This AI Wiki collects contributions of AI systems to the understanding of ErdΕs problems.
If you are interested in getting started with using AI for research mathematics, we have some free advice.
If you are looking for famous solutions, we have information on some notable cases.
Introduction
Color indicators
- π’: Full resolution.
- π‘: Partial progress.
- π΄: Incorrect work.
- βͺ: Unverified.
Section placement
Full details are found here.
Disclaimers
We have collected some disclaimers:
- This page is not a benchmark
- Many problems on the site lack a thorough literature review
- Keep selection bias in mind when drawing conclusions about success rates of AI systems
- In some cases, ErdΕs himself or the problem site stated the problem incorrectly
- Absence of past progress may reflect obscurity rather than difficulty
- Contributions should be evaluated holistically
- A solution to an ErdΕs problem does not automatically qualify as publishable paper in a journal
- We encourage formalizations of AI proofs in a formal language such as Lean
- This wiki is only a superficial reference and is not definitive verdict or assessment
- The information provided on this wiki is provisional rather than final
- Problem solving is only one component of mathematical research
Frequently asked questions
- How have AI companies been invested in ErdΕs problems?
- What to do when I think I managed to get AI to solve an ErdΕs problem?
External links
Sorted by the author's last name alphabetically.
- Blog post "Formalization of ErdΕs problems" by Boris Alexeev, 5 Dec, 2025.
- Webpage by Przemek Chojecki, collecting AI attempts on ErdΕs problems.
- Webpage by Mehmet Mars Seven, collecting AI attempts on ErdΕs problems.
- Webpage by Neel Somani, collecting AI attempts on ErdΕs problems.
1. Primary contributions
Notice. Sections 1(a)-1(d) are equally important. We do not intend section 1(a) to be more important than other sections.
1(a). AI standalone
Literature presence: comparable literature unknown.
Human involvement: non-significant.
| Problem | AI systems | Date | Outcome |
|---|---|---|---|
| [11] | Aristotle, GPT | 24 Jan, 2026 | π΄ Incorrect claim made |
| [38] | GPT-5.5 Pro | 25 Apr, 2026 | π’ Full solution |
| [42] | Codex, GPT-5.2, GPT-5.2 Pro | 19 Jan, 2026 | π‘ Partial result (Lean) |
| [51] | ChatGPT free version | 11 Jan, 2026 | π΄ Incorrect proof found |
| [52] | Claude Mythos | 3 Jun, 2026 | π‘ Solution to variant problem |
| [75] | Aletheia | 1 Feb, 2026 | π‘ Solution to variant problem (implicit in literature) |
| [90] | OpenAI internal model | 20 May, 2026 | π’ Full solution |
| [90] | Claude Mythos | 26 May, 2026 | π’ Full solution |
| [124] | Aristotle | 29 Nov, 2025 | π‘ Partial result (Lean) |
| [125] | DeepMind prover agent | 21 Feb, 2026 | π‘ Solution to variant problem (Lean) |
| [125] | DeepMind prover agent | 30 Mar, 2026 | π’ Full solution (Lean) |
| [138] | DeepMind prover agent | 10 Apr, 2026 | π‘ Partial result (Lean) |
| [205] | Aristotle, GPT-5.2 Thinking | 10 Jan, 2026 | π’ Full solution (Lean) |
| [233] | GPT-5.2 Pro | 18 Jan, 2026 | π΄ Incorrect (conditional) proof found |
| [251] | GPT-5.4 Pro | 15 Apr, 2026 | π‘ Solution to variant problem |
| [263] | Aristotle, Claude Opus 4.7, GPT-5.5 Pro | 9 May, 2026 | π‘ Partial result (Lean) (solution to second part) |
| [358] | GPT-5.2 Pro | 11 Feb, 2026 | π΄ Argument with major gaps made |
| [457] | Aristotle, GPT-5.2 Pro | 2 Mar, 2026 | π’ Full solution (Lean) |
| [477] | AlphaProof | 7 Jan, 2026 | π‘ Solution to variant problem (Lean) |
| [539] | Codex, GPT-5.5, ProofCouncil | 10 Jun, 2026 | π‘ Partial result (Lean) |
| [616] | Claude Sonnet 4.5, Gemini 3 Pro, GPT-5.2 Pro | 18 Jan, 2026 | π΄ Incorrect proof found |
| [619] | Claude Fable 5, Codex, GPT-5.5 | 9 Jun, 2026 | π’ Full solution (Lean) |
| [647] | ChatGPT Deep research, DeepSeek DeepThink, Gemini | 28 Jan, 2026 | π΄ Incorrect proof found |
| [654] | Aletheia | 1 Feb, 2026 | π‘ Partial result |
| [684] | OpenAI internal model | 31 Mar, 2026 | π‘ Partial result |
| [694] | GPT-5.5 Pro | 1 May, 2026 | π’ Full solution |
| [741] | DeepMind prover agent | 31 Mar, 2026 | π‘ Partial result (Lean) (solution to variant of first part; solution to second part) |
| [741] | OpenAI internal model | 31 Mar, 2026 | π‘ Partial result (solution to second part) |
| [741] | DeepMind prover agent | 16 Apr, 2026 | π’ Full solution (Lean) |
| [783] | GPT-5.2 | 23 Jan, 2026 | π‘ Partial result |
| [836] | GPT-5.5 Pro | 27 Apr, 2026 | βͺ Candidate partial result (solution to second part) |
| [872] | GPT-5.2 Pro | 16 Feb, 2026 | π‘ Partial result |
| [888] | Claude Opus 4.5, Gemini 3 Pro, GPT-5.2 Thinking | 18 Jan, 2026 | π΄ Incorrect proof found |
| [949] | AlphaProof | 7 Jan, 2026 | π‘ Solution to variant problem (Lean) |
| [951] | GPT-5.2 Pro | 27 Jan, 2026 | π‘ Solution to variant problem |
| [960] | OpenAI internal model | 9 Apr, 2026 | π’ Full solution |
| [963] | Gemini 3 Pro | 22 Jan, 2026 | π΄ Argument with major gaps made |
| [987] | OpenAI internal model | 9 Apr, 2026 | π’ Full solution |
| [990] | OpenAI internal model | 9 Apr, 2026 | π’ Full solution |
| [1014] | OpenAI internal model | 23 Apr, 2026 | π’ Full solution |
| [1039] | GPT-5.5 Pro | 7 May, 2026 | π‘ Partial result |
| [1040] | Aletheia | 1 Feb, 2026 | π‘ Solution to one part of problem; π΄ incorrect solution to other part |
| [1041] | GPT-5.4 Thinking | 22 Apr, 2026 | π΄ Argument with major gaps made |
| [1044] | GPT-5.2 Pro | 5 Jan, 2026 | π΄ Incorrect claim made |
| [1051] | Aletheia | 29 Jan, 2026 | π’ Full solution (Lean) |
| [1091] | OpenAI internal model | 9 Apr, 2026 | π’ Full solution |
| [1101] | GPT-5.5 Pro | 27 Apr, 2026 | βͺ Candidate partial result (solution to second part) |
| [1131] | GPT-5.5 Pro | 26 Apr, 2026 | βͺ Candidate partial result |
| [1141] | OpenAI internal model | 9 Apr, 2026 | π’ Full solution |
| [1194] | GPT-5.4 Pro | 23 Apr, 2026 | π‘ Partial result |
| [1196] | GPT-5.4 Pro | 13 Apr, 2026 | π’ Full solution |
| [1202] | GPT-5.4 Pro | 1 Apr, 2026 | π’ Full solution |
| [1217] | GPT-5.4 Pro | 16 Apr, 2026 | π’ Full solution |
1(b). AI alongside literature
Literature presence: comparable literature discovered afterwards.
