Hugging Face's logo

Datasets:
ulamai
/
UnsolvedMath

Tasks:
Question Answering
Text Generation
Modalities:
Document
Tabular
Text
Formats:
json
Languages:
English
Size:
10K - 100K
Tags:
mathematics
unsolved-problems
math
research
latex
Libraries:
Datasets
pandas
Polars
License:
Dataset card Data Studio Files
xet
 Community
4

Status updates for UnsolvedMath entries (our preprints + stale "open" labels)

#4
by AlperTheKing - opened
Discussion
AlperTheKing

Hello, and thank you for curating UnsolvedMath. Over the past weeks we worked through the dataset and would like to report two kinds of status information so that others can avoid duplicated effort. All our results are unrefereed preprints with Zenodo DOIs, produced with substantial AI assistance (disclosed in each paper) and each checked by an independent AI audit pass (not human refereeing); please treat them accordingly.

A. Entries addressed by our preprints

Categories are based on an independent audit of each preprint against the exact dataset statement. Entries already marked solved in the dataset are listed last, as independent verifications only.

Resolved as stated (8)

Entry Preprint What is established DOI
AIM-ALGEBRAIC_NUMBER_THEORY-0109 A Positive-Rank Elliptic Curve with No Dense Prime Negative answer: the rank-one curve y^2 = x^3 - 1516563 has E(Q) dense in E(Q_p) for no prime p. 10.5281/zenodo.22245533
AIM-ARITHMETIC_GEOMETRY-0067 A Seventeen-Dimensional Component of the Hilbert Scheme of Eighteen Points on an Integral Curve Yes: an integral projective rational curve (one non-Gorenstein point) whose Hilb^18 has a 17-dimensional component; in characteristic 0 this gives (d-1)-dimensional components of Hilb^d for all d >= 18. 10.5281/zenodo.22328080
AIM-ARITHMETIC_GEOMETRY-0078 A Generically Nonreduced Component for Hilbert Function (1,4,10,10) Settles the remaining case a = 10 left open by Jelisiejew (2024): in characteristic 0 the very-compressed locus for Hilbert function (1,4,10,10) is a generically nonreduced component; with Jelisiejew's a = 6..9 all cases are answered. 10.5281/zenodo.22328644
AIM-DYNAMICAL_SYSTEMS-0095 Ramification Portraits of Rigid Lattès Maps Complete list of weighted ramification portraits of rigid Lattès maps; every flexible portrait is realised by a rigid map in every degree (related branched-cover data: Pascali-Petronio 2009). 10.5281/zenodo.22245386
AIM-FUNCTIONAL_ANALYSIS-0027 Forcing Absoluteness of Minimal and Maximal C∗-Tensor Products Minimal and maximal C*-tensor products of ground-model C*-algebras are preserved (after completion) by every set-forcing extension, with no cardinal-preservation hypothesis. 10.5281/zenodo.22245547
AIM-PROBABILITY-0111 Nonuniformity of Free-Gradient Heat Semigroups under Finite Fisher Information No: with finite free Fisher information the free heat semigroup never converges uniformly to the identity on the unit ball (explicit L^2 lower bound). New for m = 1, 2; m >= 3 follows from Dabrowski-Ioana (2016). 10.5281/zenodo.22327310
AIM-PROBABILITY-0126 A Slice–Riesz–Bochner Characterization of Joint Brown Determinant Functions Characterisation of joint Brown determinant functions log Delta(1 - sum a_j T_j) by slice subharmonicity and a positive-definiteness condition. 10.5281/zenodo.22245595
AMR-011-0025 A Free-Uniform-Spanning-Forest Proof of Finite-Index Multiplicativity Yes: a free-uniform-spanning-forest proof that the first L^2-Betti number is multiplicative on finite-index subgroups, without using multiplicativity of von Neumann dimension. 10.5281/zenodo.22245583

Resolved in the precise sense stated in the note (2)

