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Frontier
New proofs, counterexamples, bounds and formalizations reported by people and AI systems, newest first.
July 2026 6
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New proofProbability
Gaussian moments conjecture
Explicit three-variable polynomials with the first expectation zero and the second equal to m! for every m≥1; hence failure in all n≥3.
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CounterexampleGeometry and topology
Jacobian conjecture in dimension three
An explicit map in C^3 with det JF=-2 and three different points having the same image; padding gives higher-dimensional counterexamples.
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Improved boundTheoretical computer science
Derivative-free convex-optimization oracle lower bound
A near-quadratic lower bound is reported, with formal proof artifacts.
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May 2026 1
CounterexampleCombinatorics
Erdős unit-distance conjecture
A fixed δ>0 and infinitely many n with ν(n)≥n^(1+δ), disproving that asymptotic conjecture.
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Date not recorded 2
CounterexampleCombinatorics
Devin graph and spectral-conjecture results
Nine-vertex Brandt counterexample; proofs for WoW 698 and Graffiti 39/40; independent refutations for Graffiti 143/154 with explicit earlier-priority qualification.
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New proofCombinatorics
Mendelsohn and balanced ternary design nonexistence
Nonexistence is reported for PMD(9,6,1), BTD(14,18;7,1,9;7,4), BTD(12,15;6,2,10;8,6), and BTD(12,20;4,3,10;6,4).
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