There are many profound implications of this. Consider 3, on the assumption of this being generally valid: 1. Cutting edge mathematical work produced outside of the system of current academia is unlikely ever to be recognized, bc it’s completely valid for professional mathematicians to ignore rando crazy people when it’s already this hard to verify work by known colleagues who claim a major achievement.
2. In theory it’s possible some Ramanujan-type geniuses have made major breakthroughs, but absent a Hardy as patron this will never be known or knowable, and currently there is no way around it. Think about how much is owed to Hardy actually reading Ramanujan’s work and doing justice to it.
3. The lifecycle of profound advances is in generations, and the best way to dramatically improve science is to find a way to accelerate this. That’s what I’m doing in my work currently on collapsing the time-scale of intellectual progress, as in the New Biology Project I direct. As I stress in my philosophical consulting on AI and the future of education, the problems of AGI already exist in certain areas, and most AGI speculation is nonsense because it does not understand this, or how crucial verification is and how difficult it is. Hardy said he was not a genius but simply had the distinction, if I remember this right, of being “at one time in the 20th Century the fourth best pure mathematician in the world.” Bessis’ work has taken over decade to begin to be recognized for the achievement he sees as most important, and that is with the internet allowing far faster and easy access to research and researchers. Those thinking about the nature of science (and I mean that generally, in the European sense, not just the natural sciences and math) should recognize without confronting this issue, scaling the pace of scientific progress is impossible. That’s why my major long-term focus is on how that can happen. It’s far more valuable to make a contribution to that problem, for me, than any single expert subdomain, which I’ve already done and am doing in my book. Systemic awareness, not merely local specialization (that is a necessary condition), is the framework needed to address this issue.
#math #science #scientificprogress #philosophyofscience #agi
The lifecycle of a pure math theorem:
- 1997: my PhD advisor asks me to work on one of his conjectures
- 2000: I solve the simplest case and dream of generalizing my approach
- 2003: after years of struggle, I come to the conclusion that my approach *cannot* generalize
- 2006: after reading a paper by Daan Krammer, I have a lighting bulb moment and realize that my approach works in full generality *up to equivalence of categories*... this enables me to solve my advisor's conjecture... I then use it as an ingredient in the proof of a much older and more famous conjecture (the "K(π,1) conjecture for finite complex reflection groups")
- 2007: I submit my article for publication
- 2009: referee #1 gives up
- 2010: 2 more referees have now given up, complaining that the paper is too hard to read
- 2012: referee #4 is finally able to produce a report, the revision work starts
- 2014: the paper is accepted for publication
- 2015: the paper is published
- 2007-2025: because the older conjecture overshadows the lesser known conjecture by my advisor, and because my paper is too difficult, virtually no-one asks any question about the "lighting bulb" categorical idea at the core of the proof
- Jan 22, 2026: I received an inbound email from a mathematician from another hemisphere, inquiring about the categorical aspects
- Jan 26, 2026: I have my first ever videocall discussing the specifics of this core component of my proof