Why is mathematical foundations so dead these days? The youngest Ph.D advisors I can find are like 85+.
>inb4 "Muh heckin HOTT!!!!
Why is mathematical foundations so dead these days? The youngest Ph.D advisors I can find are like 85+.
Why is mathematical foundations so dead these days? The youngest Ph.D advisors I can find are like 85+.
>inb4 "Muh heckin HOTT!!!!
Name one mathematician you can find as a PhD advisor who's 85+
Dennis Cornack
Did you misspell that?
Someone keeps poisoning those who dig too deep.
This. Allegedly there was a student who claimed to have solved the halting problem. He went to talk to his professor. On his way back home he mysteriously died in a car crash.
Did the stupid tosser not write it down?
Underrated post
And now it's overrated. If only there was a way to award him half a (You) for his effort.
what a hilarious and worthwhile post
Oh, I get it. You updooted your own joke and you're mad now.
You mad nobody thought your post was good? homosexual
Spooky!
because western man never delved deep into anything and this is the work of western man.
What are the applications of math foundations outside of math foundations? I mean, I suppose the most advanced concept 99% of mathematicians use from set theory are classes to define a category.
I don't think anyone doing math that isn't specifically set theory cares about set theory. (At any deeper level than you'd care about writing in Latin with correct grammar and punctuation. You'd care, it just wouldn't matter.)
Category theory is not suitable for foundations or even meant to be foundational. Most category theorist use an extended version of set theory through the use of Grothendieck universes.
In fact, its purpose is best seen as exactly dual to that of foundations: while set theory allows you to build things from the ground up, category theory allows you to organize things from high above. A category by itself is not so interesting; one often studies a category in terms of how it maps from and into other categories (including itself!), with functors, and, most usefully, adjunctions.
There isn't much money or prestige in it. For instance, suppose you have an IQ of 140, do you:
>A) Study computer science and some other field like finance and retire in your 30's
>B) Get a math PhD and MAYBE discover something while also dealing with students until you're 85
It only makes sense to go down the math PhD path if you're a trust fund baby or genuinely do not care about money.
or if you want to earn 300k starting on any job you want
Mathematics by itself is worthless. Unless you study on how to apply mathematics in a practical setting, you may as well be doing philosophy.
Wrong you stupid moron. Now you will suck my cock or I will put a bullet into your asshole with my gun.
Exactly the opposite is the case. Only pure mathematics has value. All application is vulgar and base.
>you may as well be doing philosophy
Right. It's just that your attitude toward philosophy is backward.
"Bourbaki's set theory" was a torturous exercise that they put themselves through only to get a certain foundational stance that they felt that they could live with. Once they published it, they almost never cited it anywhere else in the Elements afterwards, and then they busied themselves with (presenting, in their own terms, the established) "real math", the fun part, what mathematicians actually like doing. On the set theory book, one of them is supposed to have said that it was written "with pain and without pleasure, but we had to do it".
is there a particular branch of foundations you're interested in?
>branch of foundations
Come on you're not even trying.
maybe the reason you're having a hard time is that you're looking for an advisor in general foundations, but that split into several subfields decades ago
because ZFC and Bourbaki's set theory are already perfect material for foundations. Toposes, category stuff, hott etc aren't foundational, they are some advanced semantical stuff which are very useful for a lot of purposes and unifying vast amount of separate topics but they aren't foundational (every book on these matters who actually do the dirty work call ZFC to the rescue every second or third page).
Saying hott is foundational over ZFC is like saying computer programming is founded upon java or heavily templated c++ instead of assembly or machine language.
wat
because after Gödel killed off foundations big aspirations there wasn't much left to study
okay technically there is, but nothing much of important to anyone outside of the field
Then computer science came along and everyone with half a brain left there because mathematical logic is actually important in those fields as a basis, most mathematics you can get by without knowing much about mathematical logic
Filthy type system peasants LAPRing as mathematicians.
Bourbaki had already predicted HoTT
frankly because it's worthless.
The only reason it was cared about then was because hilbert and the bourbaki retards thought they could reduce mathematics to mindless axiom stepping, even though every single mathematician preceding them did not work like that.
Once Gödel buried their idea, foundations went back to being a meme. death to nicolas bourbaki
Unfortunately, mathematicians never got out of the sterile, lifeless, unmotivated definition-lemma-theorem format without any context or background that popularized by Bourbaki. Some of the applied math and complex systems is slightly better in this regard, but even they have been heavily influenced by Bourbaki. If you read older math texts, especially from the 1800s or earlier, it's way more readable and engaging. If you read someone like Dedekind or Euler, it's like reading a novel. Or maybe not like a novel, but it's a lot more readable. Like a biology or physics textbook or a work of philosophy or something like that. Dense, but it's still a lot easier to read than a modern textbook like Dummitt and Foote (which is actually pretty good my the standards of modern grad level texts) or basically any modern algebra or topology textbook.
And that's a good thing
im saying this in a nice way. I would behead all three of you in real life
don't worry you can behead them, but I'll be castrating them before you kill them. In a nice way.
lol no, those old papers are torture to read.
definition-theorem-proof is the best way of doing mathematics and the rest is vapid bullshit
I think its more a result of research math going in the 20th century from a noblemen’s hobby to a profession, like accounting or something
>go to math school
>learn standard math
>collect PhD cerificate
this breeds a caste of servile wretches looking for promotions and to “get” papers
Dedekind wrote in 80 pages what modern analysis books do in 10 pages. Maybe you'd prefer reading little stories and novels for the rest of your life, but there are people here want to do research in math by the time they die.
this is bait, I would have bitten but for that little flourish at the end
There is still some research in epistemic logic and non-classical logics like paraconsistent logics. Of course, that's mostly in philosohpy departments. Judgement agrregation is also a pretty active area that involves both logic and social choice theory, the mathematical analysis of voting. Pic related. Basically studying how collective reasoning can either enhance or inhabit rationality by examing how aggregating different beliefs together using probability or voting can result in truth, falsity, or inconsistency depending on the criteria being used to aggregate judgements (for example, when combining the judgements of jury members in a court case, or when aggregating different results or claims from different scientists).
You're talking out of your ass.
Universities generally don't allow professors to take on new students once they hit 70.