Ten advances in mathematics and theoretical computer science

In the past few days, AI has dropped two bombshells on the math world. First, Anthropic used Claude to discover cryptographic weaknesses, spending $100,000 and demanding 'no low-hanging fruit.' Then OpenAI unveiled an even more jaw-dropping result: using its internal next-gen model Astra, they solved ten problems that had seen no progress for at least a decade—each for less than $2,000 in compute cost.

It felt like Deep Blue versus Kasparov all over again, but this time the shaken community is mathematicians. OpenAI didn't disclose how many attempts didn't pan out, but the ten solved were formalized in Lean 4 with published papers and a model-generated 'reasoning walkthrough.' Decent transparency, but the prompts remain in the black box.

Why is this happening now?

AI's foray into math isn't new. From symbolic regression to automated theorem proving, it has been probing the edges. But previous efforts were mostly assistive: checking errors, searching existing theorems. This is different. Astra produced original, end-to-end proofs on handpicked hard problems that had stumped top human minds for years. The model's reasoning has clearly crossed a threshold into genuine research.

After earlier, less dramatic AI math results, mathematician Kirwin Hampshire penned 'The Dark Night of Mathematics,' describing a profound spiritual crisis. OpenAI's news will only deepen that sentiment. Yet Fields Medalist Terence Tao sees it otherwise. In an IEEE Spectrum interview, he envisions 'big mathematics'—large-scale, decentralized human-machine collaboration where humans handle creative directions and AI does the heavy technical lifting.

What actually changed?

The core revelation is that AI is no longer just retrieving known facts; it's beginning to 'discover.' And at a ridiculously low cost—$2,000 is negligible for a mathematical breakthrough. This suggests that large-scale, automated exploration of conjectures could soon be routine. A direction that took a PhD student years to vet might now yield initial results over a lunch break.

However, panic isn't unwarranted. If models can independently produce meaningful proofs, the mathematician's unique identity as a truth-discoverer is shaken. But looking closely at the published reasoning traces, the model's thinking is often counterintuitive or alien—like AlphaGo's moves no human would consider. This reveals AI is not mimicking human thought but developing an alternative form of intelligence.

How should we think and act?

For AI practitioners, this offers a valuable peek at frontier model capabilities, hinting that the next reasoning leap may be near. For math researchers, the pragmatic move is to treat such tools as part of the workflow: rapidly filter ideas, generate counterexamples, or provide inspiration at proving bottlenecks. Tao's 'big math' collaboration may be the best way to dissolve fear.

This also shatters a common illusion: many thought AI would first replace repetitive manual labor while creative jobs stayed safe. Instead, AI is cheaply assaulting the intellectual high ground we prized most. Not because it understands math, but because it has mastered a kind of 'reasoning' we haven't yet defined. That may be the real Deep Blue moment—not a machine beating humans, but a machine forcing us to redefine winning.