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.
Introduction
For some further discussion of AI contributions, see the AI thread.
Color indicators
- π’: Full resolution.
- π‘: Partial progress.
- π΄: Incorrect work.
The π΄ (incorrect) refers to works that the humans interacting with AI initially understood to be correct but were later found incorrect. Occasional AI mistake does not automatically count. The purpose is to caution against errors rather than record all mistakes. Also, even if the work is incorrect, there could be some salvageable aspects.
An entry that does not fit these colors will not have a color indicator.
Section placement
Full details can be found here.
Disclaimers
Evaluation of AI contributions is complex and nuanced and cannot be captured by simple numerical metrics.
We have collected some disclaimers in this regard:
- 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
- Why is a social media announcement about AI solving an ErdΕs problem not reflected on this wiki?
- What to do when I think I managed to get AI to solve an ErdΕs problem?
- What to do when AI seems to make some partial progress on an ErdΕs problem?
External sources
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.
- Blog post "Is AI solving open ErdΕs problems?" by Zeyu Zheng, Jan 7, 2026.
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 |
| [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 |
| [64] | AlphaEvolve | 3 Nov, 2025 | No counterexample found |
| [75] | Aletheia | 1 Feb, 2026 | π‘ Solution (using prior literature) to previous formulation of the problem |
| [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 |
| [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) |
| [460] | GPT-5.2 Thinking | 14 Jan, 2026 | π‘ Cheap solution to previous formulation of the problem |
| [477] | AlphaProof | 7 Jan, 2026 | π‘ Solution to variant problem (Lean) |
| [486] | GPT-5.2 | 11 Jan, 2026 | π‘ Cheap counterexample to previous formulation of the problem |
| [493] | AlphaEvolve | 3 Nov, 2025 | No counterexample found |
| [514] | GPT-5.2 Pro | 17 Jan, 2026 | π‘ Cheap counterexample to previous formulation of problem |
| [563] | GPT-5.2 Pro | 17 Jan, 2026 | π‘ Cheap counterexample to previous formulation of problem |
| [616] | Claude Sonnet 4.5, Gemini 3 Pro, GPT-5.2 Pro | 18 Jan, 2026 | π΄ Incorrect proof found |
| [647] | ChatGPT Deep research, DeepSeek DeepThink, Gemini | 28 Jan, 2026 | π΄ Incorrect proof found |
| [654] | Aletheia | 1 Feb, 2026 | π‘ Solution to one formulation of problem |
| [665] | GPT-5.2 Pro | 17 Jan, 2026 | π‘ Cheap counterexample to previous formulation of problem |
| [684] | OpenAI internal model | 31 Mar, 2026 | π‘ Partial result |
| [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 |
| [850] | GPT-5.2 Pro | 19 Jan, 2026 | π‘ Cheap counterexample to previous formulation of problem |
| [868] | GPT-5.2 multi-agent system | 13 Jan, 2026 | Did not find viable approach |
| [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 one formulation of 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 |
| [1040] | Aletheia | 1 Feb, 2026 | π‘ Solution to one part of problem; π΄ incorrect solution to other part |
| [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 |
| [1139] | GPT-5.2 | 26 Jan, 2026 | Initial exploration |
| [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‘ Elkies (2013); π’ China TST competition (2012) | 10 Jan, 2026; 14 Jan, 2026 | No (Elkies); Yes (TST) |
| [397] | Aletheia | 2 Feb, 2026 | π’ Full solution (Lean) | π‘ Elkies (2013); π’ China TST competition (2012) | 10 Jan, 2026; 14 Jan, 2026 | No (Elkies); Yes (TST) |
| [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 a 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 |
| [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) |
