Source: Fortune
Summary
OpenAI published AI-generated solutions to over 370 mathematical problems, including some long-standing challenges. The company used an internal AI model, which took about three hours per solution. Some mathematicians praised the results, while others criticized the approach as a threat to the field. OpenAI said it made progress on three Millennium Prize problems but did not fully solve them. The company also released a set of recommendations for publishing AI-generated proofs, but it did not fully follow them. Mathematicians remain divided on the impact of AI on mathematical research.
Our Reading
The numbers tell one story.
OpenAI claims to have solved 370 math problems.
The company used an internal AI model.
Some mathematicians are excited, others concerned.
The field is split on AI’s role in math.
AI’s solutions are hard to follow but may open new areas.
The company says it wants to push the frontier of knowledge.
Mathematicians worry about the future of the field.
OpenAI says it will fund workshops to help understand results.
Some fear AI is undermining human mathematical progress.
The field is at a crossroads.
AI is changing how math is done.
The debate over AI’s role is far from over.
Math 1.0 may be ending.
Math 2.0 needs to redefine progress.
Author: Evan Null
Showing the work
When OpenAI published its Navier-Stokes solution, two mathematicians accused the company of using their work to guide the AI model. OpenAI denied the claim, saying it did not feed the model their research. The mathematicians, including Tristan Buckmaster, remain skeptical. He said it was unclear whether OpenAI’s AI had inadvertently used their work. He criticized the company for not doing enough due diligence. OpenAI formed an advisory group on math and AI after criticism. The group recommended publishing AI-generated proofs with details on the model, prompts, and reasoning. OpenAI partially followed the recommendations, but the group said it was up to the math community to assess compliance. OpenAI said it would improve future releases by adding citations and better exposition.
The end of ‘Math 1.0’
The independent math advisory group said the future of math cannot rely only on AI results. Mathematicians must formulate their own questions and explore new directions. Access to tools and resources is essential. Terence Tao, a top mathematician, criticized AI companies for solving problems too quickly. He said this discourages students from entering the field. Tao argued that the process of solving problems, not just the solutions, is what advances math. He said AI results generate fewer collaborations and seminars. He called OpenAI’s release the end of “Math 1.0,” where solving problems was the engine of progress. He called for a “Math 2.0” era that values exposition, community building, and new directions. Dan Litt agreed that the field must change. He said OpenAI’s solutions would push the field to rethink what it rewards and how it trains PhD students. Litt was optimistic about the future, saying AI would enable more open-ended exploration. He compared it to “crawling my entire life, and now I can fly.”
AI and the future of math
OpenAI said it wants to push the frontier of human knowledge and enable further progress in math. It plans to fund workshops, conferences, and programs to help mathematicians understand its AI results. The company also said it would share formalizations of the proofs for many problems. These are versions of the proofs that can be verified by specialized software. OpenAI said it would share more as it obtained them. It also said it would publish summaries of its model’s reasoning, estimates of compute spent, and statistics on the number of attempted problems. Some mathematicians have complained that AI-generated proofs are hard to follow. Litt said these concerns were overstated, saying mathematical writing is often difficult to follow anyway. He said extracting understanding from OpenAI’s results will require a lot of human labor, but it’s not different from what mathematicians have always done. Litt approved of most aspects of how OpenAI published the solutions. He said having them on GitHub made them accessible and praised the company for not hyping any particular advance. He said OpenAI lacks the capability to publish all results in research papers that meet academic standards. This is because AI models don’t write mathematical exposition well and struggle to cite prior work. OpenAI also doesn’t have enough mathematicians with expertise in enough areas to understand all the proofs.
Divided reactions
Some mathematicians are excited about OpenAI’s results. Dan Litt, a professor at the University of Toronto, said he was excited and wanted to understand the solutions. He said it was great to have new solutions to questions he and others were interested in. He also said it was important for society to reaffirm support for human mathematical expertise. Litt warned that if people think AI has solved math, funding organizations might withdraw support for research. He also said this could discourage young mathematicians from entering the field. Litt approved of most aspects of how OpenAI published the solutions. He said having them on GitHub made them accessible and praised the company for not making too much of any particular advance. He said OpenAI lacked the capability to publish all results in research papers that meet academic standards. This is because AI models don’t write mathematical exposition well and struggle to cite prior work. OpenAI also doesn’t have enough mathematicians with expertise in enough areas to understand all the proofs. Litt said he thought AI would enable human mathematicians to engage in more open-ended exploration than before. He said he was optimistic about the future, saying AI would make mathematicians more productive.
OpenAI’s role in math
OpenAI said it wants to push the frontier of human knowledge and enable further progress in math. It said it would fund workshops, conferences, and programs to help mathematicians understand its AI results. The company also said it would share formalizations of the proofs for many problems. These are versions of the proofs that can be verified by specialized software. OpenAI said it would share more as it obtained them. It also said it would publish summaries of its model’s reasoning, estimates of compute spent, and statistics on the number of attempted problems. Some mathematicians have complained that AI-generated proofs are hard to follow. Litt said these concerns were overstated, saying mathematical writing is often difficult to follow anyway. He said extracting understanding from OpenAI’s results will require a lot of human labor, but it’s not different from what mathematicians have always done. Litt approved of most aspects of how OpenAI published the solutions. He said having them on GitHub made them accessible and praised the company for not making too much of any particular advance. He said OpenAI lacked the capability to publish all results in research papers that meet academic standards. This is because AI models don’t write mathematical exposition well and struggle to cite prior work. OpenAI also doesn’t have enough mathematicians with expertise in enough areas to understand all the proofs. Litt said he thought AI would enable human mathematicians to engage in more open-ended exploration than before. He said he was optimistic about the future, saying AI would make mathematicians more productive.
