AI Is Reshaping Mathematics, but Mathematical Judgment Still Matters

Summary

In this opinion article, the author argues that artificial intelligence is moving mathematics from a niche interest toward a much more visible and contested field. The author points to a claimed AI-assisted disproof of the Jacobian conjecture in dimensions three and higher, described as a breakthrough after nearly 90 years of resistance, as the development that intensified the debate in 2026. The article says AI can lower the barrier to learning by generating curricula and explaining material, while agents can search literature, assess an idea’s feasibility and novelty, and work through large calculation spaces. It also argues that AI may expand mathematical knowledge by producing results that would otherwise remain undiscovered, citing a controversial, claimed AI-generated Navier-Stokes blowup solution as an example that has nevertheless given mathematicians material to examine. The author accepts AI use when researchers disclose the specific roles it played, including prompts or literature consulted, and cite relevant sources; merely stating that AI was used is presented as inadequate. The article predicts that mathematicians, journals, and academic hierarchies will persist, but that professional competition will broaden to include amateurs and well-funded laboratories. It warns that increased output could bury important work under technically elaborate but uninteresting “slopmatic” papers and lead to higher rejection rates. At the same time, the author notes that many problems may remain resistant to AI and that the most powerful systems can require proprietary models, large agent swarms, and computing resources unavailable to most researchers. The overall position is that AI is a net positive for mathematics, but only if the field preserves transparency, appraisal of correctness, and standards of mathematical taste and significance.