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I work in theoretical computer science: a field that doesn’t itself win Fields Medals (at least not yet), but that has occasions to use parts of math that have won Fields Medals. Of course, the stuff we use cutting-edge math for might itself be dismissed as “ivory tower self-indulgence.” Except then the cryptographers building the successors to Bitcoin, or the big-data or machine-learning people, turn out to want the stuff we were talking about at conferences 15 years ago—and we discover to our surprise that, just as the mathematicians gave us a higher platform to stand on, so we seem to have built a higher platform for the practitioners. The long road from Hilbert to Gödel to Turing and von Neumann to Eckert and Mauchly to Gates and Jobs is still open for traffic today.
Yes, there’s plenty of math that strikes even me as boutique scholasticism: a way to signal the brilliance of the people doing it, by solving problems that require years just to understand their statements, and whose “motivations” are about 5,000 steps removed from anything Caplan or Bostrom would recognize as motivation. But where I part ways is that there’s also math that looked to me like boutique scholasticism, until Greg Kuperberg or Ketan Mulmuley or someone else finally managed to explain it to me, and I said: “ah, so that’s why Mumford or Connes or Witten cared so much about this. It seems … almost like an ordinary applied engineering question, albeit one from the year 2130 or something, being impatiently studied by people a few moves ahead of everyone else in humanity’s chess game against reality. It will be pretty sweet once the rest of the world catches up to this.
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