mathematics

OpenAI announced the establishment of an independent advisory group on mathematics and artificial intelligence in collaboration with mathematicians, hosted by the Institute for Advanced Study in Princeton. OpenAI stated that its new internal model, which began training on August 28, has solved the Navier-Stokes Millennium Prize Problem and addressed over 100 long-standing open problems in most areas of mathematics, with progress that surprised its internal mathematicians.The group will provide advice on the review and dissemination of emerging results, academic and professional standards in mathematical research, and how OpenAI tools can support mathematical research and learning. Initial members include François Charles, Camillo De Lellis, Timothy Gowers, Martin Hairer, Nikhil Srivastava, Ulrike Tillmann, Ravi Vakil, Edward Witten, and Melanie Matchett Wood.The group operates independently of OpenAI, and members are not compensated by OpenAI; they can proactively provide advice, comment on its impact on mathematics, and make public recommendations. Previously, mathematicians expressed concerns in an open letter titled "A Severe Misalignment of AI in Mathematics" regarding the use of solving open problems as a benchmark for AI. The group is not responsible for providing advice on the pace of OpenAI's internal mathematical progress.

OpenAI stated to The New York Times that since announcing progress on the Navier-Stokes equations on September 8, it has made "substantial progress" on one of the Millennium Prize Problems, but did not disclose which specific problem it is or provide a timeline for disclosure. The Millennium Prize Problems are seven mathematical problems established by the Clay Mathematics Institute since 2000, each with a reward of one million dollars.Speculation suggests that the problem may be the Hodge Conjecture, a 76-year-old problem regarding how to calculate the number of "holes" in complex geometric shapes. OpenAI has not confirmed this speculation and has not responded to rumors that its underlying model is a version of Aeon specifically designed for long-duration tasks. Previously, on September 8, OpenAI announced that its unreleased internal model generated a proof verified by Lean, indicating that the Navier-Stokes equations could "blow up" to physically impossible infinite speeds, involving about 10,000 coordinated AI agents and taking approximately 88 hours.However, this statement has sparked controversy. New York University mathematician Tristan Buckmaster stated that he and Anthropic researcher Levent Alpöge had been working on the related proof for nearly a year prior and completed it on August 22, while OpenAI's Sébastien Bubeck published his findings first upon learning of it. OpenAI stated that it is not pursuing the one million dollar prize, but rather using these problems as a public benchmark to measure the speed of model progress. The review of the Navier-Stokes proof by the Clay Mathematics Institute is still ongoing, and verification of past Millennium Prize Problems typically takes several years.

ChainCatcher news, according to Cointelegraph, Trump's crypto and AI advisor David Sacks recently stated: "Bitcoin offers a different type of currency that is not backed by the government, but by mathematics."

ChainCatcher news, according to Cointelegraph, Professor Massimiliano Sala from the University of Trento in Italy recently discussed the future of blockchain with the Ripple team, particularly the potential threat of quantum computing to cryptographic technologies. Professor Sala emphasized that the maturity of quantum computing technology could pose a serious threat to existing cryptographic methods, thereby bringing risks to the entire blockchain technology system. He pointed out that quantum computers will be able to easily solve the fundamental problems of digital signatures, undermining the security mechanisms that protect user assets on blockchain platforms. He proposed the concept of "Q Day," which refers to the moment when quantum computers become powerful enough and accessible enough for malicious actors to break traditional cryptographic methods.While this will have far-reaching implications for any field where data security is critical—including emergency services, infrastructure, banking, and defense—it could theoretically destroy the world of cryptocurrencies and blockchain. Sala suggested that to address this potential risk, all traditional public key cryptosystems should be replaced with corresponding systems that can withstand quantum attacks. Although practical quantum computers capable of performing such operations have not yet emerged, governments and research institutions around the world are already preparing for the arrival of Q Day. Professor Sala expressed satisfaction with the progress in the field of quantum computing and recommended that blockchain developers maintain close collaboration with cryptographic experts who understand modern systems' quantum protection standards and innovations to face this challenge together.