Solving Math’s Greatest Problems Was an Art Form. Then Came AI

The mathematician Juspreet Singh Sandhu likens the development of new mathematical ideas to the artistic process, rather than the quick, practical approach often associated with math. Mathematicians typically follow a thoughtful, deliberate process to generate their ideas, unlike the brute force method employed by OpenAI in solving a long-standing math problem.

Hardy, a pacifist mathematician, wrote an essay during World War II advocating for the pursuit of mathematics for its own sake, separate from practical applications. This "useless" mathematics, he believed, could lead to unexpected and valuable discoveries. A famous example Hardy cited is Carl Friedrich Gauss' work in number theory, often considered a beautiful yet seemingly impractical branch of mathematics.

Despite the initial belief that certain mathematical fields were useless, they have later proven valuable. For instance, number theory, which deals with integers, has found applications in encryption protocols used to secure emails and bank accounts. However, the OpenAI proof of a mathematical problem known as the Navier-Stokes equations, which describe the behavior of viscous fluids, does not offer any practical benefits.

The equations, developed in the 19th century, were initially used to model airflow for airplane design, but mathematicians were more captivated by the equations themselves and the intricate puzzles they posed.

The Navier-Stokes equations have intrigued mathematicians due to their mathematical complexity and the challenge of understanding how they apply to real-world scenarios. Mathematicians have been working on the Navier-Stokes problem for decades, developing a deep and beautiful theory around the equations. However, when OpenAI's AI proved that the equations could imply a physically impossible situation, this solved a decades-old puzzle but offered no practical application.

OpenAI's proof, consisting of a 166-page document, has not undergone peer review yet, and its validity is yet to be confirmed by experts. Critics argue that the AI lacks transparency in its processes, and there are concerns about potential plagiarism. The proof was generated by the AI before mathematicians could fully understand how it arrived at the solution.

This lack of understanding and the speed at which LLMs can produce results may hinder human creativity, as they may miss valuable insights by relying solely on AI-generated calculations.