| [1077] | Aristotle | 24 Dec, 2025 | π‘ Trivial counterexample to previous formulation of problem (Lean) | π’ Jiang and Longbrake (2025) | 28 Dec, 2025 | No |
| [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) |
| [52] | AlphaEvolve | 3 Nov, 2025 | π‘ Bloom (2025) | Did not match past constructions |
| [67] | AlphaEvolve | 3 Nov, 2025 | π‘ Konev and Lisitsa (2015) | Did not match past constructions |
| [75] | GPT-5.4 Pro | 12 Apr, 2026 | π‘ ErdΕs, Hajnal, and SzemerΓ©di (1982) | π‘ Partial result |
| [106] | AlphaEvolve | 3 Nov, 2025 | π‘ HalΓ‘sz (1984) | Matched past construction |
| [124] | Gemini Deep Think | 30 Nov, 2025 | π‘ Aristotle (2025) | Did not reproduce a known partial result despite hints |
| [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); no progress on remaining open problems |
| [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 |
| [391] | AlphaEvolve | 3 Nov, 2025 | π’ Alexeev, Conway, Rosenfeld, Sutherland, Tao, Uhr, and Ventello (2025) | Did not match past constructions |
| [392] | Aristotle, GPT-5.2 Pro | 31 Dec, 2025 | π‘ ErdΕs and Graham (unpublished, 1980) + Cambie (2025) | Unable to reconstruct unpublished proof (which is now believed to be incomplete) |
| [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‘ Barreto, GPT-5.2-Pro, Aristotle (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, Leeham (2026) + GPT-5.2 Thinking, Sothanaphan (2026) [solution to one formulation of problem] | π‘ New solution to one formulation of 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) |
| [1007] | Aristotle | 19 Jan, 2026 | π’ House (2013); π’ Chaffee and Noble (2016) | π’ New proof found (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); no progress on remaining open problems |
| [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 |
|---|---|---|---|---|
| [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 |
| [138] | Nat Sothanaphan | GPT-5.4 Thinking | 10 Apr, 2026 | π‘ Partial result of variant problem |
| [342] | Przemek Chojecki | GPT-5.2 Pro, GPT-5.4 Pro | 20 Jan-23 Mar, 2026 | π‘ Partial result |
| [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) |
| [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 (Lean) |
| [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] | MalekZ | Claude, Gemini, GPT-5.4 | 12-15 Mar, 2026 | π΄ Incorrect proof found |
| [396] | MalekZ | 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, Leeham, Nat Sothanaphan | Aristotle, GPT-5.2 Pro | 10-11 Jan, 2026 | π’ Counterexample to alternate formulation; full solution to revised formulation (Lean) |
| [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 |
| [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 |
| [521] | Vjeko Kovac | GPT-5.5 Pro | 25 Apr, 2026 | π‘ Solution to variant problem |
| [524] | Brayden Letwin, Mehtaab Sawhney | GPT-5.4 Pro | 21 Apr, 2026 | π‘ 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) |
| [659] | Benjamin Grayzel | Gemini 3 | 13 Jan, 2026 | π’ Full solution (Lean) |
| [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, Vjeko Kovac, MalekZ, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc | 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 |
| [749] | Aron Bhalla | GPT-5.4 Thinking | 4-6 Apr, 2026 | π‘ Partial result; π‘ Solution to variant problem |
| [776] | Yixin He, Quanyu Tang | GPT-5.2 Thinking | 11 Feb, 2026 | π‘ Partial result |
| [848] | MalekZ | 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 |
| [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 |
| [872] | Om_Buddhdev_sensho | GPT-5.4 Pro | 16 Apr, 2026 | π‘ Partial result |
| [931] | MalekZ | Claude, GPT-5.4 | 12-15 Mar, 2026 | π‘ Partial result |
| [943] | Przemek Chojecki | GPT-5.4 Pro | 3 Feb-18 Mar, 2026 | π‘ Partial result |
