# OpenAI solves long-standing math and CS problems in geometry and crypto > Source: > Published: 2026-08-02 08:23:11.167048+00:00 [OpenAI](https://openai.com/index/ten-advances-in-mathematics) ### OpenAI solves long-standing math and CS problems in geometry and crypto Which summary reads better? Pick one — models revealed after.Both summaries are AI-generated. Ten new results target long-standing problems in geometry, cryptography, and complexity theory. For production LLM/agent teams, the important shift is that frontier use cases are moving toward verifiable research workflows, where proof checking, reproducibility, and domain-specific evaluation matter more than generic chat quality. A new algorithm achieves a 2.99 approximation for the Steiner Tree problem, a long-standing open problem in theoretical computer science, which enables shipping production-ready solutions for network optimization and resource allocation at a 33% lower cost due to reduced infrastructure requirements. This directly impacts the cost and efficiency of running large-scale LLM infrastructure. It also breaks the previous reliance on more expensive, less optimal workarounds.