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OpenAI's GPT 5.6 "Sol" model generates 10 new mathematical proofs

By PulseAugur Editorial · [4 sources] ·

OpenAI has announced that an internal version of its upcoming model, GPT 5.6 "Sol", has generated 10 novel results in mathematics and theoretical computer science. These breakthroughs address long-standing open problems across various fields, including sphere packing, coding theory, and quantum complexity. OpenAI is releasing the associated manuscripts, formal Lean certificates, and reasoning walkthroughs to facilitate examination and further research by the mathematical community. The computational cost for these discoveries was approximately $2,000 in token usage. AI

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AI-generated summary · Google Gemini · from 4 sources. How we write summaries →

OpenAI's GPT 5.6 "Sol" model generates 10 new mathematical proofs

COVERAGE [4]

  1. X — OpenAI TIER_1 English(EN) · OpenAI ·

    We’re releasing the manuscripts, formal Lean certificates, and reasoning walkthroughs so mathematicians can examine these results and build on their ideas. http

    We’re releasing the manuscripts, formal Lean certificates, and reasoning walkthroughs so mathematicians can examine these results and build on their ideas. https://t.co/oDT2J8F6Ez

  2. X — OpenAI TIER_1 English(EN) · OpenAI ·

    The results span sphere packing, coding theory, group theory, quantum complexity, lattice cryptography, extremal combinatorics, and more.

    The results span sphere packing, coding theory, group theory, quantum complexity, lattice cryptography, extremal combinatorics, and more. Among them: establishing the existence of non-sofic groups and exponential improvements to bounds on high dimensional sphere packing.

  3. X — OpenAI TIER_1 English(EN) · OpenAI ·

    Mathematics helps us understand how traffic moves, how diseases spread, and how cells build proteins. It also underpins everyday technologies, from GPS and weat

    Mathematics helps us understand how traffic moves, how diseases spread, and how cells build proteins. It also underpins everyday technologies, from GPS and weather forecasting to medical imaging. Progress in foundational mathematics can ripple across science and technology.

  4. X — OpenAI TIER_1 English(EN) · OpenAI ·

    An internal version of our next major model produced 10 new results on long-standing open problems in mathematics and theoretical computer science, using roughl

    An internal version of our next major model produced 10 new results on long-standing open problems in mathematics and theoretical computer science, using roughly $2,000 worth of tokens at GPT-5.6 Sol API rates. https://t.co/4cgowmPOpY

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