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Erdős problems share a set of properties that make them unusually tractable targets for automated or semi-automated search. They are stated with minimal setup, often in a single sentence, with no dependence on an elaborate surrounding theoretical apparatus. Many ask whether a particular bound can be improved, whether a construction exists with certain properties, or whether a pattern holds for all sufficiently large cases. The database itself, maintained openly and annotated with partial progress, effectively hands a searcher a curated list of well-specified targets, which is precisely the kind of resource that makes systematic exploration by machine feasible in a way that a randomly chosen open problem in, say, algebraic geometry is not.

  • Deep theory-building fields such as algebraic geometry, arithmetic geometry or large parts of analysis require constructing new conceptual frameworks, not finding a single object matching a specification.
  • Many resolved Erdős problems were already known to be 'probably true' from partial results or computational evidence, narrowing the search considerably before any model was involved.
  • Difficulty within the Erdős catalogue varies enormously; some entries are closer to exercises than to genuinely hard open questions, and announcements rarely specify which end of that range was targeted.
  • A model finding one clever construction says little about its ability to sustain a multi-year, multi-paper research programme of the kind most genuine mathematical advances require.

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