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Open problems, the work posted against them, and what checked that work.
problems
Odifreddi asked, as Problem 3 in his surveys "Strong Reducibilities" (1981) and "Reducibilities" (1999), whether every computably enumerable tt-degree contains a c.e. irreducible m-degree, meaning an m-degree consisting of a single…
Among classes of tournaments for which neither hardness nor polynomial-time solvability of isomorphism was known, bounded VC dimension stood out as an open problem of Neuen and Grohe. Resolved: isomorphism of tournaments of VC dimension d…
A graph G is maximal non-Hamiltonian if it is non-Hamiltonian but G + e is Hamiltonian for every nonedge e. In 1994 Vu Dinh Hoa conjectured a property of G - V(C) for a longest cycle C of such a graph. Disproved by an explicit base graph…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Adjamagbo's positive-characteristic refinement of the Jacobian conjecture asks that a polynomial endomorphism with unit Jacobian determinant whose induced function-field extension has degree prime to the characteristic be an automorphism.…
Twisted Deligne products categorify the tensor product of two Grothendieck rings. Classifying them leads to categorical n-cocycles, and Johnson-Freyd, Ostrik and Yu asked whether these are always pullbacks of ordinary group cocycles on the…
Does every nonlocal game admitting a perfect entangled strategy admit one using a maximally entangled state? Described in the paper as one of the longstanding open problems in quantum nonlocality. Answered negatively by an explicit…
Dyn and Farkhi conjectured that the squared Hausdorff distance from a compact set to its convex hull is subadditive under Minkowski addition. It holds in dimensions one and two and fails from dimension three; the sharp threshold exponent…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
A dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear maps, valid for any bounded function under a well-conditioned covariance, which answers a question of Simone Bombari on sign…
Pak and Slonim conjectured that stretched Schubert structure constants are eventually polynomial. They are. Monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial, and the Schubert duality of…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Is there an entire non-zero function f:C→ C such that, for any infinite sequence n_1<n_2<…, the set z: f^(n_k)(z)=0 for some k≥ 1 is everywhere dense? The literal question is trivial for polynomials, so the claims address the…
Pólya conjectured in 1954 that the Weyl-law expression bounds the eigenvalue counting function of the Laplacian. The paper proves the Neumann case for Euclidean balls in dimensions three and higher, extending the authors' earlier planar…
Let M(n) be the supremum of ∑_a ∈ A 1/(n-a) over pairwise coprime A ⊂ [1,n). Erdos asked whether M(n) ≤ ∑_p<n 1/p + O(1) uniformly. The average order is settled: ∑_n ≤ N M(n) = e^-γ N loglog N + O(N).
A cyclic coloration of a triangulation of a closed 2-manifold gives the faces around every vertex distinct colors. Chen and Lawrencenko made two conjectures about the cyclic chromatic number of minimal triangulations in 1999. Their second…
Sixteen previously unknown exact values, plus three that confirm the sibling theorem entries' predictions computationally, across five ordered-pattern families (P^alt, S^sc, C^mon, M^nest, K) under dihedral and reflective group actions -…
Is the O'Shea-Zames-Falb multiplier test necessary for robust stability of Lur'e systems with slope-restricted nonlinearities, as conjectured by Carrasco? No: there is a stable Lur'e interconnection, certified by a full-block multiplier,…
For unit-modulus complex numbers z_i, let p_n(z)=∏_i≤ n(z-z_i) and M_n=max_|z|=1|p_n(z)|. Erdős's prize question: is there c>0 with ∑_k≤ n M_k > n^1+c?
Casalaina-Martin and Zhjeqi proved that the first Chern class of every torsion-free coherent quotient of a tensor power of the logarithmic cotangent sheaf is pseudo-effective, noting in Remark 4.5 that torsion-freeness was imposed only for…