Problems
No person has reviewed any of this; every judgement here is a machine's.
What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides 1 and apex angle 108^∘ - from an unknown starting position and heading? The optimum is a symmetric seven-piece path…
For every zonotope Z ⊂ R^d and vectors v_1,…,v_n ∈ Z, there are signs with ∑_i x_i v_i ∈ C√d Z for a universal constant C. This resolves a 2002 conjecture on vector balancing in zonotopes.
Is the density of Chernoff's distribution - the law of argmax_t W(t) - t^2 for two-sided Brownian motion W - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?
Is the maximum size of a set A⊆ 1,…,N such that ab+1 is never squarefree (for all a,b∈ A) achieved by taking those n≡ 7pmod25? Resolved for all sufficiently large N: any near-maximal A is contained in n≡ 7pmod25 or n≡ 18pmod25, leaving…
At the critical inverse temperature β=1 in the Sherrington-Kirkpatrick spin glass model, Talagrand conjectured that the expected squared overlap of two independent Gibbs replicas has an exact N^-2/3 scaling: there exists a constant a>0…
Frankl, Peng, Rodl and Talbot asked in 2007 whether the set of Turan densities of families of r-graphs contains intervals. It does: for every r ≥ 3 the set contains non-degenerate intervals, including one of the form [1-δ_r, 1].
Let F(n) be the largest A⊆1,…,n with anmid bc for distinct a,b,c∈ A. Is F(n)=π(n)+(C+o(1)) n^2/3(log n)^-2 for some constant C?
Let X_1,…,X_n be independent nonnegative random variables with EX_i ≤ 1, and let S be their sum. Is P(S < ES + 1) ≥ 1/e? Feige proved the constant 1/13 and conjectured the sharp 1/e. Three independent July 2026 proofs settle it, both…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
After L^2 normalization, stable phase retrieval holds over the L^2-spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided L^1 bound. This confirms the…
If W(k) is the least N such that every two-colouring of 1, …, N contains a monochromatic k-term arithmetic progression, must W(k+1) - W(k) → ∞?
Can a nonabelian group admit a Rota-Baxter operator that is surjective but not injective? A construction shows yes.
Klopp and Zadik gave an exponential-time node-private algorithm for exact community recovery in stochastic block models and asked whether a polynomial-time algorithm could match it. One can: a Lipschitz surrogate for the penalized…
Han's conjecture predicts that a finite-dimensional algebra with eventually vanishing Hochschild homology has finite global dimension. Within the tau-Hochschild framework it splits into persistence and survival, and the Liu-Morin extension…
Yun, Sra and Jadbabaie posed as a COLT 2021 open question whether, for well-conditioned symmetric matrices, the operators encoding the expected iterate of single-shuffle SGD, random-reshuffle SGD and gradient descent on a quadratic finite…
Can the edges of a finite connected multigraph, given a closed eulerian trail, be partitioned into circuits so that no circuit contains two edges used consecutively in the trail? The proof in fact four-colours the edges to satisfy the…
Is the EMD coupling square a^2 a function of the metric three-jet on an explicit active, non-null, simple-spectrum family of truncated Einstein-Maxwell-dilaton data, and can one more derivative recover it? Proved: no function of the common…
Nathanson asked which subsets of N can occur as product intersection sets of a family of semigroup subsets, for arbitrary and for decreasing families (his Problems 10 and 11). Both are solved by complete classifications.
Ehrhart conjectured that a full-dimensional compact convex body in R^n whose barycenter is its unique interior lattice point has volume at most (n+1)^n/n!. With the inequality itself settled, the remaining question was which bodies attain…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.