alt Hacker NewsThat’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle.
Mathematics has always been highly competitive.
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The story of the cubic equations is another great example: https://en.wikipedia.org/wiki/Cubic_equation
Dudes straight up used to hoard solutions to equations and use them in math battles.
My computer contains the prime factorization of probably several dozen (if not more) large integers, and I refuse to share them with anyone!
(Because they are my private RSA keys)
Andrew Wiles was also careful about communicating progress on his Fermat's Theorem proof during the years in his attic. So yes I take the point.
I read the Mastodon thread as more about the 'flattening' and 'rawness' of the proofs these systems and their operators are producing. I mean what is the cultural significance of a lean proof that is half a million lines long or something? And what tools can be extracted for further work from such a construction?
The late William Thurston wrote about the culture of mathematics in that sense.
Also Andrew Wiles working in secret for 7 years out of fear of someone scooping him.
It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle
Yeah but a highly productive last two decades of math research from https://en.wikipedia.org/wiki/Polymath_Project has come from collaboration.
You miss the point. Humans don't mind competing with others. I love competition, but I don't want to compete with you and your machine. I love to play chess, I don't care if you are grand master, whoop my ass. But not if you are going to pair up with stockfish. I don't even care if you are a newbie that started playing yesterday with an ELO rating of 900. If I wanted to play the damn computer I'll do it myself. Likewise, mathematicians will not mind sharing and competing with other fellows, but if another has a billion dollars worth of GPU and you don't? Then you best be carefully what you say.
this is not untrue but it's a pendulum swinging back to ancient times man
Between people.
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Surprised to see someone on HN arguing against open science. Seems like the opposite of the lessons we should learn from Newton and Gauss, actually, hoarding results for decades at the expense of progress.
(the Pythagorean thing isn't really competition either, is ahistorical, and from what we actually do know it's again people hoarding results instead of sharing them).
FWIW, your post comes off as a middlebrow dismissal, surface level and not actually engaging with the substance of the comment. It's also just wrong. You claim "it’s also a misstatement of mathematical history", but don't specify which part. That there's "centuries of traditions of open science"? But your examples are from centuries (and millennia) ago, and there was never any claim that these traditions are universal.
But more fundamentally, competition doesn't mean you can't also have open science. And the very long, damaging events like the Leibniz/Newton feud are exactly what make many mathematicians work to maintain a spirit of collaboration and attribution even when they're competing on approaches.
The mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.