An assessment has emerged that artificial intelligence is developing faster than expected in its ability to solve mathematical problems, blockchain outlet U.Today reported on Sept. 9.

Cardano founder Charles Hoskinson (찰스 호스킨슨) said in a recent YouTube broadcast that AI has rapidly advanced to the point where it can generate complex mathematical proofs and formally verify them.

Hoskinson pointed in particular to claims of AI-generated solutions related to the Navier-Stokes equations. The Navier-Stokes problem is one of the Clay Mathematics Institute's seven Millennium Prize problems. It involves proving whether solutions always exist for equations describing the motion of three-dimensional fluids and whether those solutions are smooth. It is considered an important problem in physics as well as mathematics.

He said he once expected formal mathematical systems to evolve in a way that helps mathematicians collaborate, but he did not think AI would reach the level of completing proofs directly.

Hoskinson said that even though he has followed the field for a long time, including setting up a formal mathematics centre at Carnegie Mellon University, the recent pace of AI model progress was unexpected. He focused in particular on the growing ability of large language models to formalise complex mathematical ideas and generate and verify proofs.

He stressed, however, that caution is needed over the provenance of AI-generated mathematical results and the protection of research data. Hoskinson said that if OpenAI claims it has actually solved the Navier-Stokes problem, it would fundamentally change the paradigm of mathematics. He added that what research and ideas such a result is based on is a separate issue.

He warned that if researchers share their ideas and work records with cutting-edge cloud-based AI models, that knowledge may no longer remain entirely their own. Companies as well as universities and research institutes could face the same risk, he said.

Hoskinson therefore argued that there is a need for private AI environments that can use powerful AI models without exposing sensitive research data and intellectual property to centralised AI services.

He offered a positive assessment of AI's mathematical achievements themselves. He said it was impressive that AI can analyse the work of outstanding researchers, then improve and iterate on it and formalise it to the point of solving difficult problems. He also stressed that this way of working resembles human research activity.

His remarks show that AI is advancing beyond simple calculation or research support to a level where it directly intervenes in high-level knowledge work. At the same time, he said, the faster the competition over AI model performance becomes, the more important discussions will be over what environment should be used to handle and protect research ideas and intellectual property.