is topology the most advanced type of mathematics? if not, what is?

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>>8391913
Memeology, obviously.

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Depends on what you mean with advanced. If advanced means novelty, then probably IUTeich is the most advanced (assuming it is consistent and shit), but advanced could mean abstraction, and then it'd be the most abstract parts of category theory, etc. Topology is advanced in the sense that topologists were somewhat forced to find a way to flank their field's problems that were too hard for them, this then gave birth to algebraic topology.

>>8391913
[math]\infty[/math]-category theory

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>>8391913

Honestly, philosophy is. Nothing's harder than finding the actual meaning behind all the abstract symbol diddling. When mathematicians learn everything about traditional maths, they move on to become philosophy majors.

if topology is the most advanced type of mathematics and I am acing my topology course, does that make me a genius?

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>>8391913
Infinite-Dimensional Meme Theory

>>8392020
>This is what /his/ actually thinks

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>>8392020

>learn everything about math

>>8392020
The only way to get definitive answers to philosophical questions is to put them into precise language (e.g., math).

>>8392031

>there are brainlets on /sci/ right now who still haven't finished learning mathematics yet

It's just a bunch of old tricks. Get through it already so you can share in the magic of independent thought and creativity that is Philosophy.

>>8392032

>precise language
>HURR LET'S EXTEND LOGARITHMS TO THE COMPLEX PLANE NOW EVERY NUMBER HAS INFINITE LOGARITHMS LOL

>>8392044
Obviously there are plenty of mathematical constructions whose meaning isn't clear. That doesn't contradict what I said.

>>8392051

If mathematics is so precise why does every human being on the planet choose to communicate in words with each other instead of with numbers?

>>8392060

if words are so precise then why don't we build houses out of words

>>8392063

Because houses aren't smart enough to understand words.

>>8392060
Because precision [math]\ne [/math] applicability.

is topography the most advanced area of geoscience?

Is?

What is the "deepest" and most inaccessible field of mathematics?

>>8392102

calculus, or more specifically, calculus 3

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>>8392102
Orthotopology https://youtu.be/57woJ1akD8c?t=1m47s

>>8392102

triple integrals

triple integration

>>8392102

I found haar measure to be pretty "out there", you have to have a solid understanding of analysis and a good familiarity with lie groups to get much out of a study of haar measure.

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>>8391913
multi-dimensional supersymmetry.

>>8392222

einstein notation does not make something complicated, I have found that many of the more complicated ideas in mathematics are symbolically parsimonious, moreover, that's not mathematics.

>>8392060
because most people are brainlets

>>8392235

>parsimonious

I have to use a fucking dictionary to browse this fucking board only to find out that you morons don't know what the words you're using mean anyway

>>8392279

don't be silly, I said symbolically parsimonious, and it is perfectly acceptable in that context, for example occham's razor is know in latin as lex parsimoniae, which translates as law of parsimony. I am perfectly free to use it in its figurative sense. It can be used to describe more than fiscal niggardliness.

>>8392285

do you think typing like that makes you look smart? when you're around people that you know won't know what the word niggardly means, do you use the word anyway to demonstrate your superiority?

>>8392279
Get a better dictionary m8.

>>8392293

no I use the word because it sounds like 'nigger'

>>8391913
I dunno if it is the most advanced, but for sure is the most useless.

>>8392072
Kek

>>8392206
Is this a meme?

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algebraic geometry

reply "sleep tight dormant bundle" for good dreams

>>8392423
lurk moar

>>8392418
>most useless.
comps aint shit eh?

>>8392102
algebra 2 relies on deep proofs for its understanding of concepts (quadratic reciprocity theorem, understandings of natural log and growth sans calculus)

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>>8392285
>>8392235
Please tell me this is how you also talk to people IRL

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>>8392293
>niggardly

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>>8392444
kek
i'm genuinely not able to distinguish between random paper generator works and this notation diarrhea
also sleep tight dormant bundle!

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>>8392418
t. Doesn't know shit about big data

>>8391913
Sheaf theory is where it's at

>>8392866
I'm an UG taking topology right now, so my knowledge of the topic and its applications are loose. Are its applications to big data fruitful and still developing?

>>8392206
>>8392216
Check the video at 1:47. He does QUADRUPLE INTEGRALS!!! >>8392109

>>8392948
fuck off. a quadruple integral is what killed Gauss

>>8392977
GauB was weak