What should we tell our students?

Álvaro Lozano-Robledo addresses urgent student anxieties about whether advances in large language models will obliterate academic careers in mathematics, answering a distraught undergraduate’s questions about employability, the narrowing of opportunities to only the “brightest minds,” and whether AI will surpass humans in pure-math research within a decade. He issues two upfront disclaimers: developments are fast and unpredictable, and his tenured perspective differs from early-career precarity. He critiques the narrative pushed by frontier model companies - highlighting incentives tied to upcoming IPOs and costly, publicized attempts to solve famous problems (an OpenAI investment figure is cited) - and warns that such narratives overstate autonomous capabilities by hiding countless failed attempts. He frames current community reaction as mostly confusion and emphasizes seeking a range of informed views via his “Human Mathematicians in the Age of AI” interviews.

His verdict is hopeful and practical: LLMs are powerful accelerants but so far operate within the “convex hull” of existing human ideas rather than generating genuinely alien concepts, as illustrated by recent celebrated proofs that recombine known techniques (for example, work around the unit-distance conjecture). Daily academic life remains centered on teaching, collaboration and conventional research, now amplified by a surge of new projects and student opportunities. He urges students to continue studying mathematics, argues that human mathematicians will remain central in steering and interpreting AI tools, and calls for sensible academic norms to harness LLMs for transformative progress.