OpenAI's Next-Gen Model Solves 10 Long-Standing Math and Computer Science Problems
OpenAI announced that an internal version of its next major model has successfully generated 10 new results for long-standing open problems in mathematics and theoretical computer science. The model achieved these breakthroughs using advanced reasoning capabilities, costing approximately $2,000 worth of tokens at GPT-5.6 Sol API rates. This milestone demonstrates that large language models are transitioning from mere text generation to solving complex, unsolved scientific problems, which could accelerate research in cryptography, quantum computing, and mathematics. It also hints at the capabilities of OpenAI's upcoming GPT-5 class models. The solved problems span fields such as sphere packing, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics. Notably, the model established the existence of non-sofic groups and achieved exponential improvements to bounds on high-dimensional sphere packing.
## BACKGROUND
Non-sofic groups are a concept in group theory introduced as a generalization of amenable and residually finite groups, and proving their existence has been a long-standing mathematical challenge. Lattice-based cryptography is a leading paradigm in post-quantum cryptography, relying on the hardness of high-dimensional geometric lattice problems to secure data against future quantum computer attacks.