VibeMathedMath problems solved by AI

Dittert's Conjecture in Dimension 16

Dittert's conjecture asserts that among nonnegative n×nn\times n matrices whose entries sum to nn, the functional φ(A)=∏iri+∏jcj−per⁡(A)\varphi(A)=\prod_i r_i+\prod_j c_j-\operatorname{per}(A) is uniquely maximized by Jn/nJ_n/n. The paper proves the case n=16n=16 which, with Pang's result for n≥17n\ge17, establishes the conjecture for every n≥16n\ge16.

Result
Proved(see note)
Status
Partial result
AI contribution
AI-discovered
Method
Argument
Field
Linear Algebra, Permanents
Posed by
Eberhard Dittert
Year posed
—
Years open
—
Solved
2026-07-21
Model
GPT-5.6 Sol
Vendor
OpenAI
Collaborators
Boris Kafidov
Verification
Unreviewed
Publication
Preprint
Significance
15 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What was actually shown

Partial: this settles n=16 only. Combined with Pang's n>=17 the conjecture holds for all n>=16, leaving the small cases open.

What the AI did

The disclosure states that the proof strategy, the joint-deficit scaling lemma, and most of the original proof text were produced by GPT-5.6 Sol through ChatGPT in response to the author's prompts; ChatGPT also revised the exposition and prepared the manuscript.

Verification

No independent check, and the model is credited with the strategy and the central lemma rather than with support. Preprint, not refereed.

Source

arXiv

Discussion