Alex Kontorovich

Kontorovich argues, citing calculators and times tables, that students should master skills even when machines can perform them.

“just because a calculator can do it, you're going to be much better off if you can also do it yourself”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 3:24:59

Kontorovich reports that undergraduate grades have become bimodal, split between students who use AI to learn and those who use it to get answers.

“What we're seeing at the undergraduate level is a bimodal distribution”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 3:26:37

Kontorovich says the method behind the AI's quasi-RH proof fundamentally cannot reach the critical line, so the full Riemann hypothesis needs a new idea.

“that method sort of fundamentally can't get down to one half. So a new idea is needed”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 1:33:10

Kontorovich judges that the AI's quasi-Riemann hypothesis proof combined well-known techniques rather than introducing a genuinely new idea.

“at least in the case of quasi RH, I would not say it's a genuinely new idea. It's a beautiful combination of a lot of things that were very well known”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 44:09

Kontorovich argues that pure mathematics remains valuable even if machines can prove theorems, because its value lies in human understanding.

“I think the value of pure mathematics is that it lives in the heads of human beings”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 20:11

Kontorovich argues that AI is ushering mathematics into a golden age of knowledge rather than merely a crisis.

“I think we're entering, if we're not already, in a period of some kind of golden age of mathematical knowledge”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 10:25

Kontorovich says mathematicians already questioned this summer whether the Fields Medal might no longer be awarded, which he hopes is not the case.

“Already this summer, we were thinking, is this the last time that a Fields Medal is awarded? I sure hope not”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 3:18:13

Kontorovich reports that the Lean formalization of Fermat's Last Theorem involved only a few humans who mostly told the AI to continue.

“I believe it was two or three humans. And I believe most of their involvement was keep going”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 1:24:42

Kontorovich concludes after the Fermat's Last Theorem formalization that autoformalization of human-written proofs into Lean is essentially solved.

“can you get a sorry free proof of something that human beings have written down on paper? I think that problem is”

Lex Fridman Podcast: #503 – AI Crisis in Math: Navier-Stokes, Riemann Hypothesis & Complexity Theory (Oct 26, 2026) · Listen from 1:26:46