The mathematician Terry Tao writes and speaks a lot about math and AI. Recently, in response to AI encroachment into mathematics, Tao has been quoted as saying something akin to "the age of heroes is over". This refers to the long history of mathematicians developing a mathematical conjecture that goes unproven, sometimes for centuries, followed by the appearance of a "hero" who comes up with a brilliant idea and proves the conjecture, e.g. Andrew Wiles and Fermat's Last theorem. Or, a mathematician building a whole area of fantastically useful mathematics that changes the way humanity thinks, e.g. Isaac Newton and calculus.
Wiles, Newton and others are the heroes to which Tao refers. And, by saying that the age of heroes is over, he is saying that AI will now solve those big open questions and build those big new beautiful areas of math, possibly with a mathematician in attendance, but not as the intellectual driver of proof.
This view feels right to me. The mathematician's new role is to be the guide for the AI, to direct attention, to interpret results, and to identify the empty spaces. The role of proof is now delegated to machines. (For a really rich discussion of this, see the video There's never been a better time to go into math by Grant Sanderson of 3Blue1Brown.)
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Why is this even important? After all what does a mathematician even do?
For the overwhelming majority of people, their exposure to math ends when their schooling ends. Even while they're in school, they only learn about settled mathematics. As a result, the idea that there can be "new" mathematics is almost nonsensical. To most people, math is part of the air they breathe and the earth they walk. It's almost as if God created math during the first week, maybe on the 4th or 5th day and since then, there math has stood, unchanging. But, nothing could be further from the truth.
Math has developed over time. For example, we started with counting numbers: 1, 2, 3, 4... Then, we added fractions, negative numbers, irrational numbers. And, don't even get me started on the invention of zero--possibly the greatest intellectual advancement in human history. Before 300-400 BC, there was no zero.
Before 200 BC there were no negative numbers.
Before 1650 or so there was no calculus. Harvard predates calculus. At some point, Harvard faculty had to decide whether to start teaching this "newfangled calculus stuff".
As math developed, some mathematicians earned a kind of immortality for their contributions to the field. Euclid for geometry, Pythagoras, Descartes, Newton, Leibniz, Riemann etc. These are the "heroes" to which Tao refers. This is the group of people that Tao thinks has stopped growing because of AI.
I'm still thinking this through. But, I know it's critical, for the sake of my students, to figure out what the role of a mathematician looks like moving forward. I need to have a coherent idea of this if I'm going to continue to motivate and teach the next generation of mathematicians.
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