Erdős Problem #119

Precise statement

For unit-modulus complex numbers $z_i$, let $p_n(z)=\prod_{i\le n}(z-z_i)$ and $M_n=\max_{|z|=1}|p_n(z)|$. Erdős's prize question: is there $c>0$ with $\sum_{k\le n} M_k > n^{1+c}$?

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.6

GPT-5.6, with Samuel Korsky, resolved Erdős's prize question, proving $\sum_{k\le n} M_k \gg n^{5/4}/\sqrt{\log n}$ (hence $M_n > n^{1/4-o(1)}$ infinitely often).

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Marked solved on erdosproblems.com; carried an Erdős prize of USD 100. Resolved via a proof claim by GPT-5.6 and Samuel Korsky; not formally Lean-verified.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-01

   erdosproblems.com

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.