>research interests started with logic and the theory of surreal numbers, while he was still in high school.[6]
>He is best known for his work, starting with his thesis, on infinity-categories and derived algebraic geometry. Derived algebraic geometry is a way of infusing homotopical methods into algebraic geometry, with two purposes: deeper insight into algebraic geometry (e.g. into intersection theory) and the use of methods of algebraic geometry in stable homotopy theory. The latter area is the topic of Lurie's work on elliptic cohomology. Infinity categories (in the form of Joyal's quasi-categories) are a convenient framework to do homotopy theory in abstract settings. They are the main topic of his book Higher Topos Theory.
I think it looks kinda cool with those specific Math words desu.
Also you can look less autistic in Math if you're into Mathematical Finance, Mathematical Physics and Mathematical Biology desu. But not gonna lie, "Pure" Math sounds autistic yet it doesn't look like it once you call it "Theoretical Math".
I seriously wonder what's the most and the least autistic science though >inb4 all of them
Adam Ward
I think they make up words to sound "cool".
Christopher Harris
Also could be that, but oh boy, they can do lots of good shit like working with our computers, building and studying things, work with big corps, etc.
And Math is quite interesting if you read more of them though, read about the Collatz conjecture for example.
Ryan Gutierrez
>collatz conjecture >interesting
Luke Myers
k
Levi Wilson
>infinity-categories >homotopical methods >intersection theory >stable homotopy theory >elliptic cohomology >Infinity categories >Joyal's quasi-categories >homotopy theory >Higher Topos Theory.
Literally try-hard
Ryan Ross
Because they are austistic
Logan Rodriguez
Lurie is probably a bad example of this, Too much abstract nonsense. IMHO his greatest acheivement was probably that perfect score on the IMO.
Alexander Watson
What's up with the abstract nonsense? Why waste your time on going that deep in it?
Anthony Williams
>mfw I actually sort of understand what that all means Fuck. I saw so much math, but never saw a female naked. fml
Blake Butler
I dunno, generalizations of generalizations, theorems about theorems, and math about math never appealed to me. At that point you can no longer feasibly claim that mathematics possesses any universal qualities, as you are essentially just making things up, there is absolutely no tie in with anything real. atleast in geometry, and analysis, there are (or were) important questions at stake, questions which people other than masturbatory 'pure mathematicians' cared about.
Christian Reed
It's funny because Lurie looks like he could be a massive Chad, but then he's pretty autistic. Similarly with Tao. He looks normal enough, but despite his fame, when he speaks he allmost sounds like he's spilling Spaghetti on purpose
Noah Harris
Category theorist seem to claim to go higher than logic, as your logical systems can themselves be though of as "objects", but what is the real difference between some metamathematics (such as seeing the strength one needs to prove systems of mathematics, i.e., logic) and category theory that is making generalizations about mathematics?
I get what you're saying, generalizing generalizations and just making stuff up. Wonder if they intentionally choose these names to sound "cool", e.g., the name 'Tropical Geometry'.
Charles Roberts
Lurie and witten are pretty bad, both sound like faggots, but I must say, Saul Kripke is easily the worst sounding, the most autistic man ever to hold a professorship.
I never liked this kind of justification for doing things. Maybe there are theories just like category theory, in the sense that they generalize classes of mathematical objects, but in a non categorical fashion, maybe there are multitudes of such theories. We could then develop a theory in which these theories are the objects, and we've gone one step higher.
This ultimately illustrates my concern, if you were really clever, you could fill in the details and make it work, stacking generalizations on top of generalizations in a never ending race to over-generalize.
We need the generality of logic in a sense, so that we can get to peano arithmetic and eventually to rigorous analysis.
A tower of babel of generalizations, which is where certain parts of mathematics are headed, is not servicing anything other than its own vanity and narcissism.
Jonathan King
Agreed. Well said.
Carson Green
>atleast in geometry
Some things in geometry can only be properly expressed via category theory.
Eli Rogers
maybe there are, but category theory is still more or less dispensable in geometry, it is not the linchpin on any major result I know of.
Andrew Brooks
What the FUCK.
How is it even possible that someone like this is anywhere except a mental hospital? Just because he's saying things that sound profound?
Nolan Anderson
>but category theory is still more or less dispensable in geometry
A big part of modern algebraic geometry is the study of moduli problems. A moduli space is essentially space whose points are isomorphism classes of some type of object (for instance a moduli space of elliptic curves).
The naive idea would be to take the set of such objects and quotient by isomorphism. Sometimes this carries a geometric structure (structure of scheme/manifold), but most of the time it doesn't.
In order to make geometric sense of such spaces we need something more than set theory, we need category theory.
Nathaniel Roberts
Virgins.
Juan Edwards
>see "Lurie" being namedropped here >google it >the guy is pretty handsome Feels good to know that there are good-looking people out there with too little social skills to use their looks at their favor.
Camden Kelly
I'll have to defer to you on modern algebraic geometry, specifically with respect to the "geometries" of "fictional spaces", When I mentioned geometry I was speaking more of synthetic geometry, classical differential geometry, and its riemannian extensions, sure commutative diagrams occasionally occur here, but little else.
you can take [math] L^{2} [/math] with its standard norm and then produce notions of length and angle in the usual fashion and you have a notion of geometry for the 'fictional space', but that is just a ghost of a geometry, as we have just extrapolated from a space where we have physical intuition to a space where we don't.
certainly still worth studying, but I wouldn't count it as 'primary' geometry.
Owen Brooks
Category theory does come into place in Diff. Geometry too on occasion.
For instance, Fukaya categories of Kahler manifolds.
They are important for a few things, but the most significant probably being Mirror Symmetry.
Mirror Symmetry was initially a physical result that had no pure math analog, but it was later rigorously expressed as an equivalence of fukaya categories and derived categories.
Isaac Nelson
eh, I think you're missing the point.
Sebastian Barnes
I don't think so. Certain things in geometry just cannot be studied without category theory.
I think the Mirror Symmetry example is a good one. It may be a very non-standard type of geometry, hence why it was discovered via physics, but it is none the less a very real geometric symmetry fundamental to certain types of manifolds.
Jack Harris
>applied math combinatorist >pure math autists
pcik one
Xavier Gonzalez
How do I become more like this guy? It seems like he has taken the ultimate redpill. I don't know what he's going on about, but he sounds very enlightened.
Hudson Rivera
get vaccinated
Cooper Cruz
>Attractive She's literally average.
Michael Carter
If kid Tao had decided to exercise in his youth a little, instead of solving equations 18 hours a day, he would've been kpop tier
James Hill
>tfw you are currently reading an ODE book
>tfw you realize you are literally reading a children's book
Tyler Gomez
Brainlets, get out.
Adrian Gonzalez
bump
Landon Torres
Math is just a really jargon heavy field. You can make physics sound cool by relating it to everyday experiences but when you're talking about abstract structures that can't really be observed and can only be reasoned about there's some communication barriers. Every little idea has to have an unambiguous definition, and to create those definitions you have to make use of a bunch of other unambiguous definitions and clear terminology, so explaining even a basic theorem to someone is basically giving a lesson in a foreign language.
