Written by: Gandalf, Techub News
Summary
On September 11, 2026, 25 Fields medalists released a statement titled A Severe Misalignment of AI in Mathematics as the first signatories. The statement does not deny the potential of AI-assisted mathematics; it criticizes the logic of announcing “solving famous problems” as a display of model capabilities and competitive metrics. The signatories argue that this narrows mathematical research from conceptual understanding, method dissemination, student training, and academic attribution, to high-speed production of “true/false” conclusions.
The immediate background of the statement is OpenAI’s claim on September 8 that its internal multi-agent system provided an example solution for the existence and smoothness of three-dimensional incompressible Navier–Stokes equations: constructed under smooth external forces with finite time singularity formation in fluid evolution. OpenAI also released a 166-page argument and Lean formal verification. The controversy is not just about the mathematical conclusion itself, but focuses on incomplete independent human review, prioritization and authorship of adjacent research results, and whether the data isolation and disclosure when researchers use products are sufficiently clear.
1. Positioning and Judgement of the Statement
The statement defines mathematics as a system of concepts, methods, abstractions, and tools accumulated across generations. Famous problems were originally “signposts” and “lighthouses”: their value lies in generating new ideas that can be discussed, simplified, written, taught, and ultimately reused by the community, rather than simply producing a final answer that can be deemed true or false.
Therefore, “severe misalignment” refers to the conflict of objective functions: AI companies measure progress by speed, ranking performance, and problem-solving completion; the mathematical community centers on understanding, explainable methods, reliable attribution, learnable, and transferrable knowledge. The statement also sees this as a precursor to a broader alignment issue between scientific and creative labor.
2. Core Demands of the Statement
Demand | Basis of the Statement | Operational Implications |
1. Give Mathematics Time to "Digest" | Rushing to announce results often lacks time for rigorous writing, separating new methods from new ideas, and for discussion and simplification. | Releases should not solely aim for speed; independent experts should be given time to read long proofs, reproduce formal verification environments, identify key lemmas, and clarify applicability and limitations. |
2. Transparency in Attribution and Citation | The statement clearly points out that hasty publication will often lack citations of prior work, leading to serious authorship and plagiarism issues. | Disclose the sources of issues, boundaries for hints and training/retrieval, relevant parallel work, toolchains, and contribution distribution; for research not yet public but potentially influenced by product data, stricter isolation, auditing, and explanation should be adopted. |
3. Human Digestion and Knowledge Transmission | Mathematical ideas must be disseminated through reports, private discussions, and detailed writing; without mathematicians nurturing and incorporating AI concepts into paradigms, they will not truly "come alive". | Transform results into understandable proofs, lecture notes, methodologies, and textbooks; maintain a training chain for students to form problem awareness and propose new questions through solving. |
Key Distinction
The statement does not advocate for the discontinuation of AI. Its conclusion acknowledges that AI can enhance and accelerate genuine mathematical learning and understanding; the condition is that humans make prudent choices regarding technical goals, publication pace, integration methods, and responsibilities.
3. The 25 Initial Signatories
The following list is organized in the order presented in the public statement; all 25 are Fields medalists, with award years ranging from 1978 to 2026.
No. | Signatory | Fields Medal Year |
1 | Artur Avila | 2014 |
2 | Manjul Bhargava | 2014 |
3 | Caucher Birkar | 2018 |
4 | Pierre Deligne | 1978 |
5 | Yu Deng | 2026 |
6 | Simon Donaldson | 1986 |
7 | Hugo Duminil-Copin | 2022 |
8 | Alessio Figalli | 2018 |
9 | Martin Hairer | 2014 |
10 | June Huh | 2022 |
11 | Maxim Kontsevich | 1998 |
12 | Elon Lindenstrauss | 2010 |
13 | Pierre-Louis Lions | 1994 |
14 | James Maynard | 2022 |
15 | Curt McMullen | 1998 |
16 | Shigefumi Mori | 1990 |
17 | Ngô Bảo Châu | 2010 |
18 | Andrei Okounkov | 2006 |
19 | Peter Scholze | 2018 |
20 | Stanislav Smirnov | 2010 |
21 | Terence Tao | 2006 |
22 | Maryna Viazovska | 2022 |
23 | Cédric Villani | 2010 |
24 | Wendelin Werner | 2006 |
25 | Efim Zelmanov | 1994 |
4. OpenAI Navier–Stokes Controversy Timeline
Note: The following distinguishes between “party statements” and “publicly verifiable technical status.” Lean formal verification checks the logical link between verified formal code and its definitions and theorems, but does not automatically replace human review of modeling choices, problem mapping, research novelty, and scientific explanation.
