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A proof Gauss might have found

A mix of human-written and AI-generated textHuman understanding: no partsmath.NT — Number Theory

Contributed by Roelof van Dijk ↗

Version 1 / Oct 26, 2026 / CC BY 4.0

Abstract

Ben Green’s historical variant of Tao’s recent tenth discriminant challenge [5] asks how early Gauss’s class-number-one conjecture could have been proved using mathematics then in print. Through discussions with GPT-6 Astra and Opus 5.5, we construct a proof of Gauss’s class-number-one conjecture [1] from ingredients published by 1808, specializing the Frobenius determinant argument [6]. Counting values of the principal form and summing factorial valuations reduce the proof to a residue sieve below 17000.

Tools used

OpenAI
ChatGPTVersion 6 Astra
OpenAI
ChatGPTVersion Terra 6.1
Anthropic
Claude OpusVersion 5.5

References

  1. C. F. Gauss, Disquisitiones arithmeticae , Leipzig, 1801. https://doi.org/10.3931/e-rara-4025.DOI
  2. A.-M. Legendre, Essai sur la théorie des nombres , second edition, Paris, 1808, Introduction, art. XVI, pp. 8--9. https://archive.org/details/bub_gb_BwcxjGuIohMC.link
  3. P.-S. Laplace, Recherches sur le calcul intégral et sur le système du monde , Mém.\ Acad.\ Sci.\ Paris, année 1772, seconde partie (1776), 267--376.
  4. P. L. Chebyshev, Mémoire sur les nombres premiers , J.\ Math.\ Pures Appl.\ 17 (1852), 366--390.
  5. T. Tao, An experimental AI-math challenge: using tenth discriminant bounds to explore arguments ruling out Siegel zeroes , What's new, 20 October 2026. https://terrytao.wordpress.com/2026/10/20/an-experimental-ai-math-challenge-using-tenth-discriminant-bounds-to-explore-arguments-ruling-out-siegel-zeroes/.link
  6. R. van Dijk, A Frobenius determinant proof of the non-existence of Landau--Siegel zeros , hexagon:2610.00409v2 (2026). https://hexagonmath.org/2610.00409v2.hexagon

Version history

  1. v1Submitted by Roelof van DijkInitial depositCurrentOct 26, 2026