Jeremy Avigad is a professor at the Department of Philosophy and the Department of Mathematical Sciences at Carnegie Mellon University. He received his B.A. from Harvard University and his Ph.D. from the University of California, Berkeley. His research focus is mathematical logic and proof theory. Notably, Avigad has helped develop the online theorem prover Lean which provides users with tools and methods to create thorough and fully specified axiomatic proofs. Overall, his work attempts to further our understanding of the relationship between mathematics and philosophy.
Please describe your specific field of study and what it is that sparked your interest.
My field is mathematical logic, understood, roughly, as the mathematical study of the principles of mathematical reasoning itself. This circularity makes it an unusual branch of mathematics. It is also unusual because of the subject matter: while most mathematicians study number systems, algebraic structures, abstract spaces, and so on, logicians are also interested in linguistic objects likes terms, formulas, expressions, and programs.
I like the philosophical flavor of the subject, since modeling mathematical reasoning in mathematical terms provides interesting insights into what the subject is all about. And since computer scientists also often have to reason about terms, formulas, expressions, and programs, logic provides both a foundation for computer science and means for computational implementation of mathematics.
What events in your life have contributed to where you are today with your career? How would you describe your interaction with math during high school?
I grew up interested in mathematics, surrounded by the rise of personal computers like the TRS-80, the original Apple computer, and the original IBM-PC. I also grew up reading books like Isaac Asimov’s “Asimov on Numbers,” Douglas Hofstadter’s “Gödel, Escher, Bach”, and “The Mathematical Experience” by Phillip J. Davis and Reuben Hersh. These inspired me to think about mathematics and how it works.
In your list of papers, you have collaborated many mathematicians across multiple institutions. How do these groups form and what are particular moments from these collaborations that you cherish
I interact not only with logicians but also nonlogicians in mathematics, computer science, and philosophy. I am particularly proud of this fact. It is never easy to leave your comfort zone and engage with someone else on their own turf. People in different communities have different ways of approaching problems and talking about them, and they have different kinds of expertise. But I have found that if you are willing to listen and be respectful in situations where others know much more than you, interesting things often come about.
What is it like to attend a mathematics conference?
Of course, it is a lot of fun. It is nice to be a part of a community of people interested in similar things. All the information can be overwhelming at times, but the interactions can be transformative.
What advice would you offer to youth today looking into pursuing mathematics?
Don’t be afraid to stray outside your comfort zone. Interesting things happen when you talk to others about what you are doing and what they are doing, even (or especially) when on the surface your interests seem far apart.