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The AI helped run the search that split a set into 86 zero sum parts

A researcher studying rare zero sum congruences wanted to split a 629 number interval into as many disjoint zero sum subsets as possible. He used AI to help with the implementation and the computational search, including randomised searches for the larger subsets, and found a partition into 86 zero sum subsets covering the whole interval. Whether 86 is the maximum is still open.

How it works

  1. He sets up a meet in the middle search over triples
  2. The AI helps with the implementation and the computational search
  3. Randomised searches handle the larger subsets
  4. The found subsets are checked to be disjoint and to cover the whole interval
  5. He posts the partition of 86 with its size distribution

Why it’s worth knowing

The construction is a concrete extremal object, 86 verified parts covering all 629 numbers, produced by an agent assisted search rather than by theory.

Where it’s from

Summarized from a public post on mathoverflow.net. See the original ↗

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