AI is both the best and worst thing to ever happen to mathematics
Mathematicians now have a formidable tool for breaking open challenging problems, but working out how best to use it isn't going to be easy
The Navier-Stokes equations, first formulated 200 years ago, have long been a cornerstone of mathematics. Despite their utility in various fields, such as aircraft design and heart modeling, one question remained unresolved: do these equations sometimes produce infinite velocities, resulting in "blow-ups"? This problem is so significant that it has been included among the prestigious Millennium Prize Problems, offering a $1 million reward for a solution.
Recently, OpenAI made headlines by announcing that their AI agents had successfully identified the answer: indeed, the equations can indeed blow up under certain conditions. However, this revelation isn't merely about fluids behaving unpredictably; it signifies that the equations themselves may not be entirely perfect. While this discovery is a monumental breakthrough in mathematics, the manner in which it was achieved and its subsequent implications could reshape the field in profound ways.
Terence Tao, a renowned mathematician, cautioned that AI companies may be inadvertently harming the discipline. OpenAI's approach involved using thousands of AI agents, funded by $15 million, to solve the problem within just 88 hours. This rapid progress underscores the remarkable capabilities of AI in mathematics, a field that once struggled to gain the respect it deserves.
It seems that AI is poised to become both a boon and a bane for mathematics. While AI has solved some of the most stubborn problems, its methods often lack the clarity and insight that human mathematicians value. This raises questions about the future of mathematical proofs and the role of AI in this process. As mathematicians grapple with this new reality, the potential for AI to accelerate mathematical discovery is undeniable.
However, the challenges ahead—ranging from integrating AI into the research process to ensuring equitable access to this powerful tool—must be addressed. Just as the introduction of algebraic geometry transformed the mathematical landscape in the 17th century, AI may usher in a new era of mathematical progress. The question remains: will AI prove to be the best thing to happen to mathematics, or will it ultimately prove to be its worst enemy?
Written by urgent.news from New Scientist's reporting — not their text. Machine-written — may contain errors; check the original before relying on it.
