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ADA Cardano founder Charles Hoskinson: Artificial intelligence has advanced more than expected mathematics
Cardano founder Charles Hoskinson believes that artificial intelligence has far surpassed expectations in independently generating and formally verifying increasingly complex mathematical proofs. This view has sparked widespread discussion about AI's reasoning capabilities and their potential impact in fields such as mathematics, engineering, fluid mechanics and modern physics.
From assistive tools to autonomous proof generation
According to Hoskinson, researchers originally expected that the formal system would mainly improve collaboration between mathematicians working on complex problems. However, large language models have moved beyond mere auxiliary roles and have the potential to write and formally verify complex mathematical proofs. "We never expected artificial intelligence to develop to this extent," he said in a recent live YouTube broadcast.
He had previously believed that automated tools would help experts review certificates, identify errors, and coordinate difficult academic projects. Still, counting on artificial intelligence to generate complete mathematical proof at once has seemed impractical even to developers of formal systems. "The idea of having AI itself fully write proof seemed very remote at the time," he commented.
In addition, Hoskinson thanked large language models for changing his understanding of what automated systems can achieve in mathematical research.
Dispute over the Navier-Stokes equation highlights AI's mathematical capabilities
Hoskinson's remarks related to reports of AI-generated Navier-Stokes existence and smoothness issues. The unsolved problem is one of the Clay Mathematical Institute's Millennium Award problems, with a prize of up to $1 million. This problem investigates whether there is always a solution to the equations describing the motion of fluids in a three-dimensional environment that has "good behavior." Solving this problem will have a major impact on mathematics, fluid mechanics, aerospace engineering, mechanical engineering, and multiple branches of physics.
Thus, Hoskinson points out that a proven AI-generated solution could fundamentally change traditional perceptions of mathematical discovery and machine intelligence. "If OpenAI claims they have solved this problem, it will fundamentally change the mathematical paradigm," he explained.
Alert to data breach risks from centralized AI platforms
However, Hoskinson questioned the source of the work and expressed concerns about submitting confidential research to centralized AI providers. He warned academia and businesses that sharing proprietary materials with cloud-based models could weaken controls on intellectual property. His warnings support the use of private AI environments that allow researchers to review sensitive theories without exposing unpublished work or valuable technical information.
Despite doubts about the source of the reported method, Hoskinson admitted that the artificial intelligence system demonstrated impressive mathematical capabilities.
