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A 2024 collection of articles in the Bulletin of the AMS asked “Will machines change mathematics?”, suggesting that “Pure mathematicians are used to enjoying a great degree of research autonomy and intellectual freedom, a fragile and precious heritage that might be swept aside by a mindless use of machines.” and challenging readers to “decide upon our subject’s future direction.”
This was a response to the mathematical capabilities of emerging technologies, alone or in combination. These techniques include software such as LEAN for providing formal proofs; use of LLMs to produce credible, if derivative, research papers with expert human guidance; specialist algorithms such as AlphaGeometry; and sophisticated use of machine learning to search for examples. Their development (at huge cost in compute power and energy) has been accompanied by an unfamiliar and exuberant level of hype from well-funded start-ups claiming to “solve mathematics” and the like. And it raises questions beyond the technical concerning governance, funding and the nature of the mathematical profession.
To try and understand what’s going on we look historical examples of changes in mathematical practice – as an example we consider key developments in the early days of computational group theory.
The speaker is keen to hear of colleagues using LLMs, LEAN or similar things in research, even if they can’t come to the talk.