| [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 one formulation of 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] | jspier, Junnosuke Koizumi, Nat Sothanaphan, Terence Tao | AlphaEvolve, GPT-5.2 Thinking, GPT-5.4 Thinking | 16 Dec, 2025-19 Mar, 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 |
| [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 |
| [1138] | Kireet Cheri, Sourish Kumrawat, and Hrishi Sunder | GPT-5.5 Pro, GPT-5.5 Thinking | 25 Apr, 2026 | π’ Full solution |
| [1141] | Quanyu Tang | GPT-5.2 Pro, GPT-5.2 Thinking | 25 Jan, 2026 | π‘ Partial result of variant problem |
| [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 |
| [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 |
| [1196] | Nat Sothanaphan | GPT-5.4 Thinking | 16 Apr, 2026 | π’ Full solution (stronger than literature) |
| [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 |
| [96] | ChatGPT Deep research | 12 Jan, 2026 | No new results found |
| [120] | GPT-5.4 Thinking | 14 Mar, 2026 | π’ Solution to variant problem found |
| [124] | ChatGPT Deep research, Gemini Deep Research | 30 Nov, 2025 | No significant results found |
| [167] | GPT-5 | 12 Oct, 2025 | π‘ Partial results found |
| [188] | GPT-5 | 13 Oct, 2025 | π‘ Partial results found |
| [203] | ChatGPT Deep research, Gemini Deep Research | 19 Oct, 2025 | No significant results found |
| [205] | ChatGPT Deep research | 10 Jan, 2026 | No significant 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 |
| [248] | Gemini Deep Research | 19 Oct, 2025 | No significant results found |
| [281] | ChatGPT Deep research, Claude, Gemini Deep Research | 17 Jan, 2026 | Failed to find the two literature results which, when combined, solve the problem |
| [288] | Claude | 2 Feb, 2026 | No significant results 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 |
| [334] | Gemini Deep Research | 19 Nov, 2025 | No significant results 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 |
| [367] | ChatGPT Deep research, Gemini Deep Research | 22 Nov, 2025 | No significant results found; did not find ErdΕs problems community proof |
| [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 |
| [401] | Claude | Jan 10, 2026 | No significant results found |
| [421] | ChatGPT Deep research, Gemini Deep Research | 18 Oct, 2025 | No significant results found |
| [434] | GPT-5 | 29 Oct, 2025 | Literature proof not 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 |
| [519] | ChatGPT Deep research | 31 Jan, 2026 | No significant results found |
| [524] | GPT-5.2 Pro | 27 Dec, 2025 | π‘ Partial results found |
| [533] | GPT | 26 Jan, 2026 | π’ Full solution found |
| [543] | ChatGPT Deep research, Claude, Gemini Deep Research | 21 Jan, 2026 | No significant results 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] | ChatGPT Deep research | 17 Jan, 2026 | Failed to find the literature result that essentially solves the problem |
| [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 |
| [686] | Gemini Deep Research, Gemini Deep Think, GPT | 18 Oct, 2025 | No significant results found |
| [689] | ChatGPT Deep research, Gemini Deep Research | 29 Oct, 2025 | No significant results found |
| [672] | GPT | 7 Jan, 2026 | π‘ Partial results found |
| [700] | ChatGPT Deep research | 17 Dec, 2025 | No significant results found |
| [705] | GPT | 26 Jan, 2026 | π’ Full solution found |
| [705] | Aletheia | 1 Feb, 2026 | π’ Full solution found |
| [707] | GPT | 22 Oct, 2025 | Literature proof not found |
| [728] | ChatGPT Deep research | 15 Dec, 2025 | No significant results 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 |
| [786] | ChatGPT Deep research, Gemini Deep Research | 18 Oct, 2025 | No significant 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 |
