Using AI and formal reasoning to break hard math problems
Joined May 2025
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Excited to share a new podcast, this time with Fabrizio Montesi, Professor of Computer Science at SDU and lead maintainer of CSLib (Lean library for CS)
We kept landing on a question most AI code talk skips: we can prove software correct, but correct against what?
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Why are formal languages not used as programming languages?
Most were built only for mathematics. Lean lets you write real code, but its compiler assumes a garbage collector, threads, and an operating system underneath.
So I rewrote it.
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Why this matters for AI:
Today, people prompt Claude Code. It needs supervision, fakes tests to pass, bugs slip through.
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In Lean, you only write the theorems. The AI writes the code and the proofs. Full autonomy, no risk.
Code becomes like assembly. No human review needed.
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Excited to share a new podcast, this time with Fabrizio Montesi, Professor of Computer Science at SDU and lead maintainer of CSLib (Lean library for CS)
We kept landing on a question most AI code talk skips: we can prove software correct, but correct against what?
Thread👇
2
4
795
And the closing line that’s making me dust off my old maths books :)
"We're all going to be math engineers. The math is correct, but what is the math saying? That's going to be the crux of the problem."
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Just released a podcast with @AlexKontorovich, Distinguished Professor of Maths at Rutgers. He has also been a forward looking thinker on how mathematics will evolve alongside AI. He has shared his forklift analogy for AI & learning here before, but it’s too good to not reshare!
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On the maths community and AI startups:
"We're very non-confrontational as a culture. If someone is claiming things and you don't agree with them, you just don't invite them to your next conference. What we as mathematicians need to do is not just play defence."
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And on what's coming:
"There's plenty I can say AI can't do well now. But something they'll never be able to do, I always come up short. I'm not able to articulate what I do that these systems won't ever be able to do."
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