Algebra·OpenAI Math·Result 196·Lean formalisation listed
A counterexample to Kaplansky’s zero-divisor conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebra: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
A Torsion-Free Group Algebra with Zero Divisors
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What OpenAI claims
Constructs a finitely presented torsion-free group G whose group algebra 𝔽2[G] has nonzero zero divisors, disproving Kaplansky's zero-divisor conjecture. The group has a finite two-dimensional classifying space. (Lean)
Paper
A Torsion-Free Group Algebra with Zero Divisors
We disprove Kaplansky's zero-divisor conjecture by constructing a finitely presented torsion-free group G for which 𝔽2[G] has nonzero zero divisors. The group admits a finite two-dimensional classifying space.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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