Human involvement: non-significant.
| Problem | AI systems | Date | Outcome | Literature | Literature found on | Similar? |
|---|---|---|---|---|---|---|
| [120] | DeepMind prover agent | 14 Mar, 2026 | π‘ Solution to variant problem (Lean) | π‘ de Reyna (1983) | 14 Mar, 2026 | No |
| [152] | DeepMind prover agent | 3 Apr, 2026 | π’ Full solution (Lean) | π‘ ErdΕs, SΓ‘rkΓΆzy, and SΓ³s (1994) | 3 Apr, 2026 | Yes |
| [218] | GPT | 28 Jan, 2026 | π‘ Conditional solution | π‘ Banks (2023) | 28 Jan, 2026 | Yes |
| [281] | GPT-5.2 Pro | 17 Jan, 2026 | π’ Full solution | π’ Davenport and ErdΕs (1936) + Rogers (in Halberstam-Roth (1966)) | 18 Jan, 2026 | No |
| [333] | Claude Opus 4.5, GPT-5.2 Pro | 25 Dec, 2025 | π’ Full solution (Lean) | π’ ErdΕs and Newman (1977) | 25 Dec, 2025 | Yes |
| [366] | Automated research pipeline | 14 Apr, 2026 | π‘ Conditional partial result | π‘ AktaΕ and Murty (2017) | 15 Apr, 2026 | Yes |
| [397] | Aristotle, GPT-5.2 Pro | 10 Jan, 2026 | π’ Full solution (Lean) | π’ China TST competition (2012) | 14 Jan, 2026 | Yes |
| [397] | Aletheia | 2 Feb, 2026 | π’ Full solution | π’ China TST competition (2012) | 2 Feb, 2026 | Yes |
| [543] | GPT-5.2 Pro | 21 Jan, 2026 | π’ Full solution | π‘ ErdΕs and Hall (1977) | 26 Jan, 2026 | Yes |
| [629] | Gemini 3.1 Pro, GPT-5.4 Thinking | 4 Apr, 2026 | π‘ Partial result | π‘ ErdΕs (1964) + ErdΕs, Rubin, and Taylor (1980) | 4 Apr, 2026 | Yes |
| [635] | Aristotle, GPT-5.2 Pro | 30 Jan, 2026 | π‘ Solution to one part of problem (Lean) | π‘ Elliott (1979) (reduces one part of problem to a much simpler one) | 30 Jan, 2026 | Yes (for a large portion of the proof) |
| [650] | GPT-5.4 Pro | 6-7 Mar, 2026 | π’ Full solution (stronger than literature) | π’ ErdΕs and Selfridge (1978) | 7 Mar, 2026 | No |
| [659] | Aletheia | 2 Feb, 2026 | π’ Full solution | π‘ Sheffer and Lund (2014); π’ Grayzel (2026) | 2 Feb, 2026; 14 Jan, 2026 | Yes |
| [728] | Aristotle, GPT-5.2 Pro | 6 Jan, 2026 | π’ Full solution (Lean) | π‘ Pomerance (2014) | 5-6 Jan, 2026 | Yes |
| [846] | DeepMind prover agent; OpenAI internal model (independently) | 21-25 Feb, 2026 | π’ Full solution (Lean); π’ Full solution | π‘ Reiher, RΓΆdl, and Sales (2024) | 25 Feb, 2026 | No |
| [851] | GPT-5.2 Pro | Feb 5, 2026 | π’ Full solution (building upon π‘ Romanoff (1934)) | Matthews (1982); π’ Green and Sawhney (unpublished) | 6 Feb, 2026 | Yes |
| [897] | Archivara, Aristotle | 26 Dec, 2025 | π’ Full solution (Lean) | π’ Wirsing (1981) | 26 Dec, 2025 | Yes |
| [935] | Aletheia | 1 Feb, 2026 | π‘ Solution to one part of problem | π‘ van Doorn (2025) (solution to one part of [367]) | 2 Feb, 2026 | Yes |
| [983] | GPT-5.5 Pro | 30 Apr, 2026 | π‘ Partial result (solution to first part) | π‘ ErdΕs (1970) | 19 May, 2026 | Yes |
| [997] | OpenAI internal model | 31 Mar, 2026 | π’ Full solution | π‘ Benatar (2014) | 1 Apr, 2026 | Yes |
| [1026] | Aristotle | 7 Dec, 2025 | π’ Full solution (Lean) | π’ Tidor, Wang, and Yang (2016) | 8 Dec, 2025 | Only after applying an argument from Seidenberg (1959) |
| [1082] | DeepMind prover agent | 14 Feb, 2026 | π‘ Counterexample to one part (Lean) | π‘ Fishburn (2002) | 25 Feb, 2026 | Yes |
| [1089] | Aletheia | 1 Feb, 2026 | π’ Full solution found | π’ Bannai and Bannai (1981) | 1 Feb, 2026 | Yes |
1(c). AI building on literature
Literature presence: comparable literature known beforehand and not discovered afterwards.
Human involvement: non-significant.
| Problem | AI systems | Date | Literature | Outcome |
|---|---|---|---|---|
| [12] | DeepMind prover agent | 7 Apr, 2026 | π‘ ErdΕs and SΓ‘rkΓΆzy (1970) | π‘ Partial result (Lean) (solutions to first part and second part) |
| [26] | DeepMind prover agent | 6 Apr, 2026 | π’ Ruzsa | π’ Solution to stronger problem |
| [36] | AlphaEvolve | 3 Nov, 2025 | π‘ Haugland (2016) | π‘ Slight improvement to past construction |
| [43] | Aristotle | 4 Dec, 2025 | π‘ Barreto (2025) | π‘ New proof of partial result (Lean) |
| [75] | GPT-5.4 Pro | 12 Apr, 2026 | π‘ ErdΕs, Hajnal, and SzemerΓ©di (1982) | π‘ Partial result |
| [198] | AlphaProof | 2025 | π’ Baumgartner (1975) | π’ New proof found |
| [224] | Codex, GPT-5.2 Thinking | 14 Jan, 2026 | π’ Danzer and GrΓΌnbaum (1962) | π’ New proof found (Lean) |
| [258] | GPT-5.4 Pro | 14 Apr, 2026 | π‘ Tao and TerΓ€vΓ€inen (2025) | π’ Full solution |
| [264] | Aristotle | 18 Dec, 2025 | π‘ KovaΔ and Tao (2024) | π‘ New proof of partial result (Lean) |
| [349] | GPT-5.2 Thinking | 9 Mar, 2026 | π‘ van Doorn (2026) | π‘ Improved partial result |
| [379] | Seed Prover 1.5 | 21 Dec, 2025 | π’ Cambie, KovaΔ, and Tao (2025) | π’ New proof found |
| [488] | Aristotle | 27 Nov, 2025 | π‘ Cambie (2025) | π‘ New solution to variant problem (Lean) |
| [493] | Aristotle, GPT, Seed Prover | 2025 | π’ Seamans (2025) | π’ New or existing proof found (Lean) |
| [507] | AlphaEvolve | 3 Nov, 2025 | π‘ Friedman (2015) | π‘ Surpassed some past constructions |
| [513] | GPT-5.2 Thinking | 1 Mar, 2026 | π‘ He and Tang (2026) | π‘ Slight improvement to past construction |
| [524] | Gemini, GPT-5.2, Grok | 30 Jan, 2026 | π‘ Sawhney (2025) | π‘ Improved partial result |
| [679] | Aristotle | 12 Jan, 2026 | π‘ DottedCalculator (2025) | π‘ Improved proof by reducing dependence on prime number theorem |
| [729] | Aristotle, GPT-5.2 Pro | 8-10 Jan, 2026 | π‘ Aristotle, Barreto, and GPT-5.2 Pro (2026) (full solution to [728]) | π’ Full solution (Lean) |
| [788] | GPT-5.2 Pro | 20 Jan, 2026 | π‘ Hunter (2025) | π‘ New partial result |
| [848] | Gemini 3.1 Pro, GPT-5.2 Thinking, GPT-5.4 Thinking | 5-23 Mar, 2026 | π’ Sawhney (2025) | π’ Derived explicit bound; π‘ Partial result of variant problem |
| [868] | GPT-5.2 multi-agent system | 13 Jan, 2026 | π‘ ErdΕs and Nathanson (1989) | π‘ New partial result |
| [871] | Claude Opus 4.5, Gemini 3 Pro | 5 Jan, 2026 | π‘ ErdΕs and Nathanson (1989) | π’ Existing partial result upgraded to full solution (Lean) |
| [942] | Gemini | 23 Nov, 2025 | π‘ ErdΕs (unpublished, 1976) | π‘ New proof found |
| [951] | AlphaEvolve | 28 Jan, 2026 | π‘ Barreto, GPT-5.2 Pro, and Price (2026) + GPT-5.2 Thinking and Sothanaphan (2026) (solution to variant problem) | π‘ New solution to variant problem |
| [958] | Aristotle | 27 Dec, 2025 | π’ Clemen, Dumitrescu, and Liu (2025) | π’ New proof found (Lean) |
| [966] | Aristotle | 25 Feb, 2026 | π’ Spencer (unpublished) | π’ Full solution (Lean) |
| [1004] | GPT-5.5 Pro | 29 Apr, 2026 | π‘ Pollack, Pomerance, and TreviΓ±o (2013) | π‘ Partial result (implicit in literature) |
| [1007] | Aristotle | 19 Jan, 2026 | π’ House (2013); π’ Chaffee and Noble (2016) | π’ New proof found (Lean) |
| [1032] | Codex, GPT-5.5 Pro | 7 May, 2026 | π‘ Luo, Ma, and Yang (2023) | π‘ Improved partial result (Lean) |
| [1043] | Aristotle | 28 Dec, 2025 | π’ Pommerenke (1961) | π’ New proof found (Lean) |
| [1043] | GPT | 30 Dec, 2025 | π’ Pommerenke (1961); Aristotle | π’ New proof found |
| [1047] | Aristotle | 21 Jan, 2026 | π’ Goodman (1966) | π’ New proof found (Lean) |
| [1048] | Aristotle | 28 Jan, 2026 | π’ Pommerenke (1961) | π’ Proof found (Lean), which is a specific case of Pommerenke |
| [1090] | Aristotle, Gemini 3 Flash | 27 Feb, 2026 | π’ Graham and Selfridge (unpublished, ~1975) | π’ Proof found (Lean) |
| [1095] | Aristotle | 30 Dec, 2025 | π‘ Ecklund, ErdΕs, and Selfridge (1975) | π‘ New proof of (slightly weaker) partial result (Lean) |
| [1097] | AlphaEvolve | 3 Nov, 2025 | π‘ Lemm (2015) | π‘ Slight improvement to past construction |
| [1197] | Aristotle, GPT-5.4 Pro | 13 Apr, 2026 | π‘ Buczolich and Mauldin (1999) | π’ Full solution (Lean) |
1(d). AI collaborating with humans
Literature presence: any.
