Erdős Problem #514
Erdős problem #514 · erdosproblems.com/514
For a transcendental entire function, how fast can be forced to grow along a path to infinity, and how short can such a path be in terms of the maximum modulus ?
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Entire Functions
- Posed by
- —
- Year posed
- 1961
- Years open
- 65y
- Solved
- 2026-04
- Model
- GPT-5.5 Pro
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
an escape path dominating every power of |z| with bounded initial length is constructed, and universal positive-power lower bounds are ruled out; the broader variant remains open
Verification
Public manuscript with community discussion.