Entry Preprint What is established DOI
AIM-ALGEBRAIC_GEOMETRY-0125 Smooth Hypersurfaces Beyond the Chevalley-Warning Range over Prime Fields Smooth reading: for every prime p, n >= 2 and d >= n+1 there is a smooth degree-d hypersurface over F_p with #X(F_p) not 1 mod p, hence not rationally connected (without smoothness the question was classical). 10.5281/zenodo.22514087
EP-278 An Exact Fixed-Parameter Algorithm for Extremal Unions of Residue Classes Maximum-density half: an exact characterisation and a fixed-parameter exact algorithm (2^{O(r^2)} poly(input)); the minimum half was settled by Simpson (1986). Whether an exact algorithm counts as an answer to 'what is the maximum density' is for the maintainers to judge. 10.5281/zenodo.22244392

Special case only; the general question remains open (2)

Entry Preprint What is established DOI
AIM-REPRESENTATION_THEORY-0023 Quantum Symmetric Algebras on Multiple Standard Copies: Structure and Categorical Non-Equivalence Negative answer for several copies of the standard representation (the case singled out in the problem's remark); the general quantum Sym(S_lambda) question remains open. 10.5281/zenodo.22635788
AIM-SEVERAL_COMPLEX_VARIABLES-0010 An Explicit Rational Homotopy from the Faran Map to a Linear Map in Target Dimension Four An explicit proper rational homotopy from the Faran map to a linear map (B^2 to B^4); the general classification question remains open. 10.5281/zenodo.22662513

Only the literal reading is settled; the intended question remains open (3)

Entry Preprint What is established DOI
AIM-COMBINATORICS-0233 Power-Saving Lower Bounds for Additive Bases of Polynomial Sequences Power-saving lower bounds beyond the trivial exponent for bases of polynomial sequences; this settles only the literal qualitative question, good/optimal bounds remain open. 10.5281/zenodo.22245345
AIM-DYNAMICAL_SYSTEMS-0011 Maximal Finite-Set Stabilizers in Thompson's Group T An infinite family of maximal subgroups of infinite index in Thompson's group T (stabilisers of k dyadic points, isomorphic to F wr C_k); the open-ended request for genuinely new kinds of maximal subgroups remains open. 10.5281/zenodo.22324898
AIM-GEOMETRY-0263 A Compactness Obstruction to Linear Growth Along Null Geodesics Negative answer to the literal universal question (no one-form with nonzero slope along every null geodesic); the intended zero-slope statement remains open. 10.5281/zenodo.22245396

Already marked solved in the dataset — our preprint is an independent verification/write-up (10)

Entry Preprint What is established DOI
AIM-ANALYSIS-0015 The Spectrum of the Hilbert Matrix on Power-Weighted ℓ² Spaces Full spectral picture of the Hilbert matrix on power-weighted l^2 (spectrum, fine parts, index); the spectrum set and radius were announced earlier by Aleman-Siskakis-Vukotic. 10.5281/zenodo.22245611
AIM-COMBINATORICS-0230 Lacunary Counterexamples to a Distinct-Summand Freiman Container Problem Elementary proof of the negative answer via lacunary sets; the same construction appears in the dataset's own research record. 10.5281/zenodo.22245483
AIM-DYNAMICAL_SYSTEMS-0005 Maximal Generic Iterated Galois Images Do Not Determine p-Adic Julia Sets Negative answer: z^2+1 and z^2-p^{-6} over Q_p have the same maximal iterated Galois groups but different Julia sets (uses Pink's unpublished preprint Thm 1.10.2). 10.5281/zenodo.22245331
AIM-GEOMETRIC_GROUP_THEORY-0027 Free-by-Cyclic Groups with Unboundedly Many BNS Component Orbits Free-by-cyclic groups with unboundedly many Out-orbits of BNS components; the same construction appears in the dataset's own record and an earlier public note (doi:10.5281/zenodo.22201487). 10.5281/zenodo.22245655
AIM-GEOMETRY-0175 Complex Sectional Curvature Blow-Up under Circle Cheeger Collapse No: complex sectional curvature tends to -infinity under circle Cheeger collapse with a fixed component of codimension >= 4. 10.5281/zenodo.22245130
AIM-GEOMETRY-0195 Angle-Data Reconstruction for Triangulated Polyhedral Surfaces and a Genus Deficit Angle data determine realisations; the AIM dimension formula E-1 holds for genus 0 and fails for every genus >= 1. 10.5281/zenodo.22245788
AIM-GEOMETRY-0274 Parallel Nilpotent Endomorphisms Without Parallel Null Vectors No: a closed flat (8,8)-manifold with a parallel self-adjoint square-zero endomorphism but no parallel null vector, even on double covers. 10.5281/zenodo.22245515
AIM-TOPOLOGY-0102 A Four-Point Counterexample to Excision for Directed Cubical Homology of Closure Spaces Four-point counterexample: excision fails for directed cubical homology of closure spaces. 10.5281/zenodo.22245271
AIM-TOPOLOGY-0203 Variable Critical Exponents on a Fixed Free-Deck Regular Cover Yes: a fixed free-deck regular cover whose critical exponent varies over Teichmüller space. 10.5281/zenodo.22245803
AMR-011-0004 Adjoining a Haar-Generic Matrix to a Parabolic-Free Subgroup of SL₂(Qₚ) Yes: for Haar-almost every g, <Gamma, g> remains parabolic-free. 10.5281/zenodo.22245813