Date | Event | Significance and Controversy |
From August 28 | OpenAI claims to have started training a new internal model, training is still ongoing. | The model performance and training boundaries become the backdrop for subsequent controversy over whether user input could affect results. |
September 1 | OpenAI claims to have heard rumors that “two Millennium Prize problems have been solved,” and subsequently let the multi-agent system assess all unsolved Millennium problems and several high-impact problems. | OpenAI stated that initially they did not know the rumors pointed to the work of Alpöge and Buckmaster. |
September 5 | OpenAI stated that about 10,000 concurrent agents obtained Navier–Stokes results after approximately 88 hours; subsequently, about 17 hours of Lean formalization and verification was completed by GPT-6 Astra. | OpenAI disclosed the Navier–Stokes process involved about 2.7 million messages and approximately 130 billion output tokens. |
September 6 | OpenAI stated that after the Lean verification was completed, they contacted two mathematicians, proposed simultaneous publication, and acknowledged their priority; they later learned that the results were a forced Euler solution, rather than Navier–Stokes. | There was sharp disagreement between the parties over the timing of contact, wording of communications, joint publication, and how credits should be allocated. |
September 7 | Tristan Buckmaster (New York University) and Levent Alpöge (Anthropic) publicly released three works: finite time blow-up of incompressible porous media driven by smooth external forces, Boussinesq and three-dimensional incompressible Euler equations with finite time blow-up, accompanied by Lean formalization. | This is not a public full Navier-Stokes solution; but Euler is closely related to Navier-Stokes, and this result triggered prioritization, similar pathways, and citation issues. |
September 8 | OpenAI officially announced that its internal system provided a finite-time singularity proof for three-dimensional incompressible Navier–Stokes, claiming to meet cases C and D in the Clay formulation; it released a 166-page writing and Lean formalization, stating it would not claim a prize. | The company described the proof as a “forced” Navier-Stokes: initial stationary fluid under smooth external force can develop singularities in finite time; thus refuting the direction that “all smooth solutions are always smooth.” |
September 8 - 10 | Public opinion and the mathematical community focused discussions on priority, data isolation, independent review, and authorship. OpenAI initially stated that it could not completely rule out the possibility of de-identified product usage data affecting the model, on September 10, it updated to confirm that investigations found that Buckmaster’s Codex prompts over the past two months could not influence the system (including training). | The core issue is not confirmed misuse but demands for transparency and auditability; Buckmaster also stated he had not seen OpenAI’s proof and did not directly accuse them of using data. |
September 11 | 25 Fields medalists released A Severe Misalignment of AI in Mathematics. | The debate escalated from a dispute over the priority of a single result to systemic criticism of the incentives for AI mathematics publishing, the academic ecology, and knowledge transmission. |
5. Core Rebuttals and Responses from Various Mathematicians
Subject/Representative | Core Viewpoint | How to Understand |
Buckmaster and Alpöge | What they publicly released are results of finite-time blow-up of forced Euler and other adjacent fluid equations, not an already public full Navier-Stokes solution. Buckmaster expressed concerns over OpenAI's rapid release after being aware of their progress, the arrangement of credits during interactions, and that their research had existed on OpenAI's product servers; he also explicitly stated, “I do not know if their data was used,” and “I do not accuse anyone.” | This is a questioning of the narrative around programs, information boundaries, and priority, not an allegation of plagiarism that has been verified. The key point is: when AI products serve researchers and advance model development, there must be a verifiable firewall between user research content and model development. |
OpenAI | The company stated that researchers and agents did not see each other's work in any way before public release nor accessed specific user data; investigations found that Buckmaster’s Codex prompts over the past two months could not influence the system or training. The company also claims significant differences between both proofs: the counterpart's is a forced Euler, while OpenAI’s Euler result is unforced; Navier-Stokes claims have another proof. | This is a direct denial of data usage and technical independence. This denial reduces the inferences of “direct appropriation,” but the external community still needs to assess the sufficiency of investigation disclosures, independent review, and methodological context. |
