Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
49 problems
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Is every weakly quasi-complete Noetherian local ring quasi-complete? Asked by D. D. Anderson in 2014. The ring A = k^p[[X, Y]][k] with k = F_p(u_1, u_2, …) is weakly quasi-complete but not quasi-complete.
The Gaussian Moments Conjecture asks whether, for complex polynomials P,Q in n independent standard real Gaussian variables, E(P^m)=0 for all m≥ 1 forces E(QP^m)=0 for all large m. Explicit counterexamples with E(P^m)=0 and E(QP^m)=m!≠ 0…
Do a finite group's order together with ∑_g ∈ G φ(|g|) determine whether the group is simple? A simple and a non-simple group of order 6048 share the statistic 23984.
Must the right-relatively convex subgroups of a right-orderable nonabelian group form a sublattice of its subgroup lattice? A construction shows they need not.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For a family F of an odd number n of unit disks in the plane, let OA(F) be the area covered by an odd number of disks. It was conjectured that OA(F) ≥ π, the area of a single disk. False: configurations exist with smaller odd area.
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.…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For every connected graph G, is α(G) ≤ ⌊ b(G) - log(ecc_avg(G)) ⌋, where b(G) is the largest induced-bipartite-subgraph order? An 11-vertex counterexample - a triangle with four leaves on each of two vertices - has α = 9 against bound 8.
Albertson and Berman conjectured that for every simple planar graph G on n vertices, the largest vertex set inducing a forest has size at least n/2. The standing lower bound since the same year has been Borodin's 2n/5, from his acyclic…
Lorist and Schwenninger prove Crouzeix's conjecture (arXiv:2608.03841, Lemma 1) by combining a lower bound (their inequality (4)) with an upper bound (inequality (5)). In Remark 2 they observe that (5) alone gives κ ≤ 1 + √1 - ℜ⟨ E_1…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Erdős conjectured, in over a dozen papers spanning 1976 to 1997 and with a $1000 prize attached, that every finite Sidon set extends to a perfect difference set modulo p^2+p+1 for some prime p. Alexeev and Mixon establish that 1,2,4,8 is a…
Jaeger conjectured that every bridgeless cubic graph G admits a Petersen coloring: a map φcolon E(G)→ E(P) into the edges of the Petersen graph P such that, for every vertex v of G, the three edges at v are sent to three edges meeting at a…
Ramachandra and Natarajan conjectured a bound on the pairwise independent correlation gap in their 2025 Operations Research Letters paper. An explicit counterexample refutes it.
For A ⊆ F_p let A^* = (A+A) ∪ (AA). Sárközy conjectured that for all large primes, every set of size at least c√p has A^* = F_p-like covering behaviour. Disproved with an explicit construction from the classical cross-ratio orbit, together…
Every polynomial map C^n → C^n with constant nonzero Jacobian determinant is invertible, with a polynomial inverse.