There's never been a better time to go into math

gist

Grant Sanderson answers a math PhD student who asked what to do tomorrow, arguing that this is the best time to enter and to fund math. He maps what mathematicians do, why math is valuable and where its money comes from, then asks what survives if machines get better at proofs, conjectures, theory and applications in turn. His answer is that teaching, problem-solving training and the joy of math hold up, while academic credit must change.

ideas

• Proof becomes raw data. Sanderson argues proofs have long stood in for understanding, and that machine proofs should be treated like numerical calculation, inputs to theory building rather than the goal.
• Training works like the gym. Machines lifting heavier weights does not remove the value of lifting, so the case for training human problem solvers holds at every stage of his thought experiment.
• Joy splits the community. He sees some mathematicians deflated by machine results and others, such as Constantin Kogler in an interview he shows, exhilarated to see answers to problems they care about.
• Most money follows teaching. Even if machines did everything better, he expects teaching to stay relational and funded, since learning is limited by motivation more than by clear explanation.
• Newcomers can shape the field. His closing advice is that because the community knows it must change, new entrants can influence what math becomes, and he would pursue visual exposition like his own channel.

quotes