David Bessis argues that the traditional theorem-proving economy is declining as automated proof assistants and formalization shift mathematics toward intuition and visualization. This essay critiques the system's obsession with theorem-proving priority while real progress often occurs outside that loop. This matters because it signals a transformation in how mathematics is practiced and valued, with AI and formal tools challenging the core incentive structure of academic mathematics. It could reshape priorities toward insight and understanding rather than pure theorem production. Bessis highlights that AI-written proofs in systems like Lean often fail to convey useful human insights, yet they are increasingly used. He contends that the intuitions gained from proving are more valuable than the proof itself.
Background
A proof assistant is a software tool that helps humans develop formal proofs through human-machine collaboration. Formal verification uses mathematical methods to prove correctness of systems. The term 'theorem economy' refers to the academic culture that prioritizes proving new theorems as the primary currency of mathematical achievement.
References
Discussion
Comments reference Greg Egan's 'truth mining' concept from the novel Diaspora, foreseeing mathematics evolving into visualization and insight after formalization. Another comment draws parallels to software testing, suggesting that mathematicians may adopt a culture of 'battle-tested' confidence rather than formal proof. Some note the article's prior submissions on Hacker News.