Once I got past the first few paragraphs, all I learned from that is that I don’t understand the Poincare conjecture or really anything about topology
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quilan@lemmy.world 1 week ago
For any not in the loop: en.wikipedia.org/wiki/Grigori_Perelman
NielsBohron@lemmy.world 1 week ago
davidagain@lemmy.world 1 week ago
2D: If you draw a perhaps wobbly circle shape (loop) on the ground, it has an inside that you can colour in. If your loop is elastic, it can contract to be all in a tiny heap. Topologists call this “simply connected”.
3D: The water on your bath is also simply connected. Your elastic loop, whatever its shape, can shrink back down to tiny.
2D: The surface of your tennis ball is simply connected because any elastic loop on its surface can shrink to nothing, but the surface of your ring donut isn’t, because you could cut your elastic and wrap it arround the donut and it couldn’t shrink because the donut would stop it. Ants living on the surface of the donut might not immediately realise it wasn’t simply connected because they’d never drawn a big enough loop to find out that it couldn’t be shrunk.
3D: The solid donut is also not simply connected, because the ring could contain an elastic band that goes all the way around the ring and back to the start, and it couldn’t shrink to nothing because it would have to leave the donut.
2-Manifolds: a 2-manifold is some kind of surface that doesn’t have an edge and when you look up close it looks like it’s flat-ish. You could make it by sticking lots of tiny sheets of rubber flat to each other but there’s not allowed to be an edge. The simplest 2-manifolds are an infinite plane, the surface of a ball and the surface of a donut. The small ones are called closed. The technical reason for that is to do with not having any edges but still being finite, but you can think of closed to mean finite.
Manifolds may not be as the srrm: If you live in a 2-manifold you might not immediately realise that it’s ball surface and you might not realise it’s a donut surface. If you have a computer game from yesteryear where when you go off the top of the screen you come back on at the same angle and position on the bottom of the screen, and the same for left and right, that’s actually got the same layout as the surface of a donut. To help you see that, imagine your screen was triple widescreen and made of rubber. Roll it up to glue the top to the bottom and then glue the two ends of the tube to each other. You haven’t changed the game play at all but now you can see it’s the surface of a donut shape.
3-manifolds: anything that looks like 3D space up close is a 3-manifold. The simplest 3-manifolds are an ordinary infinite 3D space, a 3-sphere, which is like the 3D version of the surface of a ball, but it’s hard to imagine the 4D ball it’s wrapped around, and the 3D version of the computer game.
The universe: It looks simply connected, but we can’t see that directly, because maybe there’s a very long loop we haven’t gone on yet that gets back where you started without being shrinkable. This is hard to imagine, but it could be like being in the 3D version of the computer game where there’s a long loop that can’t shrink because it goes through one side of the screen and comes out the other before coming back. It can’t be shrink at all, especially not to nothing. The universe is a 3-manifold.
The Poincare conjecture says that every simply connected “closed” (finite) 3-manifold is essentially the same as the 3-sphere. If ALL your loops shrink, no matter how big, and the universe is finite and has no end wall, then it’s the 3 sphere.
restingboredface@sh.itjust.works 1 week ago
From the wiki article :
Anybody have any idea what the ethical standards might be that he’s referring to? Not sure if there’s a scandal or something or just an overall sense of displeasure with the field.
reallykindasorta@slrpnk.net 1 week ago
I tried to google it and it’s not super clear. -Perelman gets his phd in russia super young and is hired at NYU/SUNY -Publishes some groundbreaking stuff on arxiv (a free site to post white papers in math and physics) in 2002/2003 -There is some drama with another scientist who is known for stealing people’s work trying to downplay Perelman’s contribution -Perelman quits his US jobs and returns to russia to work in math (making wayyyyyyy less money), then quits that job too and becomes a recluse -Turns down fields medal and millennium prize (1M dollars for solving) -Says some mathematicians are unethical but the rest of them tolerate it so they’re shit too so the whole thing is shit. Also says he doesn’t want to be put in a zoo or treated like a pet about it.
