OpenAI Codex Discovers Counterexample Disproving Jacobian Conjecture
An OpenAI researcher says an internal Codex model, prompted without web search, independently arrived at essentially the same counterexample a mathematician had just found.
Entities: Aaron Lou, Levent
In a post on X, Aaron Lou said an internal version of OpenAI's Codex, working "without web search," independently discovered essentially the same counterexample that mathematician Levent Alpoge had just announced. Lou linked a PDF write-up of the model's strategy at aaronlou.com, while Sebastien Bubeck praised the reasoning and pointed readers to Lou's exact prompt. For now, the public record is still narrow: the researchers' own posts and Lou's linked write-up.
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yes GPT can do it too ;-). I highly recommend looking at Codex's write-up, its reasoning to find the counterexample is superb. So much for "the illusion of thinking" 😅. Also @aaron_lou's tweet includes the exact prompt he used on our internal Codex.
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/jacobian_counterexample_derivation.pdf https://twitter.com/__alpoge__/status/2079028340955197566
Interesting what’s special about that specific counterexample
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/jacobian_counterexample_derivation.pdf https://twitter.com/__alpoge__/status/2079028340955197566
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/jacobian_counterexample_derivation.pdf
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
this guy, though, this guy sure does ML
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/jacobian_counterexample_derivation.pdf https://twitter.com/__alpoge__/status/2079028340955197566
it's kinda crazy that, given how much openai spends, they don't regularly try disproving open conjectures?
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/jacobian_counterexample_derivation.pdf https://twitter.com/__alpoge__/status/2079028340955197566
This one has a prompt too!
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/jacobian_counterexample_derivation.pdf https://twitter.com/__alpoge__/status/2079028340955197566