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

Large language models (LLMs) and the research systems built around them have shown impressive capabilities in generating mathematical proofs. These tools have the potential to accelerate discovery and bring about extraordinary advances in mathematics, science, and technology. However, the integration of LLMs into STEM ecosystems must be carefully managed to ensure a "golden age" scenario, where human scientific activity is preserved and an open, collaborative, and intellectually independent scientific enterprise thrives.

In a "dark age" scenario, despite short-term increases in scientific and technological output, independent human scientific activity could weaken, and the production of new knowledge could become increasingly concentrated in a small number of hands. This would lead to a situation where knowledge becomes alien to human understanding.

While LLMs have demonstrated remarkable abilities in mathematics, their usefulness in providing human-understandable proofs is limited. The translations of LLM-generated proofs into natural language tend to be complex and require intensive study by mathematicians to achieve human understanding. This raises the question of why we should care about studying mathematics or obtaining proofs if we cannot fully comprehend them.

Mathematics is an essential part of human culture and cognition, with innate mathematical concepts present in humans. Despite the growing capabilities of LLMs, mathematics will continue to play a significant role in human society. This necessitates a focus on developing and training more mathematicians to maintain and advance the field.