| [906] | ChatGPT Deep research, Gemini Deep Research | 17 Oct, 2025 | No significant results found |
| [915] | ChatGPT Deep research | 26 Oct, 2025 | π‘ Partial results found |
| [940] | ChatGPT Deep research | 24 Oct, 2025 | No significant results found |
| [942] | ChatGPT Deep research | 23 Nov, 2025 | π‘ Partial results found |
| [965] | GPT | 2 Jan, 2026 | π’ Full solution found |
| [967] | GPT-5 | 29 Oct, 2025 | No significant results 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 |
| [1002] | ChatGPT Deep research, Gemini Deep Research | 3 Nov, 2025 | No significant results 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 |
| [1022] | ChatGPT Deep research, Gemini Deep Research | 4 Dec, 2025 | No significant results found |
| [1038] | Gemini Deep Research | 16 Nov, 2025 | No significant results found |
| [1041] | GPT-5 | 16 Nov, 2025 | No significant results found |
| [1043] | GPT-5 | 12 Oct, 2025 | π’ Full solution found |
| [1044] | ChatGPT Deep research | 14 Jan, 2026 | No new significant results 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 |
| [1139] | ChatGPT Deep research | 24 Jan, 2026 | No significant results found |
| [1147] | GPT-5.2 Thinking | 26 Jan, 2026 | π’ Full solution found |
| [1148] | ChatGPT Deep research | 24 Jan, 2026 | No significant results found |
| [1150] | Gemini Deep Research | 4 Feb, 2026 | Claimed solution found |
| [1153] | ChatGPT Deep research | 1 Feb, 2026 | No new significant results found |
| [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, 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 |
| [43] | π‘ Barreto (2025) | Aristotle, Claude | 21 Dec, 2025 |
| [56] | π’ Ahlswede-Khachatrian (1995) | Aristotle, GPT | 25 Nov, 2025 |
| [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 |
| [178] | π’ Beck (1981) | Aristotle | 21 Apr, 2026 |
| [189] | π’ KovaΔ (2023) | Aristotle, Gemini 3 Pro | 17 Dec, 2025 |
| [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 |
| [204] | π’ Adenwalla (2025) | Aristotle | 15 Mar, 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 |
| [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, 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 |
| [290] | π’ van Doorn (2024) | Aristotle | 14 Jan, 2026 |
| [296] | π’ Hunter and Sawhney | Aristotle | 22 Apr, 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 |
| [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 |
| [355] | π’ van Doorn and Kovac (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’ Yang and GPT (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 |
| [418] | π’ Browkin and Schinzel (1995) | Aristotle, GPT | 22 Nov, 2025 |
| [419] | π’ Sawhney (2025) | Aristotle | 31 Jan, 2026 |
| [426] | π’ BradaΔ and Christoph (2024) | Aristotle | 20 Apr, 2026 |
| [429] | π’ Weisenberg (2024) | Aristotle | 29 Jan, 2026 |
| [433] | π’ Dixmier (1990) | Aristotle, Claude Sonnet 4.6, Gemini 3 Flash, Gemini 3.1 Pro, Project Numina, | 24 Feb, 2026 |
| [434] | Continued from [433] formalization | Aristotle | 24 Feb, 2026 |
| [435] | π’ Cambie (2025) | Aristotle | 4 Feb, 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 |
| [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 |
| [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 |
| [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, 2026 |
| [650] | π’ He, Li and Tang (2026) | Aristotle | 6-8 Mar, 2026 |
| [658] | π’ Solymosi (2004) | Aristotle | 20 Apr, 2026 |
| [659] | π’ Grayzel, Gemini (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 |
| [698] | π’ Bergman (2011) | Aristotle | 16 Jan, 2026 |
| [707] | π’ Hall (1947) | GPT | 23 Nov, 2025 |
| [728] | π’ Pomerance (2026) | Aristotle | 22 Jan, 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, 2026 |
| [762] | π’ Steiner (2024) | Aristotle, GPT | 8 Feb, 2026 |
