Impressive breakthroughs by U of T's youngest faculty member in math, Jacob Tsimerman

February 10, 2016 by Peter McMahon - A&S News

"I wish I had Spider-Man’s powers,” said U of T number theory prodigy and assistant professor Jacob Tsimerman. “All that flipping around looks pretty fun,” he added, when asked about getting in the mindset to solve complex theorems.

Whether it’s dominating the International Math Olympiad or proving part of a decades-old conjecture, Tsimerman — a longtime Torontonian and U of T alum — stays grounded thumbing through comic books, practicing Judo and playing guitar (everything from classical to the Beatles to modern movie soundtracks.)

Born in Russia in 1988, Tsimerman moved with his family to Toronto in 1996, receiving his bachelor’s degree in math at U of T just 10 years later. He received his doctorate from Princeton in 2011 and did post-doctoral work at Harvard before being awarded a Sloan fellowship and starting as an assistant professor at U of T in 2014.

No magic formula

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With a laid-back intensity (on top of all his other achievements and leisure pursuits, he’s also learning to tango) Tsimerman insists he has no single formula for success, save for hard-work, tempered with ample play.

“I might be at a bar taking a shot and something will occur to me — but it’s not because I’m Matt Damon in Good Will Hunting,” he said, laughing at the absurdity of how people often perceive math discoveries. “It’s because I’ve been thinking about it for months or years and that just happened to be when I figured it out.”

Infinite ‘nesting dolls’ metaphor for complex math theorem

Perhaps Tsimerman’s most amazing breakthrough is proving the André-Oort conjecture, which involves collections of multi-structured points along an algebraic curve — like a line of wooden Russian nesting dolls with potentially infinite numbers of dolls within.

These points — called CM Points — are at the heart of the conjecture, which attempts to classify different types of Shimura varieties. Shimura varieties are highly symmetric objects which encode information about the arithmetic of integers — whole numbers with no fractions.

According to the André-Oort conjecture, every algebraic variety that has yet more Shimura varieties within is itself a Shimura sub-variety.

Tsimerman has proven a particular case of this long-pondered conjecture by finding a way to differentiate Shimura varieties from the rest, using the CM points contained within them.

Beauty in numbers

“It’s a very elegant way of looking at a fairly complex theorem,” said Tsimerman. “We’re very good at guessing at things — there are lots of mathematical statements we suspect are true. But few we can prove.”

He said such specific breakthroughs can actually have wider-reaching benefits: “If you can prove one statement, the tools you’ve used are almost more important than the proof, because you can often use them to prove other theorems.”

While such breakthroughs in analytic number theory themselves are highly academic, understanding number theory overall is critical to being able to make advances in areas such as cryptography, which can benefit everything from network security to the next generation of supercomputers.

A rising mathematics superstar

In 2015, Tsimerman became the first Canadian to win the prestigious SASTRA Ramanujan Prize, awarded each year to a young mathematician 32-or-under who makes an outstanding contribution to mathematical analysis, number theory, infinite series, or continued fractions.

The $10,000 prize was his first major international award, but peers and mentors are already speculating Tsimerman may even win a Fields Medal — often described as the “mathematician’s Nobel Prize” — if he continues on his current trajectory.

While he appreciates the praise, Tsimerman has a much more specific legacy he’d like to leave.

“I’d like to come up with some sort of technique or tool that changes the world’s perspective,” he said, “coming up with an idea so powerful that it becomes standard usage. That’d be pretty cool.”