Two front-line AI systems wey dey work on their own don do wetin no human mathematician fit do for thirty years: dem don disprove the Exponential Time Hypothesis (ETH).
OpenAI talk say e research model find one natural-language disproof of ETH on 16 October, and dem formalise am the next day inside Lean, the machine proof checker. The 67-page manuscript carry "OpenAI" as the author.
Some hours before, Anthropic don publish e own 49-page paper, "A 2^o(n) Time Algorithm for 3-SAT", wey dem credit to "Claude, Anthropic". One internal Claude research model find the main algorithm on the same day, 16 October.
ETH, wey Russell Impagliazzo and Ramamohan Paturi propose around 1999, talk say no algorithm fit solve the Boolean satisfiability problem faster than exponential time. Na im be the foundation for hundreds of conditional hardness results for graph theory, databases, computational biology and computational geometry.
Both teams dey now claim say dem get one deterministic algorithm wey dey count satisfying assignments in subexponential time, with the same leading term for the exponent. If the claim stand, one load-bearing wall for complexity theory don fall.
The verification machine strong well well. Dem formalise the proof for Lean, wey dey check every step mechanically. Stefan Szeider for TU Wien, wey look the materials wey dem release, expect say e go survive scrutiny. The one wey shock pass: OpenAI set up independent review group wey include Impagliazzo and Paturi themselves - the people wey write the conjecture dey audit the refutation. Their open letter talk say e fit change one important part of computer science.
The limits matter as much as the result. P versus NP remain untouched. The new algorithm still dey superpolynomial, so no faster SAT solver go come out from am. Wetin change na the map of wetin dey theoretically possible, and who - or wetin - dey redraw am.
For business leaders, the signal no dey the mathematics. E dey the fact say AI don cross from writing text and code to producing original, machine-verified research. The belief say machines no fit do new science just collect heavy blow, and the capability frontier dey move faster than most planning cycles now.
Companies wey go treat AI as research partner, no be typing assistant, go set the pace for the next decade.
Think am mathematically. Engineer am well-well. Lead with strategy. Build am responsibly. Scale am globally. Use artificial intelligence create real business value.
