Office Hours with… Sam Raskin

There is something magical that happens when grown-ups share books and puzzles with the children in their lives — and for Sam Raskin, something mathematical.

Raskin, the James E. English Professor of Mathematics in Yale’s Faculty of Arts and Sciences, fondly remembers the way his grandmother, who has a deep curiosity about mathematics and its structures, introduced him to the playful side of math when he was a kid.

It’s something Raskin came to appreciate as well. Today he is a leading figure in introducing new geometric methods for studying exotic algebras and mathematical constructs.

Specifically, his research focuses on what is known as the geometric Langlands program, part of a sprawling, grand tapestry of conjectures and studies suggested by Canadian mathematician Robert Langlands (who got his Ph.D. from Yale in 1960 and was a member of the Yale faculty from 1967 to 1972). The Langlands program suggests profound connections between many disparate threads of mathematics, providing a unified framework for mathematicians to think about a range of seemingly unrelated problems.

In the latest edition of “Office Hours,” a Q&A series that introduces new Yale faculty members to the broader community, Raskin discusses math, the value of diverse approaches to problem solving, and the joy of reading to children.

Were you always enamored with math?

Sam Raskin: I remember math was my favorite subject in school. It just always made my brain feel good. There’s something very focusing and meditative about doing math, something that can be emotionally calming. Part of my interest as a kid was that my grandmother really had a big interest in mathematics and still does. She’d always bring a number puzzle when she would visit and want to discuss it.

One Thanksgiving Day at my grandmother’s house, I came across a book about the solution of Fermat’s last theorem. It had all these interviews with people who were mathematicians — some are people I’ve now met in my life – and it was the first time I realized it was possible to be a mathematician. That hadn’t made sense to me before. What would a mathematician do? Just spend all day multiplying numbers together?

That was the moment when I thought, this is what I want to do.

How would you describe your work to someone who isn’t a mathematician?

Raskin: The research I do is in something called the Langlands program. The overall story there is that in the 18^th century mathematicians started discovering weird coincidences and weird formulae that struck people at the time as odd, even though they were eventually verified through mathematical proof. These coincidences became known as reciprocity laws.

You would count solutions to a family of equations labeled by different prime numbers and there would be some type of deep relationship between the numbers that showed up. It was surprising to people, and it developed into a whole industry of sorts within mathematics.

Then in the 1960s, Robert Langlands had some insights that took it much further — ideas that there were fundamental relationships between different kinds of mathematical objects, relationships of a very deep nature. In my research, I use algebraic geometry to try and understand these relationships.

Langlands spent time at Yale as student and faculty member. Is that meaningful to you as you begin your time here?

Raskin: It’s definitely something I was aware of. I remember looking at some old notes and books that Langlands put out in the late ’60s and early ’70s and seeing he was at Yale. The Department of Mathematics here has a lot of history and amazing mathematicians who have been here and who are here now. It’s meaningful to be in a place with such a storied past.

How would you describe your approach to mathematics?

Raskin: In a lot of ways, I wish I was more disciplined. I find I beat my head against the wall of math 364 days a year, and then I have one day with a good idea that I spend a bunch of time developing. One of the things I try to do is give myself lots of time to pursue things that maybe aren’t going to work out.

I think the field benefits the most when we have lots of different people who think in lots of different ways. When I spend time really trying to find a common language with someone who thinks differently than I do, I find it’s always extremely beneficial.

What do you like to do when you’re not teaching or doing research?

Raskin: I have two children at home, a 1-year-old daughter and a 7-year-old son, and I love reading to them and with them. There’s something about reading children’s literature that is so enjoyable. And I love biking. My son and I just did our first ride where he could ride his bike beside me, rather than me running alongside.