Cardano founder Charles Hoskinson highlighted the accelerating progress of artificial intelligence in producing and verifying advanced mathematical proofs, saying it has far surpassed his original expectations. Hoskinson, who established the Cardano blockchain and has a background in mathematics, discussed these advancements on a recent YouTube broadcast, examining the latest claims about AI’s ability to tackle major unsolved mathematical problems.
AI’s Leap in Advanced Mathematics
Hoskinson said artificial intelligence has moved well beyond merely assisting mathematicians, noting that systems can now independently generate and formally verify complex proofs. Referencing recent developments, he specifically discussed reports that AI models had contributed possible solutions to the Navier-Stokes Millennium Prize problem, one of the most challenging and well-known unsolved questions in mathematics.
He explained that he had originally expected formal systems would allow larger groups of mathematicians to collaborate with increased efficiency. However, the rapid growth of large language models (LLMs) surprised him. Hoskinson commented, “We never anticipated the extent to which AI would come in. The idea of the AI itself would fully write the proof, it was pretty far out. LLMs really surprised us.”
It’s pretty remarkable to see how far these things have gotten and what they’ve been able to achieve and do.
Hoskinson, known for his interest in formal mathematics, previously launched a center for formal mathematics at Carnegie Mellon University. He said even he had not fully anticipated that LLMs might become capable of independently constructing mathematical proofs.
He emphasized how striking the capabilities of modern AI systems were, saying their mathematical output had reached an extraordinary level.
The Navier-Stokes existence and smoothness problem is one of seven Millennium Prize Problems designated by the Clay Mathematics Institute. The question asks whether sufficiently well-behaved solutions always exist for the equations describing three-dimensional fluid motion. If solved, this problem would mark a major breakthrough for both mathematics and physics.
Mini dictionary: Navier-Stokes Millennium Prize problem: One of the Clay Mathematics Institute’s Millennium Prize Problems, addressing whether solutions to equations governing the motion of fluids in three dimensions always exist and are smooth. A solution carries a $1 million prize due to its importance in mathematics and physics.
Risks and Implications for Research
Hoskinson remarked that if an AI system like the one developed by OpenAI has produced a solution to the Navier-Stokes problem, it could fundamentally alter the mathematics landscape. He stated, “For OpenAI to claim that they have solved this, this is something that would fundamentally change the mathematics paradigm.”
For an academic, if you’re an entrepreneur, know that your ideas, if you share them in AI with these frontier models in the cloud, they’re not your ideas anymore.
Underscoring the importance for scientists and academics, he compared the current era to a mathematician discovering another’s research notes in the open. Hoskinson used this moment to promote the concept of private AI environments as crucial for protecting intellectual property and confidential research. He argued researchers should have access to powerful models without exposing sensitive work to centralized AI providers.
Although he cautioned about the origins of the AI-generated mathematics, he acknowledged that the progress itself was notable. “What this does mean is that a model is sufficiently advanced that it knows how to steal a smart person’s work, take that work, improve it, iterate it, and formalize it to the extent that it actually solves a hard problem,” he observed.
Hoskinson concluded that the ability of AI systems to build upon prior work and enhance it is, in his view, a significant development for both technology and mathematics.
