this post was submitted on 20 Jul 2026
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Among the three big results I've looked at (unit distance problem, cycle double cover, Jacobian), two were counterexamples and one of them had a short 3 page proof using ideas from the 1970s. The Jacobian conjecture is an extreme case because a single counterexample is enough (for unit distance, you technically need a family of counterexamples), and it is easy to check with very basic computations. It is telling that all of these announcements came from OpenAI or Anthropic employees, who presumably have unlimited access to their AI. Nobody really knows how many resources they spent on this, or what else they tried. Nobody really seems to care about this question, either.
I think there is a phenomenon where supposedly hard questions are much easier than expected, because by chance nobody found the right approach for a while, and eventually it becomes famous as a "hard problem" which makes nobody want to attempt it.
What I'm more worried about is many people starting to use AI to try and prove small lemmas for them in their projects. Of course, a $200/mo subscription is absolutely necessary to them. This honestly feels like a repeat of Claude Code back in February. The software engineers eventually realized that AI is absurdly expensive after the AI companies realized that spending $14000/mo to service a $200/mo subscription is a bad idea. If the AI vendors couldn't squeeze money out of rich software companies, what exactly are they gonna get out of poor mathematicians and universities? Also, there is the cognitive decline caused by overuse of LLMs that has yet to set in.