Human involvement: significant.
| Problem | Humans | AI systems | Date | Outcome |
|---|---|---|---|---|
| [7] | Jinook Lee | Aristotle | 2 May, 2026 | π΄ Incorrect proof found |
| [12] | Nat Sothanaphan, Terence Tao | GPT-5.4 Thinking | 7 Apr, 2026 | π‘ Partial result |
| [25] | Przemek Chojecki | GPT-5.4 Pro | 19 Mar, 2026 | π‘ Partial result |
| [42] | Harjas Sandhu | GPT-5.5 Pro | 27 Apr, 2026 | π’ Full solution |
| [52] | Thomas Bloom, Will Sawin, Carl Schildkraut, Dmitrii Zhelezov | GPT-5.5 Pro | 28 May, 2026 | π‘ Solution to variant problem |
| [52] | Ingo AlthΓΆfer | GPT-5.5 | 28 May, 2026 | π‘ Improved bound to variant problem |
| [52] | Boris Alexeev | GPT-5.5 | 4 Jun, 2026 | βͺ Candidate solution to variant problem |
| [90] | Ingo AlthΓΆfer, Michael Emmerich, Paata Ivanisvili, Tomasz Kania, leloy, mlewko, Eric Naslund, norxornor, Will Sawin, Carl Schildkraut, spiderduckpig, Tseng | GPT-5.5 Pro | 21 May-9 Jun, 2026 | π’ Improved explicit bound |
| [138] | Nat Sothanaphan | GPT-5.4 Thinking | 10 Apr, 2026 | π‘ Partial result of variant problem |
| [202] | Boon Suan Ho | GPT-5.4 Pro | 23 Apr, 2026 | π’ Full solution |
| [202] | Przemek Chojecki | GPT-5.5 Pro | 30 Apr, 2026 | βͺ Candidate full solution |
| [283] | Kevin Barreto, Liam Price | GPT-5.5 Pro | 3 May, 2026 | π’ Full solution |
| [288] | Ritvik Nayak | GPT-5.5 Thinking | 3 May, 2026 | βͺ Candidate partial result |
| [306] | Shisheng Li | Claude, Claude Code | 17 Jun, 2026 | π‘ Partial result (Lean) |
| [326] | Aron Bhalla | Aristotle, Codex, GPT-5.5 | 20 May-14 Jun, 2026 | π’ Full solution (Lean) |
| [327] | Yu Leon Liu | GPT-5.5, Rethlas | 13 May, 2026 | βͺ Candidate partial result |
| [330] | David Turturean | GPT-5.5 Pro | 24 Apr, 2026 | π’ Full solution |
| [342] | Przemek Chojecki | GPT-5.2 Pro, GPT-5.4 Pro | 20 Jan-23 Mar, 2026 | π‘ Partial result |
| [345] | Wouter van Doorn | Aristotle, GPT | 16 May, 2026 | π‘ Partial result (Lean) |
| [347] | Enrique Barschkis, Wouter van Doorn, jbbaehr22, Bartosz Naskrecki, Terence Tao | Aristotle, Claude Opus, Codex, GPT | 25 Oct, 2025-4 Feb, 2026 | π’ Full solution (Lean) |
| [351] | Kevin Barreto, Liam Price | GPT-5.5 Pro | 3 May, 2026 | π’ Full solution |
| [352] | Aleksandar Bulj, Vjekoslav KovaΔ | GPT-5.4 Pro, GPT-5.5 Pro | 29 May, 2026 | π‘ Partial result of variant problem |
| [358] | Nat Sothanaphan | GPT-5.2 Thinking | 13-20 Feb, 2026 | π΄ Argument with major gaps made |
| [367] | Boris Alexeev, Wouter van Doorn, Terence Tao | Aristotle, Gemini Deep Think | 20-22 Nov, 2025 | π‘ Partial result |
| [369] | Sky Yang | GPT | 26 Mar, 2026 | π’ Full solution |
| [374] | Terence Tao | GPT-5.4 Pro | 31 Mar, 2026 | π‘ Partial result |
| [380] | Terence Tao | GPT-5.4 Pro | 31 Mar, 2026 | π’ Full solution |
| [388] | Malek Zribi | Claude, Gemini, GPT-5.4 | 12-15 Mar, 2026 | π΄ Incorrect proof found |
| [390] | Samuel Mausberg | GPT-5.5 Pro | 2 May, 2026 | βͺ Candidate partial result |
| [393] | David Turturean | GPT-5.5 Pro | 3 May, 2026 | π‘ Conditional partial result |
| [396] | Malek Zribi | Claude, Codex, GPT | 15 Mar, 2026 | π‘ Partial result |
| [396] | Justin Dehorty, Nat Sothanaphan | GPT-5.4 Pro, GPT-5.4 Thinking | 5-7 Apr, 2026 | π‘ Related result |
| [401] | Boris Alexeev, Kevin Barreto, Liam Price, Nat Sothanaphan | Aristotle, GPT-5.2 Pro | 10-11 Jan, 2026 | π’ Full solution (Lean); solution to variant problem |
| [411] | hoodieuser | Claude | 3 Apr, 2026 | π΄ Incorrect proof found |
| [415] | Przemek Chojecki | GPT-5.4 Pro | 19 Apr, 2026 | π‘ Partial result |
| [423] | Quanyu Tang, Nat Sothanaphan | GPT-5.2 Thinking, GPT-5.4 Thinking | 11-12 Mar, 2026 | π‘ Partial result |
| [451] | Wouter van Doorn, Quanyu Tang | Aristotle, GPT-5.5 Pro | 26 Apr-19 Jun, 2026 | π‘ Partial result (Lean) |
| [456] | David Turturean | GPT-5.5 Pro | 4 May, 2026 | βͺ Candidate partial result (solutions to first part and second part; conditional solution to third part) |
| [460] | Przemek Chojecki | GPT-5.2 | 13 Jan, 2026 | π‘ Reduction to a simpler problem |
| [488] | Przemek Chojecki | Aristotle, GPT-5.4 | 20 Mar, 2026 | π‘ Partial result |
| [501] | Sungchul Lee | GPT-5.5 Pro | 29 May-1 Jun, 2026 | βͺ Candidate conditional partial result (conditional solution to first part) |
| [503] | Przemek Chojecki | Aristotle, GPT-5.4 Pro | 22 Apr, 2026 | π΄ Argument with major gaps made |
| [503] | Przemek Chojecki, Junnosuke Koizumi, RealBelgian | GPT-5.5 Pro | 27-28 May, 2026 | π‘ Partial result |
| [514] | Przemek Chojecki | GPT-5.4 Pro | 20 Apr, 2026 | π‘ Partial result (solutions to first part and second part) |
| [514] | Yuta Oriike | GPT-5.5 Pro | 28 Apr, 2026 | π‘ Partial result (Lean) (solution to third part) |
| [521] | Vjekoslav KovaΔ | GPT-5.5 Pro | 25 Apr, 2026 | π‘ Solution to variant problem |
| [521] | Vjekoslav KovaΔ | GPT-5.5 Pro | 30 Apr, 2026 | βͺ Candidate full solution |
| [524] | Brayden Letwin, Mehtaab Sawhney | GPT-5.4 Pro | 21 Apr, 2026 | π‘ Partial result |
| [535] | Kireet Cheri, Sourish Kumrawat, Hrishi Sunder | GPT-5.5 Thinking | 27 Apr, 2026 | π‘ Partial result (implicit in literature) |
| [598] | Przemek Chojecki | Aristotle, GPT-5.4 Pro | 22 Apr, 2026 | βͺ Candidate partial result |
| [603] | Przemek Chojecki | GPT-5.4 Pro | 21 Apr, 2026 | π’ Full solution |
| [610] | Przemek Chojecki | Aristotle, GPT-5.4 Pro | 21 Apr, 2026 | π’ Full solution (Lean) (implicit in literature) |
