The Sound of Changing Ideas
That’s Alex Carney. He is warming up on his violin in an empty classroom in Mason Hall, where he comes some nights to practice. In addition to being a member of the University Philharmonia Orchestra, Alex is also the winner of a prestigious Marshall Scholarship. He’ll get to study for two years at Oxford and Cambridge in the United Kingdom. I asked Alex what the application process was like.
AC: So, it’s actually a pretty fast process. I eventually got invited to the national level interviews; that was November 17. I interviewed at like 11:30 in Chicago and got a phone call around 4 or 4:30 that afternoon and got the good news.
Certainly I’m very excited for the two programs I’ll be doing: the history of science next year and then math the following year. But even more than that I think it’s just the experience of going to a different country, being in a different education system, meeting all sorts of new people from such a wide range of backgrounds.
And so, sort of getting that new experience, hearing all sorts of new ideas and seeing how the ideas I have fit into that, and how they change.
The really eye-opening thing for me is when I tell people I’m working on a math research project, the first question isn’t, “Oh cool, what are you working on?”
It’s, “Math research, how do you even do that?”
You don’t really learn to think about math in that sense. But you should see that there are things even the best mathematicians in the world don’t know how to do yet. It’s still a wide open field, all kinds of opportunity for new ideas.
I do really like the research project I’m working on now. It’s essentially a very basic idea we’re looking at, which is the kind of problems I like. We’re really just looking at solving polynomial equations, which is something pretty much everyone did at some point, probably in early high school.
And so what we do is change the problem slightly. Instead of just looking for general solutions, only look for solutions in the rational numbers. So, basically that means solutions that are fractions. And what we’re mostly done proving at this point is that, actually, for rational polynomials and rational solutions, even if it’s an enormous polynomial, in most cases you won’t get any more than six solutions.
It’s a very basic thing, just solving polynomials, but you sort of add some little twist to it and get this beautiful theory out of it that’s completely different from what you might expect.