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Controversy: OpenAI's Claim to Solve Navier-Stokes Millennium Problem

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Controversy: OpenAI’s Claim to Solve Navier-Stokes Millennium Problem

Clip title: The Controversy Behind AI Solving A Million Dollar Math Problem Author / channel: Up and Atom URL: https://www.youtube.com/watch?v=cvTHBXyXM2I

Summary

The video details OpenAI’s controversial announcement on September 8th, claiming to have solved the Navier-Stokes Millennium Prize Problem, one of the seven deepest unsolved problems in mathematics, each carrying a $1 million prize. The problem fundamentally questions whether an initially smooth fluid flow can develop “singularities” or break down in finite time, specifically when a smooth external force is applied. OpenAI’s proposed solution involves a vortex that spirals inward and elongates. While a monumental mathematical achievement if verified, the video emphasizes the significant drama and ethical controversy surrounding the claim.

OpenAI’s resolution was achieved by a “system of coordinating agents” powered by an internal model, stated to be more capable than GPT-6 Astra. This process involved approximately 10,000 concurrent agents, taking 88 hours to reach a resolution and an additional 17 hours for Lean formalization and verification. The computational cost, estimated by the video, amounts to roughly 1 million prize money.

The controversy stems from OpenAI’s admission that their effort began on September 1st after hearing rumors that another AI company, Anthropic (where one of the mathematicians, Levent Alpoge, worked), had solved a Millennium Problem (later clarified to be the simpler Euler problem). OpenAI explicitly stated they were “curious if ours could do it too,” suggesting a competitive “math race.” However, the two mathematicians, Levent Alpoge and Tristan Buckmaster, who were working on the Euler and a related “hypo-dissipative Navier-Stokes” problem using OpenAI’s own Codex tool, alleged that OpenAI used data from their ongoing work to preemptively “scoop” their discovery. Buckmaster detailed communications where OpenAI allegedly suggested removing Alpoge from authorship due to his affiliation with Anthropic, offered “consolation prize” proposals, and even made subtle threats if Buckmaster went public. OpenAI later admitted they couldn’t rule out that de-identified data from customer usage of their products influenced their models.

Ultimately, this situation raises critical ethical questions about AI companies’ competitive practices, the use of customer data for developing proprietary models, and the traditional norms of academic collaboration and credit. While OpenAI’s researcher, Sebastian Bubeck, apologized for aggressive language, the conflicting accounts highlight a breach of trust between the AI giant and individual researchers. Regardless of the controversy, if OpenAI’s proof holds up, it represents a significant milestone for both mathematics and artificial intelligence, marking the second Millennium Prize Problem to be potentially resolved.

Video Description & Links

Description

https://share.google/s4UyaAalDcbJTYd6W https://openai.com/index/navier-stokes-solution/

Up and Atom on Spotify https://open.spotify.com/show/033gE0X74RZAwIh3Tbj6B7

A big thank you to my AMAZING PATRONS! Michael Seydel, Brian Wilkins, Thorsten Auth, Chris Flynn, Richard O McEwen Jr, Scott Ready, Izzy Ca, John H. Austin, Jr., David Johnston, Thomas Krause, Ave Eva Thornton, Anne Tan, abc, Nahuel Hernán Espiño, Norman Jaffe, Jim Wright, Elliot Glazer, Cumaco, John Doe, Dirk Wouters, Stoney Bair, Francisco, Marc-Antoine, Thomas Urech, chuck zegar, David Tuman, Ben Mitchell, Jim Felich, Jeremy, DONALD McLeod, Ron Hochsprung, James Matheson, Tim Ludwig, Dagmawi Elehu, Jeffrey Smith, Alex Hackman, Joel Becane, Paul Barclay, John Lakeman, Jana Christine Saout, Jeff Schwarz, Yana Chernobilsky, Michael Dean, Chris Amaris, Matt G, Dag-Erling Smørgrav, John Shioli, Gladamas, Hey kid I’m a computer, Bli Blop, Steve Archer, Antonio Gonzalez, Robert Ball, AdamM, Dhandforth, Wolf Witt, Benedict, Janusz Górecki, Prashant Savalia, Henrik Horneber, Markus S., AudioFreak, Lauren Fish, Matthew Lewis, Pawel W, Bryan Hughes, Trance Maharaj, Matt, Jonathan Rayback, Smarter Every Day, Bunny Lushington, Jane!, Motty Porat, Carlos Escolar, Keenir, robert lalonde, Cassandra Durnord, Paul Bunbury, Richard Rensman, David Shlapak, Kent Arimura, Phillip Rhodes, Michael Nugent, Roland Gibson, Joe McTee, Oleg Dats, Simon J. Dodd, Tang Chun, William Toffey, omg.science, Cameron Tacklind, Lance Ahmu, Steve Watson, Andi B, Thomas P Taft, Pablo de Caffe, Taylor Hornby, Colin Byrne, Spuddy, Sascha Bohemia, Stephen Britt, KG, Hansjuerg Widmer, John Sigwald, O C, Carlos Gonzalez, James Palermo, Thomas V Lohmeier, Chris Teubert, Wolfgang Ripken, Nicolas Frias, Louis M, ROBERT C PAYNE, Rick DeWitt, Gene Levitsky, Pat Gunn, RobF, Vincent Seguin, Michael Brunolli, Shawn, Steven Wheeler, Philip Freeman, Jareth Arnold, and Simon Dargaville.

Research and writing by Jade Tan-Holmes and Simon Mackenzie

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