| [623] | Sungchul Lee | GPT-5.5 Pro | 4 Jun, 2026 | βͺ Candidate full solution |
| [659] | Benjamin Grayzel | Gemini 3 | 13 Jan, 2026 | π’ Full solution |
| [675] | Boon Suan Ho | GPT-5.4 Pro | 18 Apr, 2026 | π‘ Partial result |
| [684] | Quanyu Tang | GPT-5.2 Thinking | 19 Jan, 2026 | π‘ Partial result |
| [684] | Nat Sothanaphan | GPT-5.4 Thinking | 2 Apr, 2026 | π‘ Partial result |
| [686] | Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav KovaΔ, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc, Malek Zribi | AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro | 9 Aug, 2025-15 Mar, 2026 | π‘ Various partial results |
| [689] | Boris Alexeev, Przemek Chojecki, Dogmachine, jleng01, Mehtaab Sawhney, Terence Tao, Malek Zribi | Codex, GPT-5.2, GPT-5.5 Pro | 29 Oct, 2025-2 Jun, 2026 | βͺ Candidate full solution |
| [690] | Davide Crapis, Shouqiao Wang | Multiscalar Fields System | 8 May, 2026 | π’ Full solution |
| [696] | Jake Mallen, David Turturean | Aristotle, Claude Code, Claude Opus 4.7, GPT-5.5 Pro | 26 Apr-5 Jun, 2026 | π’ Full solution (Lean) |
| [749] | Aron Bhalla | GPT-5.4 Thinking | 4-6 Apr, 2026 | π‘ Partial result; π‘ Solution to variant problem |
| [750] | Przemek Chojecki | GPT-5.5 Pro | 3 May, 2026 | π’ Full solution |
| [776] | Yixin He, Quanyu Tang | GPT-5.2 Thinking | 11 Feb, 2026 | π‘ Partial result |
| [819] | Yu Leon Liu | GPT-5.5, Rethlas | 15 May, 2026 | βͺ Candidate partial result |
| [848] | Malek Zribi | Claude Opus 4.6, GPT-5.4 | 12-15 Mar, 2026 | π΄ Incorrect proof found |
| [848] | Mehtaab Sawhney, Mark Sellke | GPT-5 | 12 Oct-20 Nov, 2025 | π’ Full solution |
| [852] | Aron Bhalla | GPT-5.4 | 15 Apr, 2026 | π‘ Partial result |
| [852] | Przemek Chojecki, David Turturean | GPT-5.5 Pro | 24 Apr, 2026 | βͺ Candidate partial result |
| [856] | Przemek Chojecki | GPT-5.4 Pro | 15 Apr, 2026 | βͺ Candidate full solution |
| [858] | Przemek Chojecki | GPT-5.4 Pro | 15 Apr, 2026 | π’ Full solution |
| [863] | Boon Suan Ho | GPT-5.4 Pro | 22 Apr, 2026 | π’ Full solution |
| [866] | Wouter van Doorn | Aristotle, GPT-5.3 Instant | 4 May, 2026 | π‘ Partial result (Lean) |
| [870] | David Turturean | GPT-5.4 Pro, GPT-5.5 Pro | 24 Apr-May 2, 2026 | βͺ Candidate full solution |
| [872] | Om_Buddhdev_sensho | GPT-5.4 Pro | 16 Apr, 2026 | π‘ Partial result |
| [872] | Jonas Silva | GPT-5.5 Pro | 29 Apr, 2026 | βͺ Candidate partial result |
| [873] | Ritvik Nayak | GPT-5.4 Thinking | 29 Apr, 2026 | βͺ Candidate partial result |
| [873] | Ingo AlthΓΆfer | GPT-5.5 Thinking | 30 Apr, 2026 | βͺ Candidate partial result |
| [875] | Lech Mazur | Codex, GPT-5.5 Pro | 7 May, 2026 | π‘ Partial result (Lean) |
| [888] | Przemek Chojecki | Aristotle, GPT-5.5 Pro | 25 Apr, 2026 | π’ Full solution |
| [896] | Przemek Chojecki | GPT-5.5 Pro | 26 Apr, 2026 | π’ Full solution |
| [906] | Adriano Almeida | Unspecified | 25 Apr, 2026 | βͺ Candidate full solution |
| [906] | Przemek Chojecki | GPT-5.5 Pro | 25 Apr, 2026 | βͺ Candidate full solution |
| [931] | Adenwalla, Malek Zribi | Claude, GPT-5.4 | 12 Mar-8 Jun, 2026 | π‘ Partial result |
| [942] | Scott Hughes | Aristotle, Claude Opus 4.8, Codex, GPT-5.5 | 13-14 Jun, 2026 | π‘ Partial result (Lean) |
| [943] | Przemek Chojecki | GPT-5.4 Pro | 3 Feb-18 Mar, 2026 | π‘ Partial result |
| [953] | Przemek Chojecki | GPT-5.5 Pro | 27 Apr, 2026 | π’ Full solution |
| [956] | Przemek Chojecki | Aristotle, GPT-5.5 Pro | 27 Apr, 2026 | βͺ Candidate full solution |
| [995] | Boon Suan Ho | GPT-5.4 Pro | 21 Apr, 2026 | π‘ Partial result |
| [996] | Boon Suan Ho | GPT-5.4 Pro | 21 Apr, 2026 | π’ Full solution |
| [951] | Nat Sothanaphan | GPT-5.2 Thinking | 28 Jan, 2026 | π‘ New solution to variant problem |
| [976] | Aron Bhalla | GPT-5.4 | 16 Apr, 2026 | π‘ Conditional partial result |
| [1026] | Boris Alexeev, Stijn Cambie, Terence Tao, Lawrence Wu | AlphaEvolve, Aristotle, Gemini, GPT | 8 Dec, 2025 | π’ Full solution (Lean) |
| [1038] | catsflowers5544, jspier, Junnosuke Koizumi, Kenneth Mendoza, Nat Sothanaphan, Terence Tao, Hua Xu | AlphaEvolve, Claude Fable 5, Codex, GPT-5.2 Thinking, GPT-5.4 Thinking, GPT-5.5 | 16 Dec, 2025-10 Jun, 2026 | π‘ Partial result |
| [1039] | Houi | Aristotle, Claude Opus 4.6 | 6-8 Mar, 2026 | π‘ Partial result (Lean) |
| [1041] | shtuka | Claude Opus 4.6, Gemini 3.1 Pro, GPT-5.4 | 17-24 Mar, 2026 | π΄ Argument with major gaps made |
| [1062] | Damek Davis | GPT-5.4 Pro | 19 Apr, 2026 | π‘ Partial result |
| [1092] | Przemek Chojecki | GPT-5.5 Pro | 28 Apr, 2026 | π’ Full solution |
| [1095] | shtuka | Claude Opus 4.6, Gemini 3.1 Pro, GPT-5.4 Pro | 13 Mar, 2026 | π‘ Partial result |
| [1132] | Terence Tao | AlphaEvolve, Claude, Gemini Pro, GPT-5.4 Pro | 2 Feb-24 Mar, 2026 | π‘ Partial result |
| [1133] | Przemek Chojecki | GPT-5.5 Pro | 29 Apr, 2026 | βͺ Candidate full solution |
| [1138] | Kireet Cheri, Sourish Kumrawat, Hrishi Sunder | GPT-5.5 Pro, GPT-5.5 Thinking | 25 Apr, 2026 | π’ Full solution |
| [1139] | Przemek Chojecki, gavinsherry, Liam Price, Terence Tao | GPT-5.2 Pro, GPT-5.5 Pro | 26 Jan-19 Jun, 2026 | βͺ Candidate full solution |
| [1141] | Quanyu Tang | GPT-5.2 Pro, GPT-5.2 Thinking | 25 Jan, 2026 | π‘ Partial result of variant problem |
| [1143] | Przemek Chojecki | GPT-5.5 Pro | 29 Apr, 2026 | π‘ Partial result (implicit in literature) |
