Latest / Minds, Bodies, and Terawatts / OpenAI's Unreleased Astra Cracked Ten Math Problems Nobody Had Moved in a Decade — for About $2,000 in Compute
Transcript
- 0:00[Host] This is Minds, Bodies, and Terawatts, the show where the compute bill is the headline. OpenAI published a paper on August first, Ten Advances in Mathematics and Theoretical Computer Science: ten problems cracked by an unreleased model called Astra, for about two thousand dollars in tokens at list prices.
- 0:18[Guest] Every one of those problems had sat with no progress for at least a decade.
- 0:24[Host] Labs claim things constantly. Why is this one different?
- 0:27[Guest] They attached the receipts. The model wrote each argument into Lean, a formal proof checker, and OpenAI posted the certificates on GitHub. You don't trust the press release, you run the checker.
- 0:39[Host] What did it actually crack? I want the list, not the adjectives. And I want to know whether a working mathematician would call any of it a big deal.
- 0:50[Guest] The paper leads with two. A disproof of a longstanding conjecture in operator algebras. And the first improvement since nineteen seventy-eight to the limit on how densely you can pack spheres in high dimensions.
- 1:03[Host] None of that touches my life. Does any of it?
- 1:07[Guest] One does, and not the way you'd think. There's a hardness result for the closest vector problem, the math under the post-quantum encryption your bank is migrating to now. It doesn't break that encryption. It's evidence the problem is as hard as we're betting it is.
- 1:24[Host] So it shored up the lock instead of picking it.
- 1:28[Guest] Right. And plenty stayed out of reach. OpenAI's Noam Brown posted on X, quote, sadly, no Millennium Prize problems, yet.
- 1:35[Host] Back to the price tag. What's not in it?
- 1:39[Guest] Everything that failed. Two thousand is the bill for the runs that worked. Brown said they tried other major problems without success, without pushing much compute at any one. A floor, not a price list.
- 1:52[Host] How are mathematicians taking this run of results?
- 1:55[Guest] Split. Timothy Gowers, a Fields medalist, wrote on his blog in July that having a model solve a problem he'd labored over felt, quote, very strange and not particularly pleasant.
- 2:06[Host] That's a mathematician describing grief.
- 2:08[Guest] It's the first time that field has had a price attached to the sentence I could have done that eventually. His wasn't one of the ten, but that kind of work now has a public bill.
- 2:22[Host] Not everyone took it that way.
- 2:24[Guest] Abhishek Saha at Queen Mary posted on X that in his area these models are already at least as good as a solid and indefatigable PhD student.
- 2:34[Host] Indefatigable is carrying that entire sentence.
- 2:36[Guest] Saha says he's the conductor now, not the whole orchestra. The essay The Solo Unicorn calls that the shape of expert work now: one human holding taste while the labor under it goes elastic. Gowers worries the literature outgrows the humans able to read it.
- 2:53[Host] Has the profession pushed back? If I'd spent thirty years building a career on being the person who could do this, I'd want someone writing the rules before a lab wrote them for me.
- 3:06[Guest] In June, the Leiden Declaration, endorsed by the International Mathematical Union and signed by Terence Tao. OpenAI's paper answers it: claiming human authorship for an AI-generated proof would misrepresent the work.
- 3:18[Host] Can I hire this thing? That's what decides whether this is news or a press cycle. If it's locked inside one lab, nothing about my Monday changes.
- 3:28[Guest] No. Astra has no release date, and nobody outside OpenAI has run it. The proofs are checkable by anyone. The machine that wrote them, by no one.
- 3:38[Host] So who gets nervous anyway? Not mathematicians. The person hearing this on a commute, wondering whether their own work is next.
- 3:46[Guest] Anyone whose work a computer can grade. Every one of these had a machine-checkable answer, so you search hard with a verifier attached and skip taste. Actuarial modeling, tax positions, structural load calculations.
- 3:58[Host] And on the other side of that line?
- 4:01[Guest] Deciding which problem is worth solving. Nothing verified that, and a human picked all ten.
- 4:07[Host] Unscarcity introduces Adewale, a Lagos coder whose client dropped him for an agent costing less than a Netflix subscription. Patrick Deglon calls the moment the cheapest reliable option stops being human the Substitution Threshold, and insists that's accounting, not science fiction. This week the accounting reached research mathematics before the product did.
- 4:27[Guest] For more on where the labor cliff reaches credentialed work, head to unscarcity dot ai. The book is on Amazon, the audiobook on Spotify. This has been Minds, Bodies, and Terawatts.