Will it be a golden age or a dark age for mathematics (and science)? (terrytao.wordpress.com)

In a recent guest post by Francesco Maggi, the impact of large language models (LLMs) on the fields of mathematics and science is explored, highlighting their remarkable ability to generate mathematical proofs. While these LLMs have the potential to significantly accelerate scientific discovery by crunching through vast amounts of literature and proposing solutions to complex problems, such as the Navier-Stokes equations and the Riemann Hypothesis, concerns arise about their limitations—particularly their capacity to provide comprehensible translations of these proofs. This situation raises essential questions about the nature and significance of human understanding in the study of mathematics. Maggi argues that an increased reliance on machines could lead to either a "golden age," characterized by empowered scientists and collaborative inquiry, or a "dark age," where the depth of understanding diminishes and knowledge becomes inaccessible to human comprehension. The discussion emphasizes the necessity for careful integration of LLMs into STEM fields, balanced with maintaining a culture of scientific skepticism. Maggi asserts that true mathematical creativity, particularly the act of "mathematization" (inventing new mathematical languages), remains a quintessential human endeavor. This dialogue underscores that while LLMs could transform access to proofs and foster new avenues of exploration in science, they should not replace the human insight that has driven historic mathematical breakthroughs. Ultimately, the evolving relationship between human mathematicians and LLMs presents an exciting yet complex frontier for the future of both mathematics and the broader scientific community.