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Is any of the new machine learning tech promising here? I recall some new invariants of minimal surfaces were discovered only a few years ago by a DeepMind-made

• jebarker 1y ago
  This does seem like one math domain where there's some potential for program synthesis approaches like the recent AlphaEvolve and others. I say that because some of these problems you could feasibly write automatic evaluation code and solve them by the LLM spitting out a constructor for solutions and then doing hill climbing. That's not true in many areas of math though. There's also problems here that require a proof and maybe would be approachable eventually using automated theorem proving. But there's also problems that don't obviously fit into either of those categories.
• bubblyworld 1y ago
  A technicality is that those compressors need to provably predict properties of said geometric objects to be interesting to mathematicans (a statement which itself needs appropriate encoding in mathematical language - what exactly you want probably depends on the problem you hope to solve). Something that superficially looks good but works as a black box wouldn't cut it. My understanding of ML interpretability research at the moment is that it's very early days - too early, perhaps, to hope for a general purpose compressor algorithm that produces proofs of it's own workings (that seems like the holy grail). But of course I would love to be wrong!