OpenAI releases hundreds of solutions to major mathematics problems

Summarised from 4 outlets · 5 reports · Updated 7 Oct, 18:01 · Archive

OpenAI published 722 manuscripts containing solutions to hundreds of long-standing mathematical problems using an unreleased AI model.

OpenAI has published 722 manuscripts containing solutions to hundreds of long-standing mathematical problems, the company announced this week. The breakthroughs came from an unreleased frontier model and span 372 groups of related problems across numerous areas of mathematics, including algebra, theoretical computer science and mathematical logic. The company said the average result required around three hours of ChatGPT Pro thinking time.

The release extends OpenAI's run of mathematical breakthroughs announced over recent months. In September, the company said its model had resolved more than 100 long-standing open problems. Among the key results claimed are a solution to the four-dimensional Kakeya conjecture and progress toward the Riemann hypothesis. OpenAI published the results on GitHub, including summaries of the model's reasoning, estimates of compute used, and statistics about the number of problems attempted.

The announcement has sparked significant concern within the mathematical community. The Institute for Advanced Study in Princeton said it does not endorse the practice of testing advanced mathematical problems on proprietary AI models not accessible to other mathematicians. The organisation stated that 'AI can output mathematical arguments in situations without the human who prompted it being able to understand the arguments, verify them, or take responsibility for them'. Experts worry OpenAI is not doing sufficient due diligence to vet the results.

OpenAI worked with an independent advisory group, the Advisory Group on Mathematics and Artificial Intelligence (AGMAI), on the release. AGMAI published recommendations in late September urging AI labs to release results promptly through established academic channels and to disclose details such as model names, prompts and compute costs. The group also urged companies to 'refrain from treating the release of mathematical results as marketing vehicles'.

In response to criticism, OpenAI stressed it had worked with the advisory group on the release and included detailed information about how findings were produced. The company said it would fund workshops and conferences to understand major results and would work to improve the quality of future releases. However, OpenAI did not commit to stopping testing advanced problems on proprietary models. The company said it would work with the Institute for Advanced Study to give mathematicians a voice in how it moves forward.

How it is being reported

• OpenAI’s release of mathematical findings draws concerns from expertsLeaders worry OpenAI is not doing due diligence to vet results and that AI models aren’t accessible to broader field of mathematicians OpenAI has astounded mathematicians after releasing hundreds of new mathematical findings on Tuesday. The company published over 370 mathematical results across a variety of topics such as algebra, theoretical computer science and mathematical logic, showcasing what some of its most advanced artificial intelligence models are capable of. Continue reading...Guardian Technology · 7 Oct, 16:40
• OpenAI just posted hundreds more results on major math problemsThe company said that most results were produced in a response to a single prompt given to a single AI agent.Engadget · 7 Oct, 14:08
• OpenAI says its artificial intelligence just solved some of maths’ hardest problems – but it is controversialMathematicians have criticised ChatGPT maker over its work in the field, and the ways it has chosen to announce themIndependent Tech · 7 Oct, 11:46
• OpenAI drops another batch of mathematical breakthroughsOpenAI has revealed solutions to a number of long-standing mathematics problems produced by an unreleased frontier model in a batch of 722 manuscripts, covering 372 result families that group related papers. It extends a run of breakthroughs that have both impressed and unsettled parts of the mathematical community while raising questions about research ethics and […]The Verge · 7 Oct, 00:26
• All the drama around AI’s takeover of mathematicsThis past year, OpenAI, Anthropic, and other labs have announced breakthroughs on numerous long-standing mathematical problems, in some cases pushing well beyond what researchers expected current systems to be capable of — including resolving one of the famous Millennium Prize problems. But in classic Silicon Valley style, AI labs are moving fast and breaking things, […]The Verge · 5 Oct, 20:28

In this story: OpenAI · Institute for Advanced Study · Advisory Group on Mathematics and Artificial Intelligence · Princeton

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