B. Entries labelled open that are already resolved elsewhere

Entries Problem Status Source
SET-001 (records 22 and 1135) Continuum hypothesis Independent of ZFC Continuum hypothesis
ALG-003 (record 1448), ALG-004 (record 1104) Connes embedding problem Solved (false / counterexample) MIP*=RE (arXiv:2001.04383)
HIL-018 Hilbert's 18th problem Solved (true) Hilbert's eighteenth problem
HIL-007 Hilbert's 7th problem Solved (true) Hilbert's seventh problem
HIL-014 Hilbert's 14th problem Solved (false / counterexample) Hilbert's fourteenth problem - Wikipedia
HIL-017 Hilbert's 17th problem Solved (true) Hilbert's seventeenth problem - Wikipedia
OWR-12177-008, OWR-2043-007 Polynomial Freiman-Ruzsa conjecture over F_2^n Solved (true) Marton's 'Polynomial Freiman-Ruzsa' Conjecture was
ALG-016 Graph isomorphism in quasi-polynomial time Solved (true) Graph isomorphism problem
ALG-014 (record 1114), OWR-1265-004 McKay conjecture Solved (Cabanes–Späth, arXiv:2410.20392, to appear in Annals) McKay conjecture
GRAPH-003 (record 1327), GRAPH-029, GT-004, OPG-137, AMR-030-0019 Cycle double cover conjecture Solved: proof announced by OpenAI (July 2026); expositions by S. Oum and J. Geelen; unrefereed A proof of the cycle double cover conjecture by Op
GEO-029, OWR-14298163-006 Borsuk's conjecture Refuted (Kahn-Kalai 1993); the minimal counterexample dimension is still open Borsuk's conjecture
ALG-003 (records 38 and 1103), ALG-010 (record 1455) Köthe conjecture Refuted: two independent preprints (Sept 2026), unrefereed A counterexample to Köthe's conjecture and a quest
DYN-002 (record 1142) Painlevé conjecture Solved (Xia 1992; Xue, Acta Math. 2020) Painlevé conjecture
SET-002 (record 1176) Suslin's problem Independent of ZFC Suslin's problem - Wikipedia
ALG-030 Generalized moonshine Solved (true) Monstrous Moonshine over Z? (arXiv:1804.04161), Ca
OPG-806 Hedetniemi's conjecture Solved (false / counterexample) Hedetniemi's conjecture
SET-003 Whitehead problem Independent of ZFC Whitehead problem
ALG-025 Guralnick-Thompson conjecture Solved (true) Frohardt-Magaard, Ann. of Math. 154 (2001)
GRAPH-052 Implicit graph conjecture Solved (false / counterexample) Implicit graph conjecture
ALG-004 (records 1300 and 1449) Crouzeix's conjecture Solved: preprints July-Aug 2026 (S. Jin; E. Lorist-F. Schwenninger), unrefereed Crouzeix's conjecture
SMA-016, OPG-1768, OWR-1452-011 Jacobian conjecture (all dimensions) False for every n >= 3 (the planar case n = 2 remains open) T. Tao, A digestion of the Jacobian conjecture cou
OWR-1452-013 Dixmier conjecture (all ranks) Not true in all ranks: the stable Dixmier and Jacobian conjectures are equivalent (Tsuchimoto 2005; Belov-Kanel-Kontsevich 2007), so the July 2026 Jacobian counterexample refutes it (ranks >= 3 via the classical implication Dixmier(n) => Jacobian(n); ranks 1-2 open) Belov-Kanel, Kontsevich, Mosc. Math. J. 7 (2007)

We would also gently suggest re-labelling Hilbert's 6th problem (HIL-006), Hilbert's 11th problem (HIL-011), Hilbert's 15th problem (HIL-015, ALG-018), Hilbert–Pólya conjecture (NT-068) as research programmes rather than open yes/no problems.