— I’m going to go ahead and assume I don’t understand enough about being a math superstar to understand where he’s coming from, but he certainly sounds like a principled guy and now I respect him.
Yokozuna@lemmy.world 1 week ago
Punk rock as fuck. May this dude find many morsels and enjoy the morning dew for the rest of his days.
turnipjs@lemmy.ml 1 week ago
Homie really said AMAB.
TheBat@lemmy.world 1 week ago
AMAB?
untorquer@lemmy.world 1 week ago
Just a few bad apples.
FundMECFSResearch@lemmy.blahaj.zone 1 week ago
I mean math is the backbone of science and technology. And technology can lead to fucked up things.
Nuclear bombs wouldn’t be possible without fairly recent math.
Not to mention the unethical hell that is the whole financial sector / trader type where mathematicians often end up working.
And finally these days, by making new discoveries in some fields your directly contributing to the growth of AI and LLMs.
An infamous example of someone who quit math over ethical concerns (ironic given the rest of the story) is Ted Kacyznski (the unabomber), who saw math as leading to more and more advanced technology which oppresses people and destroys nature.
AEsheron@lemmy.world 1 week ago
I think his issues more stemmed from academia and the rat race within it, not so much the ethical issues of mathematics and what they can lead to. Just shitty crabs trying to escape the bucket.
fossilesque@mander.xyz 1 week ago
I too find economists unethical by trade. Statisticians with a gambling problem, the lot of them.
fossilesque@mander.xyz 1 week ago
Goals.
474D@lemmy.world 1 week ago
Damn I didn’t know mathematicians go this hard.
daniskarma@lemmy.dbzer0.com 1 week ago
Most mathematicians I know go REALLY hard. There’s something about the field…
Omniraptor@lemm.ee 1 week ago
This new Yorker article goes into some more detail. Apparently there was some underlying conflict between rival Chinese academics over succession of university admin postings in Beijing.
According to the article it was one Chinese dude trying to hog credit and Perelman basically went “oh i’m not brave enough for politics” and bailed. If he accepted his choice was basically becoming a conformist or getting involved by trying to improve things. He chose not to choose.
web.archive.org/web/…/manifold-destiny
Yokozuna@lemmy.world 1 week ago
I’m totally for how and why he dipped out. I’ve made a few decisions in life in a similar fashion. But a man as principled as he is, with feelings and ideas that intense, is a hell of a thing to lose in the pursuit of truth. Just imagine, if instead of resigning to almost insurmountable odds where most would be against him, he instead chose to be a stubborn man in the opposite respect and didn’t rest until the truth and was common knowledge or had created groups and institutions to further pursue it if not able to do it himself.
Things like this are way bigger than one person, and to understand the problem and try to tackle it would consume your whole life. Go on and pick some mushrooms my man. You made your contribution to society and decided the rat race isn’t worth it.
dustyData@lemmy.world 1 week ago
Just speculating, maybe it has to do with belonging to Russian academia.
daddy32@lemmy.world 1 week ago
Yeah, there was some background drama with his parent institution, if I remember correctly. He didn’t have enough money to fly anywhere, his institution refused to donate and he was too embarrassed to ask elsewhere. Or something like that.
sircac@lemmy.world 1 week ago
Not from that field, and I think it depends a lot of the field, country, etc, but research is not an idilic world at all and deal with huge flaws from the real world, institutions, society and economics, not aside of human being’s flaws, so it can be deeply disappointing in some aspects. I believe is a natural in any guild (there is shit everywhere, e.g. police require internal affairs for a good reason, but not only, they suffer from funding restrictions, metrics for promotion, etc, and the same can be said for medicine, politics, etc) so in the end it may be your ability to deal with real world shit… and luck.
untorquer@lemmy.world 1 week ago
Keep reading. It’s in the “Possible withdrawal from mathematics” section.