Problem detail · source-aware
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Is there an entire non-zero function $f:\mathbb{C}\to \mathbb{C}$ such that, for any infinite sequence $n_1<n_2<\cdots$, the set $\{ z: f^{(n_k)}(z)=0 \textrm{ for some }k\geq 1\}$ is everywhere dense? The literal question is trivial for polynomials, so the claims address the transcendental entire case, in the affirmative.
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.
The probabilistic argument via the cofinite reformulation, using Sodin's Edelman-Kostlan and Offord-type estimates for Gaussian analytic functions, was developed with GPT-5.5 Pro; an independent solution by another contributor was posted first the same day.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
AI screenings reported one minor issue on each claim; no formalization (the required tools are not in mathlib) and no independent expert review; erdosproblems.com still lists the problem open.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Two independent affirmative claims (Adriano's, posted first, and a GPT-5.5 Pro note); Erdős himself wrote in 1982 that the problem had been solved affirmatively long before, without a locatable reference
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.