Most of Veeky Forums find topology, combinatorics, and number theory interesting. But what is the dryest...

The answer is combinatorics. Despite combinatorics being responsible for many powerful theorems we take for granted, many general math journals are reluctant to publish findings in combinatorics because most mathematicians find it incredibly dull.

The reason for this is that combinatorics doesn't really build on itself. Most problems in combinatorics are completely isolated from one another and the solutions to such problems cannot be used to build a more general theory. In essence, the solution to a combinatorics problem does nothing other than solve a cute puzzle using a clever trick with simple methods. It's the black sheep of mathematics

Optimization

i find analysis and set theory boring as fuck

Linear algebra.

AKA the art of taking things already intuitively comprehensible in terms of multivariate calculus and trigonometry and making them seem as arbitrary and unnecessarily complicated as possible

uhh linear algebra isn't advanced, it's an introductory class

>confused by the simple concept of a vector space
>thinks it's unnecessary
not only are you a gigantic brainlet you're also an engineer

b-b-but muh haskell

Category theory, general topology (ie. "assuming the full axiom of choice and GCH, we construct a counterexample to the following property that is satisfied by the spaces encountered in every other field of math", the field) , numerical analysis (ie. "under the vague hypotheses A, B, C, D on symmetric semidefinite matrix A we have the following improvements of the estimates of [..., 2014] on the l^2 average of the eigenvalues", the field)

This

Combinatorics

See

Combinatorics and number theory.

set theory

Numerical analysis, numerical linear algebra

Less so but still boring:
real analysis, differential equations

I didn't realize the combinatorics/finitism hate here was actually real. I'm doing combinatorics work in grad school. I like it? I have a perspective on it similar to Doron Jewwhatevername, I wish more mathematics focused on it. A lot of actual applications of math rely on it more heavily than a lot of other topics...

this
fucking numerical analysis

Optimization, by far.

I dabbled in most applied math. They all are generally very boring, but optimization takes the cake.
What's worse there is no real textbook for it.

>I'm an undergrad studying algebraic topology : the post

It's not true at all.

Since Szemeredy proof of arithmetic progression in 1975, combinatorics is now seen way more seriously that it was before. Now extremal combinatorics have papers in Annals of math regularly and guys like Tao and Gowers have been huge advocate of the fields for years now.

It's true that it's a field where a lot of papers are based on independent ideas, but it's now a well developed theory, and there are huge theorems, like the strong perfect graph conjecture or the graph minor theorem on which everybody builds upon. Plus the understanding that we have now of many tools like the regularity lemma or the probabilistic method is something that required almost a generation of very talented people, for example the Abel prize winner Szemeredy or guys Alon, to achieved and is now very useful.

Honestly, if you say that Keevash proof of the existence of design is the black sheep of mathematics, you're just a joke.

anything closely related to set theory

because your brain cannot handle mathematical machine code

inb4 no forcing

Take your pedophile cartoons back to .

>I am buttmad that algebraists are so cool

either general topology or homological algebra

All math is pretty boring to be honest. It only seems exciting every once in a while you learn about some theorem that appears really deep that blows your mind (for me this was stuff like the Nullstellensatz or the Hurewicz theorem).

The actual day-to-day practice of doing math is boring as fuck though, or at least it was for me. I only have an undergrad degree in math though, and this was probably why I stopped doing it.

>He thinks he is cool because he draws diagrams on a black board with chalks

I hope you're very smart kid

can't stand it

Indisputable answers:

-Differential Equations
-Number Theory
-Numerical [anything]

This

It's a stretch to say that the theory is well-developed as compared to number theory, or topology, or algebraic geometry. Only recently have people been coming up with unifying theories (Joyal's species, for one), and they have a long way to go. Then you have problems like 3n + 1 where there is essentially zero theory (read categorical structure) to bring to bear. Unlike the other poster I predict that such a theory can and will be found eventually, but we're not there yet.

bingo

anything to do with DE's

I like this bait.

complex analysis

A whole field of math based on arbitrary made up stuff that doesn't even exist in reality and has no applications.

Combinatorics has a bad reputation (partially deserved) of being a bunch of one-shot puzzles, whereas for example analysts have a very rich, developed history that just keeps stacking onto itself.

Obviously the people for whom this is a big criticism don't really care how useful it is to applied problems either.

Additive number theory.
>hurf primes are a multiplicative structure but dude what happens if we ADD them
you get a bunch of dumb 17th-century tier theorems that take nuclear firepower to even pseudo-prove

>muh primes

I like math and doing math, but I don't understand the obsession with primes. What is it about numbers that have only two factors that causes people to pop massive boners? It sounds like absolute and utter autism.

you don't know math, then. you don't even need number theory, learn some algebra.

Because they are the smallest piece of the multiplicative structure of the integers. Same reason why people are interested in irreducible modules, simple groups, prime ideals, irreducible markov chains or whatever.
It is often interesting, in order to solve a problem involving elements of a structure, to start by understanding the case when the elements are "indecomposable" (in any apropriate sense) and then try to see if it implies the general case.
That's a motivation for trying to understand prime numbers. In the case of integers, the rule for building numbers in terms of primes is particularly simple: every integer can be uniquely written as a product of primes (in opposition to the case of groups, where the problem of understanding the number of ways you can fit groups G in an exact sequence [math]0 \to H \to G \to K \to 0[/math], which is the relevant notion of "decomposition", is very difficult).
That's why understanding the distribution of primes is very important for multiplicative number theory

so easy to spot the people who don't know shit about anything in this thread

spotted

t. Bourbakists
Stats are extremely useful in social science and physics.

Talking out of my ass, but maybe they could help with Riemann's zeta function ? After all, it is tied to prime numbers. Maybe the reverse is also true.

t. philosophers

> social sciences

o i m laffn

are you guys talking about calc 1 optimization? like finding how to make the cheapest soda can

This or pretty much anything that includes the words "applied" or "numerical."

These are the offshoot fields where all the major theory has already been developed somewhere else, and all that's left for you to do is prove minor technical results for special cases if you're lucky, or just plug and chug into someone else's unsightly formulas if you're not.

t. Former applied statistician

you like it because you're boring and autistic

What the fuck did you just fucking say about complex numbers, you little bitch? I’ll have you know I stopped caring about math when I was introduced to the concept of imaginary numbers, and I’ve been involved in numerous secret raids on Al-Gebra, and I have over 300 crocks of shit. I am trained in equations that can only be solved by inventing numbers that can't exist and I’m the top math deity in the entire US academic forces. You are nothing to me but fucking wrong. I will wipe you the fuck out with math the flaws of which have never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of algebra solutions across the USA and your IP is being traced right now so you better say "the correct answer is whatever the correct answer is", maggot. The math that says the pathetic little thing transcribed to words. You’re fucking dead, kid. I can be anywhere, anytime, and I can mark you wrong in over seven hundred ways, and that’s just if you write it down in english instead of ancient math runes. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Logical Math Corps and I will use numbers that never lie to their full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy flaws your little “clever” human construct was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit complex numbers all over you and you will drown in it. You’re fucking dead, kiddo.

>social sciences
kek