Eric Fransen is a carpenter who has a woodworking studio in downtown Tulsa. At one point in his past, he was pursuing a doctorate in higher mathematics related to number theory and algebraic combinatorics. I’ve been working on a book related to mathematics (and psychedelics!) and was curious about what Fransen had to say about the elegant side of math that is so often missing from standard math education.
MICHAEL MASON: I look back on my math experience and I think, “I was taught arithmetic.” You know, computation. Rote, flat, dry, brute-force math. You know, not fun. Basically, teaching my brain how to act like a calculator. It was very unpleasant for me, and I don’t think I enjoyed math.
ERIC FRANSEN: Who enjoys that?
MASON: Yeah, who enjoys that?
FRANSEN: I’m a little OCD, so I think I might have enjoyed it a little too much.
MASON: But that’s not what math really is, right?
FRANSEN: No, I think math, especially higher-level math or abstract mathematics, pure math, whatever, is way more akin to art than anything. Most mathematicians I know are musicians and artists, and have very dynamic lives. They’re not this kind of stuffy person—that’s more of a computer scientist maybe, or engineer—but we should be careful about pigeonholing any of these people. I know a lot of engineers who are fabulous makers of things and so forth. But math and art I think have a lot to do with each other. Math is highly creative. When you’re doing pure math, there’s no more rote learning. People who are taking calculus I and II in college and even differential equations—these are courses that are very procedural, algorithmically driven. So you’re going to encounter a problem on a test and you’re going to be like, “Oh, that’s like the problem we did in class; I’m gonna do the same method and kind of just run through it.” So then when you start to take courses like abstract algebra or something. You have to prove things and develop a solid understanding of deductive reasoning.
MASON: Can you describe for me what you see when I say “a squared plus b squared equals c squared”?
FRANSEN: I see an invitation. I mean, Pythagoras comes to mind of course, but that’s just an invitation to what Fermat wrote down in his margin in the 1600s, I think. Fermat’s Last Theorem. I think of that as a Diophantine equation, after Diophantus, and that means: how do we find solutions to this equation where a, b, and c are particularly integers? So if you think about that, a squared plus b squared equals c squared is like a circle of radius c, in the plane, but so then you think of a circle that’s expanding. When does that circle, uh, when are all of those things integers? When do they go across integer coordinates? And the radius is an integer. These are very special things.
MASON: You’re saying that you’re seeing shapes, right?
FRANSEN: Yeah, I see shapes on that, and then a cubed plus b cubed equals c cubed (a3 + b3 = c3), you know, you up the dimensional level.
MASON: Right, and it starts to take on some wild properties.
FRANSEN: I think that’s a great way to gain intuition into a mathematical problem, and then you’ll go to the algebraic side and appeal to what we know about formal relationships, and we find all these kinds of patterns that we play out over here and then we go back to here and make statements, and this happens all the time. And it’s all through a little bridge that mathematicians love to call “isomorphism.”
MASON: What in your mind are some of the most beautiful or elegant visualizations you get that we wouldn’t suspect are there?
FRANSEN: Man, I’ve been chasing this one around forever. I mean, of course I got spun out on all the golden ratio stuff and the Fibonacci sequence. That’s been played out, I think. When I was in 10th grade I got into fractals, and it was early. I just found out about it from this college guy and I got this book on it and I ordered another books from Walden Books, special order, and I got my computer and I started writing programs. These programs would run for literally like three or four days, and I had to put a fan on it because it would overheat. And my mom sometimes would turn it off and I would be like, “What are you doing? I’m doing a thing!” So I finally get these beautiful pictures—this is 1987, and I’m 15 and really into this—then I take this file to this engineering company and print out full color iron-on transfers and make t-shirts for me and my buddies.
I was really into it. I actually took the fractal geometry and dynamic systems courses later on, and I think those are beautiful. There’s some amazing stuff there, even just the classic Mandelbrot set. From this really simple kind of property of iterative functions, meaning you take a functional value and plug it into itself over and over again, ad infinitum, and then we color the fractal pixels according to basically its escape velocity to infinity, or whether it has a finite limit point. So it’s almost like encoding limit point sets and condensation points and so forth. But, uh, man, it’s hard to beat those, and those were actually developed—this is kind of interesting—by Fatou and Julia, two French mathematicians, who came up with this in the 1890s, I believe. But the computer wasn’t there to really unlock the potential. So they started to consider these iterated functions in the simplest form, but we really almost needed the computer as kind of the key to open that door. So it was the notational kind of thing as I was talking about earlier. That’s beautiful.
Originally published in This Land: Winter 2016