| [1148] | Ingo AlthΓΆfer, Przemek Chojecki, Wouter van Doorn | Gemini 3 Pro, Gemini 3.1 Pro, GPT-5.2 Pro, GPT-5.2 Thinking, GPT-5.4 Pro | 24 Jan-16 Mar, 2026 | π’ Full solution |
| [1148] | Ingo AlthΓΆfer, Przemek Chojecki | GPT-5.5 Pro | 19 May, 2026 | π’ Solution to stronger problem |
| [1151] | Przemek Chojecki | GPT-5.5 Pro | 30 Apr, 2026 | π’ Full solution |
| [1153] | Aron Bhalla, Nat Sothanaphan, Terence Tao | AlphaEvolve, Claude, Gemini Pro, GPT-5.2 Thinking, GPT-5.4 Pro | 2 Feb-24 Mar, 2026 | π’ Full solution |
| [1183] | Przemek Chojecki, Quanyu Tang | GPT-5.4 Pro | 18 Mar, 2026 | π‘ Partial result |
| [1190] | Boon Suan Ho | GPT-5.4 Pro | 23 Apr, 2026 | π’ Full solution |
| [1190] | Przemek Chojecki | GPT-5.5 Pro | 30 Apr, 2026 | βͺ Candidate full solution |
| [1194] | Lech Mazur | Codex, GPT-5.5 Pro | 2 May, 2026 | π‘ Partial result (Lean) |
| [1195] | Boon Suan Ho | GPT-5.4 Pro | 19 Apr, 2026 | π’ Full solution |
| [1196] | Nat Sothanaphan | GPT-5.4 Thinking | 16 Apr, 2026 | π’ Full solution (stronger than literature) |
| [1201] | Przemek Chojecki | GPT-5.5 Pro | 30 Apr, 2026 | βͺ Candidate full solution |
| [1208] | Sungchul Lee | GPT-5.5 Pro | 14 Jun, 2026 | βͺ Candidate partial result |
| [1209] | Enrique Barschkis | GPT-5.4 Pro | 15 Apr, 2026 | π‘ Partial result (Lean) |
2. Secondary contributions
2(a). Literature search
| Problem | AI systems | Date | Outcome |
|---|---|---|---|
| [35] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [66] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [94] | GPT-5 | 2 Nov, 2025 | π’ Full solution found |
| [120] | GPT-5.4 Thinking | 14 Mar, 2026 | π’ Solution to variant problem found |
| [167] | GPT-5 | 12 Oct, 2025 | π‘ Partial results found |
| [188] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [214] | ChatGPT Deep research, Gemini Deep Research | 20 Feb, 2026 | π‘ Partial results found |
| [223] | GPT-5 | 13 Oct, 2025 | π’ Full solution found |
| [306] | GPT-5.2 Thinking | 25 Feb, 2026 | π‘ Partial results found |
| [325] | ChatGPT Deep research | 9 Mar, 2026 | π‘ Partial results found |
| [330] | ChatGPT Deep research, Claude, Gemini Deep Research | 19 Dec, 2025 | π΄ Partial results found with inaccuracies; literature proof not found |
| [333] | GPT-5.2 Pro | 25 Dec, 2025 | π΄ Incorrect proof claimed; literature proof not found |
| [333] | Aletheia | 1 Feb, 2026 | π’ Full solution found |
| [339] | GPT-5 | 11 Oct, 2025 | π’ Full solution found |
| [347] | ChatGPT Deep research | 25 Oct, 2025 | π‘ Partial results found |
| [354] | ChatGPT Deep research | 19 Oct, 2025 | π‘ Partial results found |
| [370] | ChatGPT Deep research, Gemini, Gemini Deep Research | 17 Oct, 2025 | π‘ Problem found to be misstated; solutions to variant problems found |
| [387] | ChatGPT Deep research | 1 Nov, 2025 | π‘ Partial results found |
| [397] | ChatGPT Deep research | 10 Jan, 2026 | π’ Full solution found |
| [481] | ChatGPT Deep research, Gemini Deep Research | 1 Dec, 2025 | π‘ Unwittingly reproduced existing proof |
| [481] | GPT | 3 Dec, 2025 | π’ Full solution found |
| [494] | GPT-5 | 13 Oct, 2025 | π’ Full solution found |
| [515] | GPT-5 | 15 Oct, 2025 | π’ Full solution found |
| [516] | ChatGPT Deep research, Claude, Gemini Deep Research | 28 Dec, 2025 | π’ Problem found to be misstated; full solution to actual problem found |
| [524] | GPT-5.2 Pro | 27 Dec, 2025 | π‘ Partial results found |
| [533] | GPT | 26 Jan, 2026 | π’ Full solution found |
| [559] | ChatGPT Deep research, Gemini Deep Research | 26 Oct, 2025 | π‘ Partial results found |
| [574] | GPT-5.4 Pro | 28 Mar, 2026 | π’ Full solution found |
| [575] | GPT | 14 Jan, 2026 | π‘ Paper identifying a misstatement to the problem found |
| [591] | ChatGPT Deep research | 17 Jan, 2026 | π’ Full solution found |
| [591] | Aletheia | 1 Feb, 2026 | π’ Full solution found |
| [602] | GPT-5.4 Thinking | 20 Apr, 2026 | π‘ Related results found |
| [621] | GPT-5 | 13 Oct, 2025 | π’ Full solution found |
| [645] | GPT-5 | 20 Oct, 2025 | π’ Full solution found |
| [650] | ChatGPT Deep research | 6 Mar, 2026 | π’ Full solution found |
| [652] | GPT-5.2 Pro | 17 Jan, 2026 | π’ Full solution by applying literature results |
| [652] | Aletheia | 2 Feb, 2026 | π’ Full solution by applying literature results |
| [659] | Gemini Deep Research | 13 Jan, 2026 | π‘ Partial results, upgradeable to full solution, found |
| [672] | GPT | 7 Jan, 2026 | π‘ Partial results found |
| [705] | GPT | 26 Jan, 2026 | π’ Full solution found |
| [705] | Aletheia | 1 Feb, 2026 | π’ Full solution found |
| [729] | ChatGPT Deep research | Jan 10, 2026 | π‘ Related results found |
| [737] | GPT-5 | 30 Sep, 2025 | π’ Full solution found |
| [749] | GPT-5.4 Thinking | 3 Apr, 2026 | π‘ Partial results found |
| [750] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [788] | GPT-5 | 14 Oct, 2025 | π‘ Partial results found |
| [793] | ChatGPT Deep research | 30 Nov, 2025 | π‘ Partial results found |
| [811] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [822] | GPT-5 | 13 Oct, 2025 | π’ Full solution found |
| [827] | GPT-5 | 14 Oct, 2025 | π‘ Partial results found |
| [829] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [847] | GPT-5.2 Pro | 19 Jan, 2026 | π’ Full solution found |
