Charles Hoskinson, founder of the Cardano blockchain platform, expressed his surprise at how rapidly artificial intelligence has advanced in tackling complex mathematical challenges. In a recent YouTube broadcast, Hoskinson focused on the ability of modern AI systems to produce and verify sophisticated mathematical proofs, acknowledging that the progress seen has exceeded his original expectations.
AI tackles the Navier-Stokes problem
Hoskinson discussed claims that artificial intelligence has played a role in approaching the Navier-Stokes equations, one of the Clay Mathematics Institute’s Millennium Prize Problems. The Navier-Stokes problem revolves around determining whether solutions to the equations underlying three-dimensional fluid dynamics always exist and behave smoothly. This mathematical challenge has significant implications for physics, fluid mechanics, aerospace engineering, and mechanical engineering.
Hoskinson emphasized the gravity of any potential breakthrough, stating that a plausible AI-generated solution would represent a major shift for mathematics and allied disciplines. He commented on OpenAI’s involvement in particular, suggesting that a true solution to the Navier-Stokes problem by an AI model could fundamentally alter accepted mathematical paradigms.
Mini dictionary: Navier-Stokes equations, a set of partial differential equations describing the motion of fluid substances such as liquids and gases. The existence and smoothness of these equations in three dimensions remain one of the most important unsolved problems in mathematics.
OpenAI’s claim to have solved this would fundamentally change how mathematics is done and would be a big deal in mathematics, impacting fields like fluid dynamics and engineering.
The Cardano founder likened this breakthrough to a mathematician unexpectedly discovering the notes of another researcher, illustrating the disruptive nature of AI in academic contexts.
The role of LLMs in formal mathematics
Hoskinson acknowledged how large language models (LLMs) have surprised him in their ability to take on such complex tasks. He explained that his previous view was that formal mathematics would mostly help teams of mathematicians collaborate more effectively, rather than AI models independently creating new proofs.
He previously founded a center for formal mathematics at Carnegie Mellon University and has long followed developments in this area. Hoskinson admitted he did not foresee LLMs becoming so proficient in generating formal mathematical proofs.
The idea that AI could fully write proofs seemed far-fetched, but LLMs have really surprised us by achieving what seemed impossible just a few years ago.
Hoskinson underscored the unique capacity LLMs have shown not only to replicate but to expand upon the work of experts. He noted that models today can improve, iterate, and formalize prior intellectual work to the point of solving previously intractable problems.
Data security and private AI environments
Drawing on ongoing debates about intellectual property in AI research, Hoskinson warned researchers and entrepreneurs of the risks associated with using centralized cloud-based AI platforms. He advocated for private AI environments, arguing that confidential research logs and intellectual property should stay out of reach of large, centralized model providers.
Hoskinson used the controversy as an opportunity to promote greater privacy standards within the AI and research communities. He maintained that as models grow more potent, securing proprietary work against inadvertent disclosure becomes increasingly crucial.
Despite questioning the originality of AI-generated mathematical solutions, Hoskinson concluded that the achievements of sophisticated AI systems demonstrate their ability to build upon and refine prior human work.
