Epoch AI — FrontierMath: Open Problems
All 49 listed research problems with automatically verifiable answers, from Epoch’s published data archive and problem pages (data updated 7 October 2026). Expanded after June 2026 workshops and featured by Scientific American (2 October 2026). Status follows Epoch’s labels: 39 unsolved, 10 marked solved (5 by AI, 5 by human + AI).
49 catalogue entries · 49 new problem records · 49 catalogue entries linked to problem records
Catalogue entries can be source pointers, solved items or groups of questions. They are not added to the main problem count. Status reflects the saved source, inspected 2026-10-10.
Original collection ↗Attribution and reuse
CC BY 4.0 (Epoch AI data and problem pages); attributed reproduction of problem descriptions and verbatim task prompts.
49 matching entries
Clear filtersApéry-Style Irrationality Proofs via Linear Recurrences
Source marks solvedNumber theory
The Arithmetic Kakeya Conjecture
Source marks openNumber theory
A Baillie–PSW Pseudoprime
Source marks openNumber theory
Chowla's Cosine Problem
Source marks openAnalysis
Large -Rank in Class Groups of Imaginary Quadratic Fields
Source marks openAlgebraic number theory
The Core in Approval-Based Committee Elections
Source marks solvedSocial choice
Condorcet Winning Sets
Source marks openSocial choice
Conway's 99-Graph Problem
Source marks openGraph theory
Sensitivity versus Degree for Boolean Multilinear Polynomials
Source marks openCombinatorics
A Rational Diophantine Septuple
Source marks openDiophantine
The Earth–Moon Problem
Source marks openGraph theory
Existence of EFX Allocations
Source marks openSocial choice
The Elliptic-Curve Discrete Logarithm Problem (ECDLP)
Source marks openNumber theory
Elliptic Curves with Prescribed Number of Points
Source marks openArithmetic geometry
Elliptic Curves over of Large Rank
Source marks solvedArithmetic geometry
Euler's Sum of Powers Conjecture
Source marks openDiophantine
A Genus 2 Curve over the Rationals with a Rational Torsion Point of Prime Order at Least 31
Source marks solvedArithmetic geometry
Many Rational Points on a Genus-2 Curve
Source marks solvedDiophantine
Hadamard Matrix of Order 668
Source marks solvedCombinatorics
Hall's Conjecture
Source marks openDiophantine
A shape with Heesch number 7
Source marks openTopology/Geometry
The Hirsch Conjecture in Dimension 4
Source marks openDiscrete geometry
The Inverse Galois Problem for the Mathieu Group
Source marks solvedNumber theory
The Jones Unknot Conjecture
Source marks openKnot theory
Littlewood Polynomials with Large Normalized Mahler Measure
Source marks solvedAnalysis
Large Steiner Systems
Source marks openCombinatorics
Leech Trees
Source marks openCombinatorics
The Lonely Runner Conjecture
Source marks openDiophantine
The Rank of the Matrix-Multiplication Tensor
Source marks openCombinatorics
The Missing Moore Graph
Source marks openGraph theory
The No-Three-in-Line Problem
Source marks openDiscrete geometry
A counterexample to Wilf's Conjecture
Source marks openNumber theory
Pólya's Conjecture for the Dirichlet Laplacian
Source marks openSpectral geometry
Polynomial Entire Minimal Graphs
Source marks openAnalysis
Dense Polynomials Whose Squares Are Sparse
Source marks openNumber theory
Improve the Best-known Classical Factorization Algorithms
Source marks openNumber theory
Prime-Generating Polynomial Systems in Five Variables
Source marks openNumber theory
A Presentation of the Absolute Galois Group of
Source marks solvedNumber theory
Class Group Algorithms
Source marks openAlgebraic number theory
The Ramsey Number
Source marks openGraph theory
Book Ramsey Numbers
Source marks openGraph theory
The Slice–Ribbon Conjecture and the GST Knot
Source marks openKnot theory
Large Integer Solutions to a Cubic Diophantine Equation
Source marks openDiophantine
The Smooth Four-Dimensional Poincaré Conjecture
Source marks openTopology/Geometry
A Prescribed Class-Group Structure for an Imaginary Quadratic Field
Source marks openAlgebraic number theory
Sum of Three Cubes
Source marks openDiophantine
Short Superpermutations over 8, 9, and 10
Source marks solvedCombinatorics
Symplectic Ball Packing
Source marks openTopology/Geometry
Conway's Thrackle Conjecture
Source marks openGraph theory