| [851] | ChatGPT Deep research, Claude, Gemini Deep Research | 5 Feb, 2026 | π΄π΄ Confused with another problem; π‘ Partial results found |
| [871] | ChatGPT Deep research | 6 Dec, 2025 | π‘ Partial results found |
| [903] | GPT-5 | 14 Oct, 2025 | π’ Full solution found |
| [915] | ChatGPT Deep research | 26 Oct, 2025 | π‘ Partial results found |
| [942] | ChatGPT Deep research | 23 Nov, 2025 | π‘ Partial results found |
| [965] | GPT | 2 Jan, 2026 | π’ Full solution found |
| [971] | Claude | 31 Jan, 2026 | π‘ Partial results found |
| [985] | GPT-5.4 Thinking | 6 Mar, 2026 | π‘ Partial results found |
| [990] | ChatGPT Deep research, Gemini Deep Research | 20 Oct, 2025 | π‘ Partial results found |
| [992] | Aletheia | 1 Feb, 2026 | π’ Full solution found |
| [1008] | GPT-5 | 29 Sep, 2025 | π’ Full solution found |
| [1011] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [1016] | ChatGPT Deep research, Gemini Deep Research | 18 Oct, 2025 | π‘ Partial results found |
| [1019] | ChatGPT Deep research, Gemini Deep Research | 18 Oct, 2025 | π‘ Solution claim found, but precise citation not found |
| [1021] | GPT | 21 Jan, 2026 | π’ Full solution (which was previously noted) found |
| [1043] | GPT-5 | 12 Oct, 2025 | π’ Full solution found |
| [1079] | GPT-5 | 13 Oct, 2025 | π’ Full solution found |
| [1084] | GPT | 21 Jan, 2026 | π‘ Partial results found |
| [1099] | ChatGPT Deep research, Gemini, Gemini Deep Research | 19 Oct, 2025 | π’ Full solution found |
| [1105] | ChatGPT Deep research | 19 Jan, 2026 | π‘ Partial results found |
| [1105] | Aletheia | 1 Feb, 2026 | π’ Full solution found; π΄ Gave some wrong references |
| [1123] | Gemini Deep Research | 31 Jan, 2026 | π’ Full solution found |
| [1124] | GPT | 31 Dec, 2025 | π’ Solution to variant problem found |
| [1129] | GPT-5.2 Pro | 17 Jan, 2026 | π’ Full solution found |
| [1130] | GPT-5.2 Pro | 17 Jan, 2026 | π’ Full solution found |
| [1147] | GPT-5.2 Thinking | 26 Jan, 2026 | π’ Full solution found |
| [1150] | Gemini Deep Research | 4 Feb, 2026 | π‘ Claimed solution found (likely incorrect) |
| [1154] | GPT-5.2 Thinking | 24 Jan, 2026 | π‘ Partial results found |
| [1161] | GPT-5.2 Thinking | 24 Jan, 2026 | π’ Full solution found |
| [1198] | GPT-5.4 | 16 Apr, 2026 | π‘ Partial results found |
| [1216] | ChatGPT Deep research | 10 Mar, 2026 | π’ Solution stronger than problem found |
| [1216] | GPT-5.4 Thinking | 12 Apr, 2026 | π‘ Related results found |
2(b). Formalization
| Problem | Proof to formalize | AI systems | Date |
|---|---|---|---|
| [16] | π’ Chen (2023) | Antigravity, Gemini 3.1 Pro | 25 Feb, 2026 |
| [24] | π’ Grzesik (2012) | Aristotle | 23 Apr-26 May, 2026 |
| [26] | π’ Ruzsa | Aristotle | 28 Dec, 2025 |
| [31] | π’ Lorentz (1954), Wouter van Doorn (2025) | Aristotle, GPT | 24 Nov, 2025 |
| [34] | π’ Konieczny (2015) | Aristotle | 5 Feb, 2026 |
| [38] | π’ GPT-5.5 Pro (2026) | Aristotle | 1 May, 2026 |
| [42] | π’ GPT-5.5 Pro (2026) | Codex, GPT-5.5 Pro | 10 May, 2026 |
| [43] | π‘ Barreto (2025) | Aristotle, Claude | 21 Dec, 2025 |
| [56] | π’ Ahlswede and Khachatrian (1995) | Aristotle, GPT | 25 Nov, 2025-27 May, 2026 |
| [71] | π’ BollobΓ‘s (1977) | Aristotle, Claude Opus 4.7, GPT-5.5 | 24 May, 2026 |
| [90] | π’ OpenAI internal model (2026) | Aleph Prover | 28 May-12 Jun, 2026 |
| [93] | π’ Altman (1963) | Aristotle, Claude Opus 4.5, Claude Opus 4.6, Gemini 3 Flash, Gemini 3 Pro, Numina Lean Agent | 17 Feb, 2026 |
| [94] | π’ Lefmann and Thiele (1995) | Codex, GPT-5.2 Thinking; Seed Prover | 15 Jan, 2026 |
| [105] | π’ Xichuan (2025) | Aristotle, GPT Pro | 17 Nov, 2025 |
| [106] | π‘ Baek, Koizumi, and Ueoro (2024) | Aristotle | 10 Dec, 2025 |
| [115] | π’ Eremenko and Lempert (1994) | Aristotle, Claude Opus 4.6, Claude Sonnet 4.6, Gemini 3 Flash, Gemini 3.1 Pro, ulam.ai scaffold with Gemini 3 Flash and Gemini 3.1 Pro | 3 Mar, 2026 |
| [134] | π’ Alon | Aristotle | 7 Feb, 2026 |
| [150] | π’ BradaΔ (2024) | Aristotle | 31 Mar, 2026 |
| [154] | π’ LindstrΓΆm (1998) | Aristotle, GPT | 6 Feb, 2026 |
| [164] | π’ Alexeev, Barreto, Li, Lichtman, Price, Shah, Tang, and Tao (2026) | Codex | 4 May, 2026 |
| [165] | π‘ Hefty, Horn, King and Pfender (2025) | Trellis | 10 Jun, 2026 |
| [178] | π’ Beck (1981) | Aristotle | 21 Apr, 2026 |
| [189] | π’ KovaΔ (2023) | Aristotle, Gemini 3 Pro | 17 Dec, 2025 |
| [192] | π’ KerΓ€nen (1992) | Aristotle | 9-10 May, 2026 |
| [194] | π’ Ardal, Brown, and JungiΔ (2011) | Aristotle | 15 Apr, 2026 |
| [198] | π’ Baumgartner (1975) | Aristotle, GPT | 24 Nov, 2025 |
| [199] | π’ Baumgartner (1975) | Aristotle | 24 Feb, 2026 |
| [202] | π’ Boon Suan Ho and GPT-5.4 Pro (2026) | Unspecified | 14 May, 2026 |
| [204] | π’ Adenwalla (2025) | Aristotle | 15 Mar, 2026 |
| [206] | π’ KovaΔ (2024) | Aristotle | 28 Apr, 2026 |
| [209] | π’ Escudero (2016) | AxiomProver | 19 Jun, 2026 |
| [214] | π’ JuhΓ‘sz (1979) | Aristotle | 2 Mar, 2026 |
| [221] | π’ Ruzsa (1972) + van Doorn (2025) | Aristotle | 31 Jan, 2026 |
| [226] | π’ Sato and Rankin (1974) | Aristotle | 29 Dec, 2025 |
| [229] | π’ Barth and Schneider (1972) | Aristotle | 28 Dec, 2025 |
| [231] | π’ KerΓ€nen (1992) | Aristotle | 9 May, 2026 |
| [237] | π’ Chen and Ding (2022) | Aristotle | 4 Apr, 2026 |
| [246] | π’ Birch (1959) | Aristotle | 28 Dec, 2025 |
| [258] | π’ GPT-5.4 Pro (2026) | Aristotle | 14 Apr, 2026 |
