Science Corner: Finding Your Way Through Math

Photo of fiddlehead fern, a naturally occurring Archimedes spiral

The math of spiral flora partly inspired the maze. (Photo by suju)

Topology is a standard topic in mathematics; topiary less so. That’s why I thought it was pretty cool to read about a mathematician-designed maze in celebration of the Abel Prize. At least, I like the idea in principle; I might feel differently after a couple of hours of wandering. Still, it is a nice little metaphor. Math, like many intellectual pursuits, involves twists and turns and blind alleys. Although unlike mazes, there are no deterministic algorithms guaranteed to get you out (eventually). So making progress and finding solutions can be much more satisfying than finding one’s way out of a maze.

Even though the maze was unrelated to the specific winner of the Abel Prize (since the whole thing had to be planned before a winner was chosen), I was still curious who won and for what. Turns out this year’s laureate is Robert Langlands for his work finding the connections between two different disciplines of math. Langlands noticed similarities and developed them into something even deeper than a metaphor, revealing ways in which solutions in one area could be applied to problems in the other and vice versa. This is very useful, because sometimes it is easier to solve a problem using one kind of math than another, even though technically it is the same problem no matter which way you solve it. It’s a little like how sometimes it is easier to solve a maze by starting at the exit.

I first learned about Robert Langlands and the Langlands Program to unify number theory and representation theory reading Edward Frenkel’s book Love and Math. Frenkel explores his own metaphorical connections with math and how he has come to be so passionate about it. In a way, Frenkel wants to do for math phobia what Tim Keller wants to do for atheism when Keller says “Tell me about the God you don’t believe in; maybe I don’t believe in that God either.” If you are turned off by math, Frenkel wants to help you discover that what you know as ‘math’ is likely just a small part, a part he probably also found boring and off-putting as well. Robert Langlands’ work is a central theme in Frenkel’s rhapsody; any work that inspired such beautiful and passionate words is no doubt worthy of a prize and a maze.

Still, as beautiful as number theory can be, abstract art is not for everyone. Fortunately, there are other, more practical approaches to spreading math enthusiasm are available. Tom Grosh brought this story to my attention: a college math curriculum focused on problem-solving and solutions relevant to everyday life situations for those who aren’t mathematicians or rocket scientists. For those who find math to be a bewildering maze, the evidence suggests this teaching approach might offer a new path forward. We’re not all going to be Abel Prize winners, but hopefully one way or another we can all find something that gives us confidence to deal with the quantitative side of life.

We’re chatting math and searches on the Peaceful Science forum in this week’s Faith across the Multiverse book club discussion. Feel free to join the conversation!

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Andy Walsh

Andy has worn many hats in his life. He knows this is a dreadfully clichéd notion, but since it is also literally true he uses it anyway. Among his current metaphorical hats: husband of one wife, father of two elementary school students, reader of science fiction and science fact, enthusiast of contemporary symphonic music, and chief science officer. Previous metaphorical hats include: comp bio postdoc, molecular biology grad student, InterVarsity chapter president (that one came with a literal hat), music store clerk, house painter, and mosquito trapper. Among his more unique literal hats: British bobby, captain's hats (of varying levels of authenticity) of several specific vessels, a deerstalker from 221B Baker St, and a railroad engineer's cap. His monthly Science in Review is drawn from his weekly Science Corner posts -- Wednesdays, 8am (Eastern) on the Emerging Scholars Network Blog. His book Faith across the Multiverse is available from Hendrickson.

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