According to the developer, an internal version of Astra, their next major AI model, produced new results for ten long-open mathematical problems whose main statements had seen no progress for at least a decade. The problems span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography and extremal combinatorics.
What happened
The company reports that while evaluating an unreleased model they previously published an AI-generated disproof of the Erdős unit-distance conjecture in May. Building on their internal evaluations, they say an internal Astra model found solutions to ten additional problems. The announcement does not reproduce full proofs in the press release; instead it describes the workflow used to produce, prepare, and formalize the arguments.
The firm states the total token usage required to discover these solutions would cost roughly $2,000 at Sol API rates. After the model produced the mathematical arguments, humans prepared the arguments into manuscripts using the same model, and the model then formalized each argument into a Lean certificate. For each solution they are also releasing the model’s narrated chain-of-thought-style explanation of its reasoning.
Which problems were addressed
The announced results concern problems that are of substantial interest within their respective mathematical communities and, in several cases, of broader interest across mathematics. The listed areas are high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography and extremal combinatorics. The company’s statement does not provide the detailed technical write-ups in the announcement itself; they emphasize that the mathematical community should examine and contextualize the results.
Authorship, formalization and attribution
The developer stresses that humans participated in preparing manuscripts and in the Lean formalizations, and that they take responsibility for the correctness of those formalizations. They also state that the underlying mathematical arguments were generated by their system, and argue that attribution should honestly reflect how a result was produced — for example, presenting a proof entirely generated by an AI as human-authored would be misleading.
The statement acknowledges concerns such as those expressed by signatories of the Leiden declaration on AI and Mathematics and expresses respect for those viewpoints while urging deep engagement from mathematicians.
Implications and follow-up work
The company frames these results as an example of how increasingly capable AI systems can become research collaborators, and says that ensuring broad access to such tools is important so that scientists and mathematicians can shape how the technology is used in their fields. The announcement also references related and subsequent research that builds on or interacts with recent developments in the area, listing several recent papers by other authors that address connected conjectures and complexity questions.
Closing note
The developer is releasing the model-generated arguments, the human-prepared manuscripts, the Lean formalizations, and the model narrations, and invites the mathematical community to validate, contextualize, and develop the ideas further. They take responsibility for the formalized proofs while attributing the mathematical discoveries to their AI system.