Gregory Eyink (Johns Hopkins University) | Although Lean has checked the formalization, no one has yet fully verified the 166-page proof at a human level; he believes the most severe and ongoing issue is how contributions are attributed when AI is involved. | Formal verification complements rather than replaces peer understanding: the former excels at mechanical correctness, while the latter is responsible for discovering conceptual errors, confirming problem equivalence, explaining innovations, and establishing usable knowledge. |
Dallas Albritton (University of Wisconsin-Madison) | If the conclusion holds, it would be a huge mathematical event because this problem has long been a “guiding issue” in the field. | This viewpoint illustrates that maintaining caution regarding achievements does not mean denying their potential significance; on the contrary, the higher the significance, the more careful, independent, and teachable the review needs to be. |
25 Signatories (according to Terence Tao's blog statement) | Rebutting the premise of “solving the problem” as the endpoint of mathematical research. Rapid production of true/false assertions, if it cannot lead to ideas that are understandable, attributable, communicable, and capable of cultivating successors, may harm rather than nourish the soil of mathematics. | This is a systemic level criticism that does not depend on whether OpenAI's single proof ultimately holds. It demands that the display of AI capabilities be realigned to understanding, attribution, education, and community integration. |
6. Evaluation: What Has This Event Truly Changed
- “Formalized” does not equal “the community has digested”
Lean can provide a strong check for formal statements, but the mathematical community still needs to compress long proofs into key mechanisms, compare with existing literature, explain why constructs are valid, and confirm that they indeed meet the precise requirements of Clay’s problems.
- “Adjacent Results” also require precise attribution
Forced Euler, unforced Euler, and forced Navier-Stokes are technically different and cannot be simply viewed as the same result; however, they share ecological and methodological backgrounds. The correct approach is not to smooth out the differences or ignore upstream and downstream ideas and prior work based solely on differences.
- Model capability demonstrations need research governance
For significant mathematical announcements, the minimum good practices include:
- Freezing and recording model versions
- Disclosing training, retrieval, and tool usage boundaries
- Providing reproducible formal artifacts
- Hierarchically explaining contributions by humans and agents
- Allowing reasonable time for independent reviewers
- Fully citing parallel research and clearly stating priority
- The “human loop” in education and research is part of the results
If AI only delivers answers, students and researchers may lose opportunities to form intuition, learn failure patterns, pose new questions, and transfer methods to new domains. The “human digestion” the statement refers to is not a public relations delay but the actual production process of mathematical knowledge becoming genuine public capability.
Conclusion
The strongest argument of this joint statement is not that “AI cannot do mathematics,” but that “mathematics cannot be left with only the answers that AI has provided.” If OpenAI's Navier-Stokes claims are established after thorough review by the human community, it will be a historically significant result; however, the controversy triggered by it has already shown that the formalizability of proofs, the speed of publication, and the narrative of capabilities do not automatically resolve the issues of research understandability, priority, data governance, and long-term talent cultivation.
For mathematics and other knowledge work, the true alignment goal should be: to allow AI to extend human understanding and creativity, rather than letting quantifiable “problem-solving victories” replace these goals.
Notes
This report primarily utilizes three types of publicly available materials:
- The complete joint statement and full list of initial signatories published by Terence Tao on September 11, 2026.
- The technical announcement released by OpenAI on September 8, 2026, and updated on September 10.
- Science News reporting on the technical status, preliminary evaluations by independent mathematicians, and the attribution controversy.
For portions that have not yet completed peer review or are still under independent human examination, this article uses expressions such as “claims,” “public materials indicate,” and “pending verification” to avoid presenting them as established mathematical conclusions.
Sources
- Tao, A Severe Misalignment of AI in Mathematics, 2026-09-11.
- OpenAI, On the Navier–Stokes Millennium Prize Problem, 2026-09-08, includes the update from 2026-09-10.
- Science News, AI may have solved one of math’s biggest puzzles, raising controversy, 2026-09-09.
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