Can someone please redpill me on why analysis and combinatorics

How fucking stupid are you, OP?

Pure maths is all about garnering prestige by working on problems outside the public's comprehension. No one is going to be impressed if they understand the statements of the problems you work on unless the problem is very famous.

Nearly all pure maths students want to the problems that are the most abstract and seemingly esoteric -- and hence the most impressive. But only the best can work on the algebraic topics and still be employable.

The most productive analysts -- Tao, for example -- work on analysis even though they could be algebraists if they tried because they know that they'll get more attention if they gather up the low-hanging fruit that the dummy analysts who couldn't make it in algebra couldn't reach.

>>9041212
>The most productive analysts -- Tao, for example -- work on analysis even though they could be algebraists if they tried

Tao has actually stated that he struggled with algebra and topology

>>9041152
That perception probably exists because the big post-modern wizardy mathematicians of the 20th century were in algebra. Serre, Grothendieck, et al.

No one actually believes this meme.

I mean why would analysis be left for brainlets, there are a lot of hard problems in it.

>>9041244
What is excelling for you is struggling for him.

pls explain why do you think analysis is easier than algebra ?

>>9041281
and how would you know that?

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>>9041311

It's a lot easier to "brute force" things in analysis, and it also seems to be far more intuitive, generally working within the comfortable restraints of R, C, or their extension fields.

Algebra, on the other hand, gets a lot more abstract and forces you to leave your comfort zones and intuitions about how math "should" work.

Disclaimer: I'm just a brainlet with barely any exposure to either, and I'm in no way implying that analysis is "easy"

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>>9041364

Because he's Terrence fucking Tao, his criteria for the norm is beyond our criteria for outstanding success.

I think that mathematicians who work on things with application to theoretical physics will naturally get more attention. There's simply more people looking at their work, and so they're more highly regarded than those who work in things with minimal application, like combinatorics.

That's my take on it.

>>9041378
Funnily enough it's almost the opposite of your post. Usually all the "nice" theorems are in algebra because the subject has more of bird's eye view and more often deals with better behaving things and structures. It has the grand everything connects kinda feel to it.

In otherhand analysis often depends alot on details and for example real analysis has so many pathological and unintuitive functions and behavior that algebra struggles to match. Yet for another example PDE's come from so many different places and changing equation even just a little bit can result in very different phenomena and the need for other technicues for dealing with it. There is no hope for general theory for PDE's.


As for the rude calculation, analysis in most cases deals with infinity so computers are not that much of an help (exept for numerical stuff for ideas etc) but if you study some finite groups for example you can do alot.