Mathematics
Open problems, research attempts and community review.
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-1501 O16 — Factoring polynomials modulo a prime
- Math-1502 O17 — Constructing irreducible polynomials over finite fields
- Math-1503 O18a — Recognizing primitive roots deterministically
- Math-1504 O19 — Finding a primitive root modulo a prime
- Math-1505 O20 — Computing multiplicative orders modulo a prime
- Math-1506 O21 — Discrete logarithms modulo a prime
- Math-1507 O22b — Factoring from composite discrete logarithms
- Math-1508 O23 — Factoring from Euler's totient
- Math-1509 O25 — Solving binary quadratic congruences
- Math-1510 O26 — Discrete logarithm versus Diffie–Hellman key distribution
- Math-1511 O27 — Elliptic curves of prescribed order
- Math-1512 O28 — Discrete logarithms in elliptic-curve groups
- Math-1513 O30 — Polynomial-factor lattice approximation
- Math-1514 O31 — Order of a polynomial's Galois group
- Math-1515 O32 — Class numbers of imaginary quadratic orders
- Math-1516 O34 — Solvability of the negative Pell equation
- Math-1517 O36 — Integer multiplication in linear bit complexity
- Math-1518 Conjecture 1.3 — Pillai
- Math-1519 Conjecture 1.9
- Math-1520 Conjecture 2.5 — Lang-Waldschmidt
- Math-1521 Conjecture 2.6
- Math-1522 Conjecture 2.14 — Mahler
- Math-1523 Conjecture 3.3 — Algebraic Independence of Logarithms of Algebraic Numbers
- Math-1524 Conjecture 3.5 — Strong Five Exponentials Conjecture
- Math-1525 Conjecture 3.6 — Roy
- Math-1526 Conjecture 3.8 — Gel’fond
- Math-1527 Conjecture 3.9 — Schneider
- Math-1528 Conjecture 3.10 — Gel’fond-Schneider
- Math-1529 Conjecture 3.15 — Goncharov
- Math-1530 Conjecture 3.16 — Zagier
- Math-1531 Conjecture 3.17
- Math-1532 Conjecture 3.18
- Math-1533 Conjecture 3.20 — Nesterenko
- Math-1534 Conjecture 4.1 — Lehmer's Problem
- Math-1535 Conjecture 4.3 — Amoroso-David
- Math-1536 Conjecture 4.11 — Wirsing and Schmidt
- Math-1537 Tensor growth rate and exact one-dimensional obstructions for constrained differences
- Math-1538 Expansion can hide only global Sidorenko obstructions
- Math-1539 A holonomy reduction to equiangular lines
- Math-1540 Random sub-neighborhood discrepancy on the Boolean cube
- Math-1541 A high-probability lower bound for random permutation discrepancy
- Math-1542 Tusnady's problem: canonical models and monotone-chain certificates
- Math-1543 Link structure and sharp edge bounds for three-edge tight-path-free triple systems
- Math-1544 The minimal empty-core tight path and the 2026 uniformity-four resolution
- Math-1545 The exceptional three-color path problem: star-forest and triangle-density reductions
- Math-1546 A saturated-list kernel for one-point extensions of four-color Ramsey colorings
- Math-1547 Endpoint-deck gluing for one-edge deletion at a 3-uniform Ramsey threshold
- Math-1548 Simplex Ramsey numbers and a robust boundary-extension lemma
- Math-1549 Loose hypergraph triangles versus cliques: an edge-rooted component certificate
- Math-1550 Free-cut decomposition for ordered matchings versus triangles