Who is Joel David Hamkins, the American mathematician claiming AI is ‘not mathematically correct’?

Joel David Hamkins is not a peripheral critic of artificial intelligence. He is a senior figure in mathematical logic whose career has unfolded inside some of the most demanding institutions and subfields of modern mathematics. He argues that current AI systems are unreliable for mathematical reasoning. In a recent podcast, Hamkins shared that he doesn't find AI ‘helpful’. He has spent decades working in areas where precision is not optional, it’s a must.

Hamkins is the John Cardinal O’Hara Professor of Logic at the University of Notre Dame. His work spans mathematical logic, philosophical logic, set theory, philosophy of set theory, computability theory and group theory. He is particularly known for advancing the idea of the set-theoretic multiverse, a framework that challenges the notion of a single, absolute mathematical universe.

An education shaped by mathematical foundations

Hamkins earned his Bachelor of Science in mathematics from the California Institute of Technology. He went on to complete his Doctor of Philosophy in mathematics in 1994 at the University of California, Berkeley, working under the supervision of W. Hugh Woodin. His doctoral dissertation, Lifting and Extending Measures by Forcing; Fragile Measurability, placed him squarely within advanced set theory, a field that requires careful handling of logical consistency and proof structure.

These early academic choices shaped the kind of mathematician Hamkins would become. His research areas demand sustained attention to formal correctness, the limits of formal systems and the consequences of small logical errors.

A career across institutions and disciplines

After completing his doctorate, Hamkins joined the faculty of the City University of New York in 1995. There, he held positions across mathematics, philosophy and computer science at the CUNY Graduate Center and served as professor of mathematics at the College of Staten Island. Over the years, he also held visiting or faculty appointments at institutions including the University of California at Berkeley, Kobe University, Carnegie Mellon University, the University of Münster, Georgia State University, the University of Amsterdam, the Fields Institute, New York University and the Isaac Newton Institute.

In September 2018, Hamkins moved to the University of Oxford, where he became Professor of Logic in the Faculty of Philosophy and a Sir Peter Strawson Fellow in Philosophy at University College, Oxford. In January 2022, he joined the University of Notre Dame, taking up his current role as John Cardinal O’Hara Professor of Logic.

This trajectory placed him at the intersection of mathematics, philosophy and computation long before large language models became a public phenomenon.

Why Hamkins rejects AI as a mathematical partner

Hamkins’ recent comments on AI were made during an appearance on the Lex Fridman podcast. Speaking about his own experiments with several paid AI models, he said, “I’ve played around with it and I’ve tried experimenting, but I haven’t found it helpful at all.”

His central complaint is not that AI systems make occasional mistakes. Instead, he objects to how they handle error. According to Hamkins, when he identifies concrete flaws in their reasoning, the systems often respond with confident reassurances rather than correction. He described responses such as “Oh, it’s totally fine,” even when the mathematics is wrong.

For Hamkins, this behaviour breaks a basic requirement of mathematical collaboration. On the podcast, he said that if a human colleague behaved the same way, he would stop engaging with them altogether. The issue, as he framed it, is trust. Mathematical work depends on the ability to challenge arguments, identify errors and revise claims without resistance.

Hamkins summarised his position by stating that the outputs are “garbage answers that are not mathematically correct,” adding that “as far as mathematical reasoning is concerned, it seems not reliable.”

Benchmarks vs research reality

Hamkins’ critique sits within a broader debate inside the mathematical community. Some researchers have reported using AI systems to explore problems from the Erdos collection. Others, including mathematician Terence Tao, have warned that these systems can generate proofs that appear polished but contain subtle errors that would not survive serious peer review.

Hamkins’ experience reinforces this concern. He draws a distinction between strong performance on standardised benchmarks and usefulness in real research settings. Success on tests does not translate into dependable reasoning when proofs must withstand scrutiny line by line.

While he acknowledges that future systems may improve, Hamkins remains unconvinced that current models function as genuine research partners. His assessment mirrors a gap between the promises surrounding AI reasoning and the standards required in advanced mathematics.
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