Just a few weeks after OpenAI released manuscripts with over 700 pages of solutions and progress for 372 major math problems, the company has announced even more discoveries. This time, the discoveries don’t just cover math results, but also results for computer science and physics problems.
For this release, OpenAI has experimented with three different strategies. It has published the math results, so researchers can look them up and make their own efforts to explain them. But for the computer science and physics results, it formed an external group of expert collaborators. OpenAI asked the group working on the computer science results to explain them in their own writeups and materials, while also releasing the AI output to the public. Meanwhile, OpenAI has deferred the release of the physics materials to the group handling them. The company is welcoming feedback “on how to broaden participation and make this process more useful.”
OpenAI has added two new manuscripts on GitHub you can access right now. One establishes Sogge’s local smoothing for waves in every spatial dimension, which is a conjecture about the behavior of solutions to the wave equation. The other shows proof that the Exponential Time Hypothesis, which is an assumption in computer science that some problems are just too hard to solve quickly, is false.
This is the only sort of thing AI should be used for.
But, also:
The refutation also doesn’t yet deliver a usable algorithm. Showing that a subexponential algorithm for 3-SAT exists is not the same as publishing one with a reasonable constant: many existence proofs in complexity theory are non-constructive or produce algorithms with constants so large they are useless in practice. OpenAI’s own announcement frames this cautiously: the refutation reopens questions about how much faster these tasks could become, but guiding the search for better algorithms is not the same as having finished it.