| [775] | π’ Gao (2025) | Aristotle | 19 Apr, 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 |
| [818] | π’ Solymosi (2009) | Aristotle | 25 Apr, 2026 |
| [835] | π‘ Likely folklore | AlphaProof | 26 Dec, 2025 |
| [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 |
| [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 |
| [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-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 |
| [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 |
| [1136] | π’ MΓΌller (2011) | Aristotle | 19 Apr, 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 |
| [1193] | π’ Trivial | Aristotle | 13 Apr, 2026 |
| [1196] | π’ GPT-5.4 Pro (2026) | Gauss | 16 Apr, 2026 |
2(c). Artifact generation
| Problem | AI systems | Part of | Date | Artifacts |
|---|---|---|---|---|
| [69] | GPT | π’ Tao and TerΓ€vΓ€inen (2025) | 1 Dec, 2025 | Numerics and images |
| [114] | AlphaEvolve, Gemini | π‘ Tao (2025) | 13 Dec, 2025 | Initial numerics, code, and images |
| [248] | GPT | π’ Tao and TerΓ€vΓ€inen (2025) | 1 Dec, 2025 | Numerics and images |
| [513] | GPT-5.2 Pro | π‘ He and Tang (2026) | 12 Feb, 2026 | Code |
| [682] | GPT | π’ Gafni and Tao (2025) | 8 Aug, 2025 | Initial code |
| [946] | GPT | π‘ Tao and TerΓ€vΓ€inen (2025) | 1 Dec, 2025 | Numerics and images |
| [1153] | Gemini | π’ Tao (2026) | 27 Feb, 2026 | Initial code |
2(d). 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) |
| [1196] | GPT-5.4 Thinking | 20 Apr, 2026 | π’ Tao (2026) |
2(e). Computation
| Problem | AI systems | Date | Computation |
|---|---|---|---|
| [42] | Grok | 20 Jan, 2026 | Verification and exploration |
| [43] | Grok | 20 Jan, 2026 | Verification and exploration |
| [271] | Unspecified | 11 Jan, 2026 | OEIS sequence generation |
| [334] | Unspecified | 3 Mar, 2026 | OEIS sequence generation |
| [396] | Claude Opus 4.6, Gemini 3.1 Deep Think, GPT-5.4 Pro | 23 Mar, 2026 | OEIS sequence generation |
| [513] | GPT-5.2 Pro | 12 Feb, 2026 | Exploration |
| [650] | AlphaEvolve | 7 Mar, 2026 | Optimal construction found numerically |
| [684] | GPT | 20 Jan, 2026 | Exploration |
| [757] | GPT-5.2 Pro | 26 Feb, 2026 | Exploration |
| [783] | AlphaEvolve | 4 Feb, 2026 | Exploration |
| [860] | Claude Opus 4.5 | 16 Jan, 2026 | OEIS sequence location |
| [872] | GPT | 11 Jan, 2026 | OEIS sequence generation |
| [993] | Claude Opus 4.6, Gemini 3 Pro, GPT-5.2 Pro, GPT-5.3-Codex | 15 Feb-12 Mar, 2026 | Exhaustive verification and exploration |
| [1044] | GPT-5.2 Pro | 5 Jan, 2026 | Exploration |
3. Pending assessment
| Problem | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| [38] | GPT-5.5 Pro | 25 Apr, 2026 | π’ Full solution? | |||
| [202] | Boon Suan Ho | GPT-5.4 Pro | 23 Apr, 2026 | π’ Full solution? | ||
| [330] | David Turturean | GPT-5.5 Pro | 24 Apr, 2026 | π’ Full solution? | ||
| [503] | Przemek Chojecki | Aristotle, GPT-5.4 Pro | 22 Apr, 2026 | π‘ Partial result? | ||
| [514] | Przemek Chojecki | GPT-5.4 Pro | 20 Apr, 2026 | π‘ Partial result? | ||
| [598] | Przemek Chojecki | Aristotle, GPT-5.4 Pro | 22 Apr, 2026 | π‘ Partial result? | ||
| [675] | Boon Suan Ho | GPT-5.4 Pro | 18 Apr, 2026 | π‘ Partial result? | ||
| [852] | Przemek Chojecki, David Turturean | GPT-5.5 Pro | 24 Apr, 2026 | π‘ Partial result? | ||
| [856] | Przemek Chojecki | GPT-5.4 Pro | 15 Apr, 2026 | ? | ||
| [870] | David Turturean | GPT-5.4 Pro, GPT-5.5 Pro | 24 Apr, 2026 | π’ Full solution? | ||
| [888] | Przemek Chojecki | Aristotle, GPT-5.5 Pro | 25 Apr, 2026 | ? | ||
| [896] | Przemek Chojecki | GPT-5.5 Pro | 26 Apr, 2026 | ? | ||
| [906] | Adriano Almeida | Unspecified | 25 Apr, 2026 | π’ Full solution? | ||
| [1190] | Boon Suan Ho | GPT-5.4 Pro | 23 Apr, 2026 | π’ Full solution? | ||
| [1195] | Boon Suan Ho | GPT-5.4 Pro | 19 Apr, 2026 | π’ Full solution? |