A machine-readable version (JSON) is available on request. Corrections welcome.

— Alper Ferudun (Mercury Software GmbH), https://eulersolve.org/papers/
AlperTheKing

Follow-up (2026-09-27): more stale "open" labels, found by syncing with sources that maintain status data. Again, this is only meant to save others duplicated effort.

1. Erdős problems. All 632 EP-* entries are labelled open in v1.6.0. As of today, erdosproblems.com lists 90 of them as resolved (we fetched each page; many resolutions are recent, several by AI systems, and most are Lean-verified). Grouped by the site's status:

The site's machine-readable status file (teorth/erdosproblems, data/problems.yaml) may be the easiest way to keep these entries in sync.

2. Ben Green's 100 open problems. The current version of the list (updated December 2025) marks these as solved. Note that the dataset's GREEN-xxx numbers differ from the numbering in Green's list.

Entry Green's problem Status Source
GREEN-001 Problem 1 (sum-free subsets of size n/3 + ω(n)) Solved: every n-set of integers has a sum-free subset of size n/3 + c log log n B. Bedert, arXiv:2502.08624
GREEN-069 Problem 26 (sums of 100 "cubes" in F_3^n) Solved (yes, already with 4 cubes); the F_p analogue remains open Y. Yu, arXiv:2510.01300
GREEN-040 Problem 67 (Waring's problem over finite fields) Marked solved by Green: asymptotic formula with s = O(k) for p ≥ 2k W. Sawin, arXiv:2412.14053

3. OWR-1452-012 (Zhao's Vanishing Conjecture for homogeneous quartics). Zhao proved that this conjecture, over all n, is equivalent to the Jacobian conjecture over all n (Trans. AMS 359 (2007), arXiv:math/0409534). The July 2026 Jacobian counterexample (see SMA-016 above) therefore refutes it for some n; we have not identified the smallest such n.

— Alper Ferudun
AlperTheKing

Follow-up 2 (2026-09-27): Kourovka Notebook, issue 21 (KOU-21.*). The arXiv version of the notebook updated today (arXiv:1401.0300v46) marks the following issue-21 problems as solved (asterisk), while v1.6.0 still labels them open:

Entry Answer (per the notebook) Source cited in the notebook
KOU-21.10 Yes (every finite group has a just finite presentation) M. Lackenby, arXiv:2605.10402
KOU-21.87 Yes J. DeCaro (preprint, July 2026); R. Sater, arXiv:2608.12432
KOU-21.88 No, there are no such groups B. Beyer de Ryke, arXiv:2608.03003
KOU-21.97 Yes S. Sureaux (preprint, 2026, linked from the notebook)
KOU-21.117 Yes, for both questions (Thompson's group V) R. Sauer, E. Schesler, arXiv:2605.30163
KOU-21.134 No, for both questions (already answered by J. G. Thompson) Y. Li, W. Shi, Ric. Mat. 74 (2025) 559–563
KOU-21.137 No (counterexamples for p = 3 and p = 2) K. Muliarchyk (preprint, 2026); A. Chang (letter, 2026)
KOU-21.142 No (for any primes p ≠ q) T. Gong, M. R. Zeng, Y. Yang, arXiv:2608.00703; I. Capdeboscq, C. Parker, arXiv:2608.03935
KOU-21.147 No, not always P. Monticone (preprint, 2026); van Doorn, Judin, Monticone, Morrison, arXiv:2607.17477

(The other nine starred issue-21 problems, 21.8, 21.12, 21.14, 21.15, 21.18, 21.24, 21.43, 21.58, 21.150, are already marked solved in the dataset.)

— Alper Ferudun

Sign up or log in to comment