OpenAI has lowered prices for its Luna and Terra AI models as competition intensifies and businesses seek lower-cost artificial intelligence services. (Image: Reuters)OpenAI has quietly unveiled that its next major family of AI models will be called ‘Astra’, and claimed that an internal version of one such model cracked ten long-standing unsolved mathematical problems, signalling a major leap in AI reasoning. The ChatGPT-maker on Saturday, August 1, said that its unreleased Astra model either resolved or “made substantial progress” on ten complex, long-standing open problems. These problems relate to a wide range of mathematical topics, such as high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. The AI-generated mathematical proofs were later prepared into manuscripts by humans with each argument formalised in a Lean certificate, according to OpenAI.