Canonization and the Overhang

7 hours ago

David Bessis argues that mathematics overvalues theorem proving while undervaluing creativity, clarity, and teaching, which are critical for progress.
LLM-powered theorem provers can prove theorems without the beneficial side effects of human collaboration and intuition.
In software, there's a parallel between code that passes tests and code that is socially constructed for team usability and iteration.
Canonization is the process of turning one-off solutions into reusable, coherent, and compatible systems or libraries, which is time-consuming but essential for long-term value.
Software benefits from canonized code through stable abstractions and reliable systems, contrasting with disposable, single-use software that may seem 'bad' by traditional standards.
The Overhang refers to unrealized potential from past creativity, where connecting existing ideas can yield new solutions, a concept applicable to both mathematics and software.
LLMs are well-suited for searching the Overhang by memorizing and pattern-matching across large corpora, unlike humans who rely on intuitive leaps.
Open source software represents an Overhang of canonized work that can be built upon for future development.
Valuing only theorem proving or coding without canonization and knowledge transmission risks depleting the Overhang and undervaluing critical 'glue work' like cleanup and teaching.

Hasty Briefsbeta