AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
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For any A subset of reals with Hausdorff dimension s in (0,1/2], either upper box dim(AA) or lower box dim(A+A) is at least 29s/23 (or 33s/26 for differences).
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Mathematical exploration and discovery at scale
AlphaEvolve rediscovered best-known solutions for most of 67 tested math problems and found improved solutions in several cases using LLM-guided evolutionary search.
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A note on the sum-product problem for fractal sets
For any A subset of reals with Hausdorff dimension s in (0,1/2], either upper box dim(AA) or lower box dim(A+A) is at least 29s/23 (or 33s/26 for differences).