| [259] | π’ Chen and Ruzsa (1999) | Aristotle | 21 Apr, 2026 |
| [268] | π’ KovaΔ (2024) | Aristotle | 13 Apr-26 May, 2026 |
| [275] | π’ Balister, Bollobas, Morris, Sahasrabudhe, and Tiba (2020) | Aristotle | 20 Jan, 2026 |
| [280] | π’ Cambie (2025) | Aristotle | 18 Apr, 2026 |
| [281] | π’ GPT-5.2 Pro (2026) | Aristotle, Gemini 3 Flash | 19 Jan, 2026 |
| [283] | π‘ van Doorn (2025) | Aristotle | 28 Mar, 2026 |
| [283] | π’ Barreto, GPT-5.5 Pro, and Price (2026) | Claude Opus 4.7, GPT-5.5 Pro | 6 May, 2026 |
| [290] | π’ van Doorn (2024) | Aristotle | 14 Jan, 2026 |
| [296] | π’ Hunter and Sawhney | Aristotle | 22 Apr-26 May, 2026 |
| [303] | π’ Brown and RΓΆdl (1991) | Seed Prover | 21 Dec, 2025 |
| [314] | π’ Lim and Steinerberger (2024) | Aristotle | 1 Apr, 2026 |
| [315] | π’ Kamio (2025) | Aristotle | 31 Jan, 2026 |
| [328] | π’ NeΕ‘etΕil and RΓΆdl (1985) | AxiomProver | 19 Jun, 2026 |
| [330] | π’ GPT-5.5 Pro and Turturean (2026) | Codex, GPT-5.5 Pro | 5 May, 2026 |
| [331] | π’ Ruzsa | Aristotle | 31 Jan, 2026 |
| [337] | π’ Ruzsa and TurjΓ‘nyi (1985) | Aristotle | 10 Dec, 2025 |
| [350] | π’ Ryavec (1974) | Aristotle, GPT | 25 Nov, 2025 |
| [351] | π’ Barreto, GPT-5.5 Pro, and Price (2026) | Claude Opus 4.7, GPT-5.5 Pro | 6 May, 2026 |
| [355] | π’ van Doorn and KovaΔ (2025) (almost the entirety) | Aristotle, Gemini 3 | 30 Jan-13 Mar, 2026 |
| [363] | π’ Ulas (2005) | Aristotle | 10 Mar, 2026 |
| [367] | π‘ van Doorn and Tao (2025) | Aristotle | 22 Nov, 2025 |
| [368] | π‘ PΓ³lya (1918) | Aristotle | 17 Feb, 2026 |
| [369] | π’ GPT and Yang (2026) | Aristotle | 27 Mar, 2026 |
| [370] | π’ Steinerberger (2025) | Aristotle, GPT | 24 Nov, 2025 |
| [392] | π’ Tao (2026) | Various | 6 Jan-23 Feb, 2026 |
| [399] | π’ Barfield (2025) | Codex | Feb 2026 |
| [403] | π’ Unspecified | AxiomProver | 19 Jun, 2026 |
| [418] | π’ Browkin and Schinzel (1995) | Aristotle, GPT | 22 Nov, 2025 |
| [419] | π’ Sawhney (2025) | Aristotle | 31 Jan, 2026 |
| [425] | π’ ErdΕs (1938) | Aristotle, GPT | 5-17 May, 2026 |
| [426] | π’ BradaΔ and Christoph (2024) | Aristotle | 20 Apr, 2026 |
| [427] | π’ Pilatte | Aristotle | 26 Apr, 2026 |
| [429] | π’ Weisenberg (2024) | Aristotle | 29 Jan, 2026 |
| [433] | π’ Dixmier (1990) | Aristotle, Claude Opus 4.8, Claude Sonnet 4.6, Gemini 3 Flash, Gemini 3.1 Pro, Project Numina | 24 Feb-29 May, 2026 |
| [434] | π’ Continued from [433] formalization | Aristotle, Claude Opus 4.8 | 24 Feb-29 May, 2026 |
| [435] | π’ Cambie (2025) | Aristotle | 4 Feb, 2026 |
| [441] | π‘ Chen and Dai (2007) | AxiomProver | 19 Jun, 2026 |
| [443] | π’ HegyvΓ‘ri (2025) | Aristotle | 4 Feb, 2026 |
| [447] | π’ Kleitman (1971) | Aristotle | 10 Feb, 2026 |
| [453] | π’ Pomerance (1979) | Aristotle | 31 Jan, 2026 |
| [459] | π’ Cambie (2026) | Aristotle | 11 Mar, 2026 |
| [476] | π’ Alon, Nathanson, and Ruzsa (1995) | Aristotle | 31 Dec, 2025 |
| [480] | π’ Chung and Graham (1984) | Aristotle | 28 Nov, 2025 |
| [481] | π’ Barreto (2025) | Aristotle, Claude | 1 Dec, 2025 |
| [484] | π’ ErdΕs, SΓ‘rkΓΆzy, and SΓ³s (1989) | Aristotle | 15 Apr, 2026 |
| [487] | π’ Kleitman (1971) | Aristotle | 16 Feb, 2026 |
| [490] | π’ SzemerΓ©di (1976) | Aristotle, GPT-5.5 Pro | 17 May, 2026 |
| [497] | π’ Kleitman (1969) | Aristotle | 4 Feb, 2026 |
| [498] | π’ Kleitman (1965) | Aristotle, Claude Opus, Gemini Flash, Gemini Pro | Jan 27, 2026 |
| [499] | π’ Marcus and Minc (1962) | Aristotle | 29 Nov, 2025 |
| [502] | π’ Petrov and Pohoata (2021) | Aristotle | 2 Feb, 2026 |
| [505] | π’ Kahn and Kalai (1993) | Aristotle | 2 Feb, 2026 |
| [519] | π’ Atkinson (1961) | Aristotle | 19 Apr, 2026 |
| [537] | π’ Ruzsa | Aristotle | 6 Feb, 2026 |
| [540] | π’ SzemerΓ©di (1970) | Aristotle | 15 Apr, 2026 |
| [541] | π’ Grynkiewicz (2011) | Aristotle, GPT | 30 Dec, 2025 |
| [582] | π’ Folkman (1970) | Aristotle | 5 Feb, 2026 |
| [603] | π’ Chojecki and GPT-5.4 Pro (2026) | Codex, GPT-5.5 | 17 May, 2026 |
| [613] | π’ Pikhurko (2001) | GPT Pro | 4 Nov, 2025 |
| [618] | π’ Alon | Aristotle | 8 Feb, 2026 |
| [621] | π’ Norin and Sun (2016) | Aristotle | 19 Apr, 2026 |
| [639] | π’ Keevash and Sudakov (2004) | Aristotle | 3 May, 2026 |
| [645] | π’ Brown and Landman (1999) | Aristotle, GPT | 23 Nov, 2025 |
| [646] | π’ Berend (1997) | Aristotle | 27 Feb, 2026 |
| [648] | π’ Cambie (2025) | Aristotle | 4 Feb, 2026 |
| [649] | π’ Tong; Sampaio | Aristotle, GPT | 7 Feb-1 Jun, 2026 |
| [650] | π’ He, Li and Tang (2026) | Aristotle | 6-8 Mar, 2026 |
| [658] | π’ Solymosi (2004) | Aristotle | 20 Apr, 2026 |
| [659] | π’ Gemini and Grayzel (2026) | Aristotle | 14 Jan, 2026 |
| [666] | π’ Chung (1992), Brouwer, Dejter, and Thomassen (1993) | Aristotle | 6 Feb, 2026 |
| [678] | π’ Cambie (2025) | Aristotle | 7 Jan, 2026 |
| [692] | π’ Cambie (2025) | Aristotle | 2 Apr, 2026 |
| [694] | π’ GPT-5.5 Pro (2026) | Aristotle, Claude Code, Claude Opus 4.7, GPT-5.5 Pro | 3 May-5 Jun, 2026 |
| [698] | π’ Bergman (2011) | Aristotle | 16 Jan, 2026 |
| [707] | π’ Hall (1947) | GPT | 23 Nov, 2025 |
| [728] | π’ Pomerance (2026) | Aristotle | 22 Jan, 2026 |
| [750] | π’ Chojecki and GPT-5.5 Pro (2026) | Claude Code, Claude Opus 4.7, GPT-5.5 Pro | 4 May, 2026 |
| [751] | π’ Bondy and Vince (1998) | GPT-5.2-Codex, GPT-5.2 Thinking | 27 Jan, 2026 |
| [753] | π’ Alon (1992) | Aristotle | 14 Apr, 2026 |
