I'm in Middletown, CT, this evening having just given the mathematics department colloquium at Wesleyan University.
Wesleyan is a medium sized liberal arts college which supports a PhD-granting science and math program. My invitation was an unusual one. It said, "We'd like to hear about your research in geometry and we'd also like to hear about your ideas on sustainability education." So I tried to come up with a one-hour talk that would combine both themes into some kind of conceptual unity. In the end I just went with a one-word title: Growth.
I started off talking about the old chessboard legend: you know, the one where the king promises to reward the inventor of chess by granting him whatever he may desire, and the savvy inventor asks with pretended modesty for just one grain of rice on the first square of the chessboard, two on the second, four on the third, and so on. That and so on conceals the terrifying power of exponential growth which by the 64th square would demand a rice mountain five miles high - half a trillion tons of rice or about 1000 times the amount produced each year everywhere on earth.
I went on to consider the superficial geometry of exponential growth: the fact that there is no "deep inside" an exponentially growing system, it is all "on the surface", and the expression of this through uniformly bounded homology and Ponzi schemes. I talked about some research mathematics here, with a bit of discussion of the index theorems that showed up in my thesis. But then I veered back to talk about growth in the usual "economic" sense, and my perception that mathematical educators owe it to our students to give them the conceptual tools to consider whether or in what sense growth can go on for ever, and what (if anything) might come afterwards.
I've never tried to give a talk like this before. I felt that it went pretty well, and I made some good connections; I need to let it settle though. Meanwhile here is a link to the slides. And if any other math department would like to invite me to give some version of this talk, I'm happy to do so!
Photo of Wesleyan University by Flickr user AmandaB3, licensed under Creative Commons
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