OpenAI Astra Solves 10 Open Mathematical Problems
OpenAI Astra has achieved significant milestones by solving a dozen open mathematical problems, some of which have been relevant for 40-50 years.
OpenAI Astra has solved 10 open mathematical problems, some of which have been relevant for 40-50 years.
OpenAI recently published a large post about this, laying out all the proofs in Lean and the reasoning process of the model. In total, approximately $2000 worth of tokens were spent on finding solutions.
Among the results are, in particular, the proof of the existence of non-sophic groups and sphere packing in high dimensions.
The existence of non-sophic groups has been a central question in group theory and operator algebras for 20 years. Sphere packing is one of the most famous problems in discrete geometry. Until now, an exact solution was known only in some dimensions, and for the 8-dimensional and 24-dimensional cases, Marina Viazovska received the Fields Medal.
Additionally, the list includes the solution to Erdős problem No. 183 about multicolored Ramsey numbers, a refutation of the Conn rigidity hypothesis, the Ehrhart hypothesis about volume, and others.
Details about the model itself are scarce. It is likely a large model from the GPT-6 (or GPT-5.7) family, the same one that hacked HuggingFace. Apparently, this is the model that Altman presented at the White House this week.
Why it matters
AnalysisThis is important as OpenAI's achievements in mathematics demonstrate the potential of artificial intelligence in solving complex scientific problems. Solving such problems can significantly impact the development of mathematics and related sciences.
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