You titled your talk, Mathematics is Truth: Or is it? Why did you choose that title?
I do believe mathematics is truth. It’s the ultimate truth. I guess at the very beginning, it’s that mathematics is the ultimate description of reality.
What is math’s status as a discipline?
I think most people view mathematics as useful, but they don’t realize it’s a living subject. Many years ago, 25 –30 years ago, was the first time mathematicians ever had lobbyists in Washington. This lobbyist was a very good mathematician. He said there was no question: everyone he talked to in Washington believed math was over. They had no clue. No, math is still ongoing, still living, still breathing. In fact, we’re in one of the greatest stages of math ever.
How does math tie into the liberal arts?
I think that the point of studying the liberal arts, the reason why people take different kinds of subjects, is that they’re always after truth. But that’s a very tricky and elusive notion. Different disciplines have different standards of what is a correct statement. Mathematics is the quintessential subject driven by methodology. If it’s an area of math, then you can do a proof of it. Sadly, with most things of interest, you can’t do a proof. It’s just too complicated. So a historian, if he had the same standards as a mathematician, tcould never say anything. So instead, when you take courses in history, you start learning what’s a reasonable historical argument. Is it absolute truth? Absolutely not, no one would think so. Economics has its theory, psychology has its theory. Math is the most rigorous discipline, and has its own standard. That’s what makes a good part of the liberal arts. It should be the model for all thinking, but most of the world is just too complicated.
What is it about math that interests you, and how did you get involved in teaching?
I still think of myself primarily as a mathematician, not a teacher. I’ve always just loved math. When I was younger in early college, thinking about what to do with my life, I started believing, hoping that math would be it. And I began to recognize in the coursework an interconnection, and it’s paid off incredibly.
Do you have a favorite mathematician (historical or current)?
I don’t know about a single favorite. If you list the ones who have really shifted and changed how people do mathematics, the top one was Riemann in the mid 1800s. It seems that he brought in a much more conceptual way of approaching mathematics. Currently there’s Grothendieck, who fundamentally changed how people view mathematics. Again, a very deep abstraction, a very beautiful way of doing math. Then there are some great ones like Terence Tao. He’s just phenomenal.
What are the benefits to studying advanced mathematics, especially for someone who is not planning on going into teaching or engineering?
If math is the ultimate structure of reality, I think that’s kind of important, no matter what. On a more practical level, I find great hints of joy. In fact, one of the things I try to get students to do is have those moments of insight when the world just falls into place. It’s joyful when that happens, which is a purely hedonistic reason. Math can actually be useful in the real world too, which is an extra benefit.