Computer science no dey see dis kain month often. One of di beliefs wey hold am down don fall, and di people wey dey check di remainders na di same researchers wey build am.
On 16 October, one research model for OpenAI produce answer against di Exponential Time Hypothesis with normal words. Within one day, dem don copy di argument enter Lean, one proof checker wey dey verify every logical step by machine. Di 67-page manuscript put OpenAI itself as di author.
Anthropic, wey work without any coordination, don reach di same place hours before. Im 49-page paper, "A 2^o(n) Time Algorithm for 3-SAT", carry Claude name, and na one Claude research model find di main algorithm dat same day.
Di hypothesis start around 1999, when Russell Impagliazzo and Ramamohan Paturi argue say Boolean satisfiability no get any algorithm wey fast pass exponential time. Dat one idea dey quietly hold hundreds of conditional hardness results for graph theory, databases, computational biology and geometry.
Both groups now dey describe one deterministic method wey dey count satisfying assignments for subexponential time, and both land on di same leading term for di exponent. If reviewers confirm di work, one of di walls wey di field trust pass go turn out to get door.
Wetin dey give di claim weight no be di model dem family background, na di checking structure wey surround dem. Every inference pass through Lean. And di review panel wey OpenAI gather include Impagliazzo and Paturi themselves, wey now dey audit di collapse of dia own conjecture. Stefan Szeider of TU Wien don examine di public material and expect say e go survive close reading.
Caution still dey necessary. Di result no talk anything about P versus NP, and di new algorithm still dey run for superpolynomial time, so no practical solver go fast tomorrow morning. Wetin shift na di theoretical map, and who, person or system, dey redraw am.
For executives, di lesson dey far from complexity classes. Software wey recently dey summarise documents dey now generate original, machine-verified mathematics. Di frontier of wetin AI fit contribute to serious research dey move fast pass wetin most planning cycles assume.
Di organisations wey go learn to work beside such systems, instead of just giving dem typing work, na dem go set di pace of di decade wey dey come.
Think am mathematically. Engineer am well-well. Lead with strategy. Build am responsibly. Scale am globally. Use artificial intelligence create real business value.
