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 growing awareness of 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.

To try and understand what’s going on we look at the factors, whether technical, social or economic, leading to the ongoing adoption and impact, or otherwise, of previous computational interventions in mathematical practice. As an example we consider key decisions made in the early days of computational group theory.