Photo Credit: Allie Ippolito 

In 2016, at the Fields Medal Symposium held in honour of Manjul Bhargava, a 28-year-old mathematician named Jacob Tsimerman took the stage to talk about bounding 2-torsion in class groups of number fields. He was, by a wide margin, the youngest member of the Symposium's organizing committee — a detail that made more sense once you knew he was already a professor at the University of Toronto, having won the SASTRA Ramanujan Prize the year before for his work on the André-Oort conjecture. The occasion itself carried a celebratory charge. Bhargava was, at the time, the only Canadian to win a Fields Medal.

A decade later, Tsimerman is the one being celebrated. This morning in Philadelphia, he became a Fields Medallist himself, recognized “[f]or his contribution in the recasting of o-minimality as a fundamental method of arithmetic and complex algebraic geometry, and his role in the proof of many central conjectures including Griffiths' conjecture on the algebraicity of images of the period maps, and the Andre-Oort conjecture for Siegel modular varieties.”

The proof, completed in 2021 with Jonathan Pila and Ananth Shankar, settles the full André-Oort conjecture, a question that had stood in one form or another for nearly 40 years. In its broadest terms, Shimura varieties — the geometric spaces at the centre of much of modern number theory — contain scattered “special points” with unusually rich algebraic structure. André-Oort asks whether every large enough cluster of these points has to sit inside a smaller, explainable algebraic subvariety, and that these apparent coincidences are never really coincidences.

Tsimerman had been chipping away at the problem since graduate school – first with Pila, borrowing tools from model theory to play with the geometry involved, and later, with Shankar, to close the remaining arithmetic gap. Their result didn't just answer the original question; it created an entire toolkit that mathematicians are now using on a wider, still-open family of conjectures in the same area.

Pila could not be more delighted with today’s news. “It has been truly a privilege to work with Jacob for the past 15 years, but at the same time immensely enjoyable. We teamed up shortly after Jacob completed his PhD, brought together by Peter [Sarnak], who supervised both our PhDs at different times. We brought complementary expertise, which we combined to work intensively on the André-Oort conjecture. Along the way we also worked on various offshoot problems concerning functional transcendence properties and cases of a more general Zilber-Pink conjecture, which remains very much open. The Thematic Program we co-organized at Fields [in 2017] was in the middle of that period, and we worked hard on various aspects throughout that time,” he writes.

Sarnak is the mathematical matchmaker whose insight brought the pair together. By the time Sarnak became Tsimerman’s doctoral advisor, he could see a promising future ahead. “Tsimerman's superb mathematical talent was clear to me soon after he arrived in Princeton as a graduate student. It proved productive to challenge him directly with some well-known problems that had resisted progress. Since then, and in joint works with different authors, he has resolved a series of longstanding central problems in Diophantine Analysis and in Algebraic Geometry. He works very well collaboratively and is generous with his ideas. He is a problem solver and also a theory builder of the very highest calibre,” says Sarnak, who has now supervised both Canadian Fields Medallists (the other being Bhargava). (We are informally nominating Sarnak for honourary Canadian citizenship.)

There are some Fields Medals that come as a surprise. Unusual paths, like June Huh’s, that may have been difficult to pinpoint at the start. Tsimerman’s trajectory is not among them. Born in Kazan, Russia in 1988, his family moved to Israel and then, in 1996, to Toronto. He represented Canada twice at the International Mathematical Olympiad (in 2003 and 2004), winning gold both times and posting a perfect score the second year. He started at the University of Toronto when he was only 16 years old, and had already graduated two years later, at an age when most of his peers were just starting their first year of studies.

Tsimerman’s first recorded visit to the Fields Institute was in 2013, when he was doing postdoctoral work at Harvard. By 2014, he was back in Toronto to teach full-time and is now a Full Professor of Mathematics. Since his return, he has become an indispensable fixture at Fields, organizing multiple programs, teaching graduate courses and participating frequently in our workshops, lectures and special events.

Kumar Murty, who served as Fields Director from 2019-2024, was Chair of the University of Toronto Mathematics Department when the possibility of recruiting Tsimerman for a faculty position appeared. Murty had met Tsimerman at Princeton and was impressed by his insightful questions. He immediately recognized what a faculty member of Tsimerman’s talents would bring to the school, the city and the country. “Of course we moved right away and I went to see Meric Gertler who at that time was Dean of the Faculty of Arts and Science. He was very supportive and we were able to quickly put together an offer. I remember telling Meric that Jacob would be our first Fields Medallist.”

Today, Murty is too humble to brag about his predictive capabilities, preferring to focus on Tsimerman’s excellent intuitions instead: “Many years later, I find Jacob has the same youthful excitement and passion when discussing mathematics, especially his favourite problems in arithmetic geometry. We were fortunate to be able to attract him back to Toronto, both at the university and at the Fields Institute. His Thematic Program on Unlikely Intersections, Heights, and Efficient Congruencing was a huge success! He is very generous with his time and his ideas, and I think many students and faculty have benefited from that. It’s an absolute delight to see his work being recognized with the Fields Medal. It's great for him, it's great for Toronto, and it’s great for Canada!"

 Photo Credit: Allie Ippolito 

Current Fields Director, Deirdre Haskell, who appeared on stage in Philadelphia for the announcement, is just as taken with his mathematics, but also notes how down-to-earth and humble he has always been: “Jacob was very young when he organized his first Thematic Program with us. It’s always exciting when different areas of mathematics come together, and the model theorists were all thrilled when the concept of o-minimality, which we had developed for very different reasons, started to be applied to outstanding conjectures in number theory and algebraic geometry,” she recalls.

“I remember later on Jacob giving a seminar at McMaster. We wanted to take him to lunch beforehand, but he found his own way to Hamilton, and showed up just before the seminar time, with great surprise that we might have helped him out!”

Jacob Tsimerman chats with a colleague during the 2024 Forward From the Fields Medal Symposium

More recently, Tsimerman spoke at the 2024 Forward From the Fields Medal Symposium to recognize the centenary of the 1924 ICM that John Charles Fields brought to Toronto. Over the past few years, he has played an important role in the ongoing Geometry and Model Theory Seminar organized by Patrick Speissegger.

Before the end of the decade, there be another Fields Medal Symposium on these very problems, this time with Tsimerman delivering the Public Opening. If the ICM watch party this morning – full of Tsimerman’s friends, colleagues and students – is any predictor, we will need to hire a few mathematical physicists to contain all the celebratory energy bursting from the building.