How do we prevent mathemathics from devolving into the Medieval Era of secrecy?
12 hours ago
- Medieval mathematics was kept secret, treated as personal knowledge essential for a mathematician's livelihood and reputation.
- Mathematicians engaged in public contests where solving problems fastest secured funding and status, creating strong incentives for secrecy.
- Example: Scipione del Ferro hid his method for solving depressed cubics for 20 years, revealing it only on his deathbed.
- This culture of secrecy persisted into the late Medieval Era, contributing to disputes like Newton vs. Leibniz over calculus.
- Modern incentives shifted toward publishing results, with funding tied to writing grant applications.
- AI and large language models are now producing proofs cheaply, threatening the traditional proof economy.
- Large companies can spend millions on compute (e.g., $6.5M–$40M for a Navier–Stokes counterexample) to solve problems quickly.
- Terence Tao warns that the ability to cheaply extract solutions may lead researchers to hoard promising problems, reversing centuries of open science.
- Proposed solutions: require human authorship for credit, and mandate publication of full methodology.
- Tao suggests designating certain problems as needing careful analysis and insight, not just raw solutions; analogized to food donation standards.
- Potential mitigations: limiting credit to humans, and requiring full methodology disclosure to disincentivize AI companies from sweeping up results.