Former NFL Player and MIT Math Professor John Urschel Says Mathematics Will Not Be Fully Solved by AI
Former NFL player and current MIT math professor John Urschel stated that there is considerable consensus in the mathematics community that "mathematics will not be solved." He pointed out that AI is helping mathematicians advance at an unprecedented speed, but there are still many areas waiting to be discovered.
Urschel said, "There is still a long way to go." He recently published a paper titled "On the Growth Factor of Random Matrices," solving a conjecture about the growth factor of Gaussian elimination in random matrices that has been around since the 1990s. This algorithm is widely used for solving linear equations, supporting applications in circuits, financial models, and searches. Mathematicians have long known it is almost always reliable in practice but lacked a rigorous proof.
Urschel retired from the Baltimore Ravens in 2017, having pursued a PhD in mathematics at MIT during his NFL career. His research focuses on applied linear algebra, numerical analysis, and spectral graph theory. His recent paper reportedly received assistance from OpenAI models. He expressed being "thoroughly shocked" while reading OpenAI's latest mathematical papers on topics like the Riemann Hypothesis.
Gaussian elimination is a fundamental tool in numerical linear algebra. Urschel's proof provides mathematical evidence of the algorithm's high stability for random matrices. Berkeley researchers have called this a "big problem" in the field. Urschel emphasizes his focus on "why" rather than just "how," and holds an optimistic view on AI accelerating exploration, while believing that humans still need to understand and expand on new results.
AI tools enable mathematicians to explore more paths in parallel, with funding and computational resources flowing towards model-assisted proofs. The speed of paper publication has increased, and some open problems have made progress. Human mathematicians still dominate in the verification, explanation, and posing of new questions, while the path to purely automated solutions for entire fields is under pressure.
Source: Public Information
ABAB AI Insight
John Urschel completed his PhD in mathematics at MIT after retiring from the NFL and is now an assistant professor. He recently solved a conjecture related to Gaussian elimination, with reports indicating AI assistance in his paper. He expressed shock in public when reading OpenAI's mathematical papers while emphasizing that mathematics will not be fully solved.
Urschel views AI as an acceleration tool for exploring literature and parallel attempts. Resources are shifting from traditional manual proofs to model-assisted searches and verifications. He focuses on the theoretical reasons behind algorithm reliability rather than merely accepting effectiveness in practice. MIT and the mathematics community are discussing the impact of AI on the speed of theorem proving.
Similar discussions have emerged in response to mathematicians reacting to OpenAI solving long-standing open problems. Current mathematical research is at a stage where AI can solve specific conjectures, but humans remain responsible for understanding and expanding upon them.
This is essentially a case of technological substitution. AI accelerates progress in searching and combining existing results, but understanding the implications of new proofs and posing subsequent questions still relies on humans. The mechanism involves models processing a large number of attempts in parallel, shortening the time from conjecture proposal to proof verification, while retaining human authority over the explanation of "why it holds true."
ABAB News · Cognitive Laws
AI solving individual problems does not equate to solving an entire field.
Accelerating search does not replace understanding "why."
Open problems decrease, but the space for new questions continues to expand.