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AI Proves Theorems

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cryptobriefing.com

OpenAI says its $10 million Navier-Stokes proof could cost $100,000 next year

OpenAI official logo (public domain, Wikimedia Commons) — CryptoBriefing brand treatment The company expects the price of AI-driven frontier math to fall sharply, even as mathematicians question who deserves credit OpenAI says a Navier-Stokes project like the one it just ran could cost about $100,000 next year. The first attempt cost roughly $10 million. That is a drop of about 99% in a single year, if the forecast holds. On September 8, 2026, OpenAI announced results from an internal AI system. The system reportedly outperformed GPT-6 Astra, the company’s flagship model. OpenAI says the system produced an analytical proof addressing the Navier-Stokes existence and smoothness problem. It also produced a formalization of that proof in Lean, a software tool that checks mathematical proofs step by step. The Navier-Stokes problem is one of the Millennium Prize Problems set by the Clay…

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Famous Problems & Conjectures

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qz.com

10 unsolved problems in computer science, explained

These 10 unsolved problems in computer science, from P versus NP to quantum advantage, bear on cryptography, algorithm design and computing's limits — here is what each asks That distinction sounds abstract, but it decides what is feasible. A problem solvable in polynomial time can usually be handled at scale. A problem that appears to need exponential time can stall the fastest hardware on inputs of modest size. Each extra element in the input can double the work. Security systems and logistics software both depend on which side of that line certain problems fall. P versus NP asks whether every problem whose solution a computer can check quickly can also be solved quickly. No one has proved the answer either way. The two labels name classes of problems. P covers problems a computer can solve in polynomial time. NP covers problems where a proposed answer can be verified in polynomial…

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Proof Assistants & Formal Math

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dev.to

The Credence Good of Inference Compute

In microeconomics, a credence good is any purchase where the consumer cannot assess the marginal utility of the service even after paying for it. The classic textbook example is an automotive repair shop. If a mechanic replaces an alternator and the car starts, you know the outcome is acceptable. You have no way of knowing whether the car actually required a new alternator or a loose ground wire tightened with a quarter turn of a wrench. The information asymmetry belongs entirely to the seller. Over the past year, frontier foundation model providers have packaged inference compute into the exact same economic structure. Instead of selling raw text completion, labs offer reasoning models equipped with an ordinal dial: low, medium, high, and maximum effort. The marketing premise sounds straightforward. If a problem is easy, the system answers quickly. If a problem requires multi-step…

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Math Test Scores

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upworthy.com

A ‘simple’ math problem has divided people 50/50. It’s a great metaphor for social division.

Half say the answer is 9, half insist it’s 1. What if they’re both right? In theory, a math problem involving four single digits and basic arithmetic—no algebraic functions, no variables, no exponents—should be easy for any high school graduate to solve. So why are people split right down the middle on the answer to this seemingly simple problem? You may have gotten 9. You may have gotten 1. If you take this poll shared by World of Statistics on X, you’ll see how others answered. As of this article’s writing, over 1.3 million people have voted, and the split is nearly 50/50. 6 ÷ 2 (1 + 2) =— World of Statistics (@stats_feed) October 26, 2026 6 ÷ 2 (1 + 2) =— World of Statistics (@stats_feed) October 26, 2026 We’ll get into the actual math problem and why people are so split on the solution shortly. But to me, the debates surrounding it represent something bigger. Nearly every element of…

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