What was already known
Erdős asked whether the minimum isolated-sum count for finite Sidon sets must diverge. The corresponding infinite-set question is a separate unformalized variant.
AI involvement
DeepMind reports that AlphaProof Nexus autonomously solved the supplied formal problem. The team formalized the target, reviewed statement fidelity and wrote a human explanation.
The research paper explicitly reports autonomous agent solution from a supplied formal theorem; humans chose and reviewed the target afterward.
Importance
Gives a quadratic lower bound for a named finite Sidon-set question.
Limitations
The statement is about finite subsets of natural numbers and does not settle the infinite-set variant. The released Lean proof is reported as complete; the team checked statement fidelity, which is separate from checking every proof step by hand.
Technical verification
The primary paper and cited proof repository report a sorry-free Lean proof of the quadratic inequality and divergence target. Team experts additionally checked fidelity of the solved formal statement to the finite original question; that is not counted as human proof checking.
Formal checking
Compilation of the agent's formal proof with no sorry in the submitted target
- Checker
- Lean 4 compiler in the AlphaProof Nexus validation pipeline
- Scope
- The finite Sidon-set quadratic isolated-sum lower bound and consequent divergence of f(n)
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The team's Appendix B.4 explains the combinatorial counting of isolated sums and the quadratic inequality; named team experts reviewed statement fidelity.
Correction and publication history
Gives a quadratic lower bound for a named finite Sidon-set question.
Read this published revision