| [756] | π’ Bhowmick (2024) | Aristotle | 15 Mar, 2026 |
| [760] | π’ Alon, Krivelevich, and Sudakov (1997) | Aristotle | 23 Apr-2 Jun, 2026 |
| [762] | π’ Steiner (2024) | Aristotle, Claude Opus 4.7, GPT | 8 Feb-3 Jun, 2026 |
| [765] | π’ Aigner and Ziegler (1998) | Aristotle | 16 May, 2026 |
| [775] | π’ Gao (2025) | Aristotle | 19 Apr-3 Jun, 2026 |
| [785] | π‘ Narkiewicz (1959/60) + π’ Ruzsa (2015) | Aristotle | 6 Mar, 2026 |
| [788] | π‘ GPT-5.2 Pro (2026) | Aristotle | 20 Jan, 2026 |
| [794] | π’ Harris (2025) | Aristotle | 5 Feb, 2026 |
| [798] | π’ Alon (1991) | Aristotle | 8 May, 2026 |
| [818] | π’ Solymosi (2009) | Aristotle | 25 Apr, 2026 |
| [835] | π‘ Likely folklore | AlphaProof | 26 Dec, 2025 |
| [844] | π’ ChvΓ‘tal (1974) + Weisenberg | Aristotle | 26 Apr, 2026 |
| [845] | π’ van Doorn and Everts (2025) | Aristotle | 8 Jan, 2026 (one form of result), 21 Jan, 2026 (second form) |
| [848] | π’ Sawhney (2025) | Aristotle, Claude, GPT-5.2 | 28 Jan, 2026 |
| [862] | π’ Saxton and Thomason (2015) | Aristotle | 21 Jan, 2026 |
| [867] | π’ Freud (1993) | Aristotle | 7 Apr, 2026 |
| [897] | π’ ErdΕs and Wirsing (1975) | Aristotle | 27 Nov, 2025 |
| [898] | π’ Barrow and Mordell (1937) | Aristotle, Gemini 3 Flash | 28 Jan, 2026 |
| [904] | π’ BollobΓ‘s and Nikiforov (2005) | Aristotle | 18 Apr, 2026 |
| [905] | π’ KhadΕΎiivanov and Nikiforov (1979) | Aristotle, GPT-5.4 | 7 Apr, 2026 |
| [907] | π’ de Bruijn (1951) | Aristotle | 7 Apr, 2026 |
| [914] | π’ Kierstead and Kostochka (2008) | Aristotle | 15 Apr, 2026 |
| [923] | π’ RΓΆdl (1977) | Aristotle | 20 Apr, 2026 |
| [927] | π’ Spencer (1971) | Aristotle | 5 Jun, 2026 |
| [947] | π’ Mirsky and Newman + Davenport and Rado | Aristotle, GPT | 2 Feb, 2026 |
| [958] | π’ Clemen, Dumitrescu, and Liu (2025) | Seed Prover 1.5 | 19 Dec, 2025 |
| [964] | π’ Eberhard (2025) | Antigravity, Aristotle, Gemini | 14 Feb, 2026 |
| [967] | π’ Yip (2025) | Aristotle | 19 Dec, 2025 |
| [974] | π’ Tijdeman (1966) | Aristotle | 27 Apr, 2026 |
| [986] | π‘ BradaΔ (2026) | Trellis | 10 Jun, 2026 |
| [990] | π’ OpenAI internal model (2026) | GPT-5.4 Pro | 10 Apr, 2026 |
| [997] | π’ OpenAI internal model (2026) | Aristotle | 1 Apr, 2026 |
| [1000] | π’ Haight | Aristotle, GPT | 28 Dec, 2025 |
| [1007] | π’ House (2013) | Aristotle | 19 Jan, 2026 |
| [1008] | π’ Conlon, Fox, and Sudakov (2014) | Aristotle | 17 Jan, 2026 |
| [1022] | π’ KoishiChan (2025) | Aristotle | 22 Jan, 2026 |
| [1023] | π’ Kleitman (1971) | Aristotle | 10 Feb, 2026 |
| [1028] | π’ ErdΕs (1963); ErdΕs and Spencer (1971) | Aristotle | 19 Jan, 2026 |
| [1034] | π’ Ma and Tang (2025) | Aristotle | 4 Dec, 2025 |
| [1036] | π’ Shelah (1998) | Aristotle | 20 Jan, 2026 |
| [1037] | π’ Cambie, Chan, and Hunter (2025) | Aristotle | 19 Jan, 2026 |
| [1039] | π‘ GPT-5.5 Pro (2026) | Codex, GPT-5.5 | 15 May, 2026 |
| [1044] | π’ Tang (2026) | Aristotle | 28 Apr, 2026 |
| [1048] | π’ Pommerenke (1961) | Aristotle | 27 Jan, 2026 |
| [1067] | π’ Bowler and Pitz (2024) | Aleph Prover, Aristotle | 28 Jan, 2026 |
| [1071] | π’ Danzer; Alexeev (2026) | Aleph Prover, Aristotle, GPT | 29 Jan, 2026 (second part); 12 Feb, 2026 (first part) |
| [1080] | π’ De Caen and SzΓ©kely (1992) | Aristotle | 28 Dec, 2025 |
| [1098] | π’ Neumann (1976) | Aristotle | 25 Apr, 2026 |
| [1102] | π’ van Doorn and Tao (2025) | Aristotle | 23 Feb, 2026 |
| [1121] | π’ Goodman and Goodman (1945) | Aristotle | 16 Apr, 2026 |
| [1125] | π’ Laczkovich (1984) | Aristotle | 11 Apr, 2026 |
| [1126] | π’ de Bruijn (1966) | Aristotle | 27 Feb, 2026 |
| [1134] | π’ Unspecified | AxiomProver | 19 Jun, 2026 |
| [1136] | π’ MΓΌller (2011) | Aristotle | 19 Apr, 2026 |
| [1138] | π’ Cheri, Kumrawat, and Sunder (2026) | Aristotle | 4 May, 2026 |
| [1141] | π’ OpenAI internal model (2026) | GPT-5.4 Pro | 11 Apr, 2026 |
| [1148] | π’ Chojecki (2026) | Claude Opus 4.6, Gemini 3.1, GPT-5.4, UlamAI Prover | 17 Mar, 2026 |
| [1151] | π’ Chojecki (2026) (main part) | Codex, GPT | 6 May, 2026 |
| [1187] | π’ Trivial (second part) | Codex, GPT-5.5 | 12 May, 2026 |
| [1190] | π’ Boon Suan Ho and GPT-5.4 Pro (2026) | Unspecified | 14 May, 2026 |
| [1193] | π’ Trivial | Aristotle | 13 Apr, 2026 |
| [1196] | π’ GPT-5.4 Pro (2026) | Gauss | 16 Apr, 2026 |
2(c). Rewriting
| Problem | AI systems | Date | Argument to rewrite |
|---|---|---|---|
| [281] | Gemini 3 Pro, GPT-5.2 Pro | 17 Jan, 2026 | π’ GPT-5.2 Pro (2026) |
| [392] | GPT-5.2 Thinking | 27 Feb, 2026 | π’ Tao (2026) |
| [457] | GPT-5.2 Thinking | 3 Mar, 2026 | π’ Tao (2026) (extension of problem) |
| [543] | GPT-5.2 Thinking | 23 Jan, 2026 | π’ GPT-5.2 Pro (2026) |
| [728] | Aristotle, GPT-5.2 Thinking | 5-7 Jan, 2026 | π’ Aristotle and GPT-5.2 Pro (2026) |
| [783] | GPT-5.2 Thinking | 24 Jan, 2026 | π‘ GPT-5.2 (2026) |
| [783] | GPT-5.2 Thinking | 21 Feb, 2026 | π‘ Tao (2026) |
| [846] | GPT-5.2 Thinking | 25 Feb, 2026 | π’ DeepMind prover agent (2026) |
| [1039] | GPT-5.5 Thinking | 8 May, 2026 | π‘ GPT-5.5 Pro (2026) |
| [1196] | GPT-5.4 Thinking | 20 Apr, 2026 | π’ Tao (2026) |
2(d). Computation
| Problem | AI systems | Date | Computation |
|---|---|---|---|
| [396] | Claude Opus 4.6, Gemini 3.1 Deep Think, GPT-5.4 Pro | 23 Mar-4 Apr, 2026 | OEIS sequence |
| [513] | GPT-5.2 Pro | 12 Feb, 2026 | Numerical certificate |
| [650] | AlphaEvolve | 7 Mar, 2026 | Numerical optimization |