Will it be a golden age or a dark age for mathematics (and science)?

Francesco Maggi examines how large language models (LLMs) and AI research systems are reshaping mathematics and science, framing two futures: a golden age where these tools empower more scientists and expand mathematization, and a dark age where discovery concentrates in a few hands and produced knowledge becomes alien to human understanding. He documents striking LLM-generated outputs - claims of formal proofs for problems like Navier-Stokes with forcing and a quasi-Riemann proposal - then highlights a core problem: LLMs often produce correct but massively long formal proofs in Lean while delivering messy, unreadable natural-language translations, leaving humans unable to internalize or understand the results. That gap makes human comprehension central: without it mathematics loses its cultural and cognitive purpose, so the response must be to train far more mathematicians and chart institutional choices rather than assuming inevitable outcomes.

Maggi urges healthy scientific skepticism about sweeping claims regarding AI creativity, noting LLMs excel at recombining vast literature and finding connections at scale but suffer from opaque development and unknown failure modes. He emphasizes mathematization - the invention of mathematical frameworks that render phenomena intelligible - as the crucial human function that should be amplified, citing Newton, Riemann, Einstein, Shannon and Grothendieck as exemplars. Mathematical progress cannot be reduced to ticking off problem lists; transformative advances often arise from new languages and synthesis (general relativity, information theory). He analyzes eight decision points shaping the future and closes with concrete proposals to integrate LLMs while preserving open, independent scientific practice.