a lot of the action also takes place in a delightfully collaborative atmosphere, across continents, which Khare evokes vividly.
Paraphrasing a famous mathematician, Khare says, ‘It is the person and not the method who solves a mathematical problem.’ So, appropriately, this book is also about a person, most poignantly about a man navigating the push and pull of creative ambition while trying to fulfil personal commitments such as wanting to be with his ill mother in Mumbai.
- GenresMathematics
320 pages, Kindle Edition
Published April 30, 2025
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Displaying 1 - 2 of 2 reviews
September 10, 2026
This book is a paean to one of the most original and striking mathematicians of our age—Jean-Pierre Serre. It covers the author's personal recollections and stories, from his childhood leading up to his proof of Serre's conjecture, in joint work with Jean-Pierre Wintenberger.
There is only one other book that, for me, matches the pace and intrigue of this one—*Birth of a Theorem* by Villani. While Villani's book is an admixture of technical mathematics (most of the equations require at least a graduate-level understanding of PDEs) and the lives of other mathematicians he encountered on the road to proving his Fields Medal-winning theorem (all told in Villani's peculiar style), Khare's book makes up for its lack of technical mathematics with a deeply human story. Though he discusses the core mathematics involved in his proof of the general Serre conjecture, he does so without introducing much formal technical jargon.
Instead, the book covers the whole gamut of his life: his childhood memories of his mathematical abilities, relationship with his parents, life as a struggling grad student, interludes about his wife and child, tortuous but tenacious route taken to proving the Level 1 case of Serre's conjecture, and, ultimately, the general proof of Serre's conjecture.
This book hooked me from page one. Highly recommended!
NB: For some reason this book was not available for sale outside India and I had to buy it online from an Indian publisher and ship it to me. This book deserves wider audience and global reach!
There is only one other book that, for me, matches the pace and intrigue of this one—*Birth of a Theorem* by Villani. While Villani's book is an admixture of technical mathematics (most of the equations require at least a graduate-level understanding of PDEs) and the lives of other mathematicians he encountered on the road to proving his Fields Medal-winning theorem (all told in Villani's peculiar style), Khare's book makes up for its lack of technical mathematics with a deeply human story. Though he discusses the core mathematics involved in his proof of the general Serre conjecture, he does so without introducing much formal technical jargon.
Instead, the book covers the whole gamut of his life: his childhood memories of his mathematical abilities, relationship with his parents, life as a struggling grad student, interludes about his wife and child, tortuous but tenacious route taken to proving the Level 1 case of Serre's conjecture, and, ultimately, the general proof of Serre's conjecture.
This book hooked me from page one. Highly recommended!
NB: For some reason this book was not available for sale outside India and I had to buy it online from an Indian publisher and ship it to me. This book deserves wider audience and global reach!
August 9, 2026
Prof. Khare shared in one of his lectures - "what matters is perseverance. One must keep on thinking about the problem one is interested about"
This is very well reflected in the book. Just like Prof. Andrew wiles, who kept on thinking about Fermat's last theorem for more than half a decade, Prof. Khare kept on pursuing the Serre's conjecture for almost a decade.
This entire book narrates the "Human" part of mathematics - the mental struggles, discussions, readings, thanking about the problem, trying to understand it better, collaborating and progressing step by step.
The book is totally non technical and anyone who is behind a good, big problem or anyone doing research may very well get connected to the narrations.
I personally liked the way the author used to take strolls or walks purposefully for getting time to think about the problem he was attacking.
This is very well reflected in the book. Just like Prof. Andrew wiles, who kept on thinking about Fermat's last theorem for more than half a decade, Prof. Khare kept on pursuing the Serre's conjecture for almost a decade.
This entire book narrates the "Human" part of mathematics - the mental struggles, discussions, readings, thanking about the problem, trying to understand it better, collaborating and progressing step by step.
The book is totally non technical and anyone who is behind a good, big problem or anyone doing research may very well get connected to the narrations.
I personally liked the way the author used to take strolls or walks purposefully for getting time to think about the problem he was attacking.
Displaying 1 - 2 of 2 reviews