Grant Sanderson: evaluation

Transcript context

…What is your recommendation to students who I’m sure email you this question all the time: “I was curious about doing mathematics. I’m really passionate about the subject, but seeing all the progress AIs are making, I don’t know if it makes sense for me to pursue this as a career.” This is relevant not only to people in mathematics, but to anyone noticing that their field is getting productivity gains from AI. Coding is very adjacent to this. What advice do you have for people? I wouldn’t trust any advice that I give. That’s how I’d couch it. But even pre-AI, it feels very important for any job you’re going to go into to really understand… If we’re talking about a job—not being a gentleman-scientist engaging with the math world or something—you should understand where the money is coming from, what value you’re actually adding, and the connection between those two. A surprisingly small amount of thought is put towards that, especially by students. They’re in this environment where they probably want to go into math because they’ve always been good at it. They’ve been rewarded in life for proceeding through the next hoop correctly. When they think they want to be a mathematician, it’s because they think it’s a way to continue engaging with that. They think, “Where do people get to do this?” rather than thinking, “What value am I adding to other people, and to what extent is that the reason a salary is flowing in my direction?” It’s actually quite different in different cases. In some cases, it’s a very prestigious mathematician, and their presence at a university lends a certain brand value, which is why the university wants them. In some cases, an NSF grant is given because of the public good belief we have around basic science. You’ve got an institution around that, and a whole bureaucracy acting as a proxy for what we think that public good is, with a whole song and dance around how to make them correctly predict that your progress will be in the spirit of that funding. Sometimes it’s just straight-up teaching. People like to send their kids to an institute that has experts teaching them. You provide brand value by being an expert, and direct value by being a teacher. Regardless of whether AIs are proving theorems or not, or whether we’re talking about 2016 or 2026, that is something not enough students thinking “I want to be a mathematician” consider. I think it’s worth thinking about. For me, I wasn’t necessarily thinking about it, and I stumbled into a career path where math exploration can be monetized as entertainment. I stumbled into that and I’m very grateful I did, but it was an accident. It wasn’t deliberate. I could have avoided relying on serendipity and done it a little bit more by design had I been thinking critically about it. To your question—if we have almost-automated theorem proving, and let’s say they’re also really good explainers so you even get the human understanding—I think a lot of the social role that mathematicians serve actually doesn’t change that much. As a public, we still feel there’s value to basic science, and we trust the judgment of mathematicians to determine where their time is best spent. The prestige comes from within that community. It’s other members saying that a result is really good, more than the grant writer really understanding algebraic number theory to understand it was a good result. There’s going to be an inner culture of what constitutes valuable contributions. eally good, more than the grant writer really understanding algebraic number theory to understand it was a good result. There’s going to be an inner culture of what constitutes valuable contributions. Maybe it shifts away from theorem proving and towards good definition writing. Maybe it’s that museum curator idea. But you’re going to have that same community as long as society as a whole is still valuing the premise of basic science. And if we’re in the abundance world that AI brings, there’s probably more funding in that direction in some sense. On the side of prestige to institutions for who their lecturers are, I actually think teaching is one of the most stable post-AGI jobs that there is, because it’s so relational. This is where parents want to spend their money if they have an abundance of wealth: on good teaching and good educating. It goes so far beyond explanations. Even if LLMs are good explainers, the thing that a teacher is doing is such a social, coaching, mentor-type thing that that’s probably one of the most stable careers that’s going to exist over the next fifty years. Insofar as a lot of mathematicians’ roles overlap with that, as the prospective student going into it, you could lean into that. I actually think a lot more students should think about and give credence to the idea of being just a math educator and the value that can serve towards the next generation. I’ll couch again that I don’t think I’m the one to say, “Here, prospective young mathematician, here’s how you should think about the future,” because I’m a YouTuber. I’m not in the institution that they’re thinking of going into, so I’m speaking as an outsider looking in. But it feels like generally good, universal advice: know where the money is coming from, know where you plug into that. And if you’re just asking those questions, you’re actually already steps ahead of all the other fledgling prospective mathematicians.…

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