>>9102862
When I started my memes with let x be....

Pretty much when I started learning analysis, it was just "so, these things are very close, so let's just say they're equal"

>>9102868
So you never actually learned analysis?

>>9102919
shitting with quantifiers and saying shit about arbitrarily small epsilons doesn't make this any more valid

I became upset with proofs that involve algebraic symbol manipulation as soon as I started learning abstract algebra because I found it difficult to extract a concise explanation for how the proof works. I was able to summarize analysis proofs easily with visual reasoning, but the fundamental tricks of abstract algebra must be learned.

What exactly differentiates an "analyst" from an "algebraist" broadly speaking? Is there really a significant gap in thought processes or is it a specialization a competent math person chooses freely past a certain level for practical purposes?

>>9103184
>"analyst" from an "algebraist"
Both analysis and algebra autistically diverge at the graduate level.

>>9103118
actually yes it does

>>9103267
Fair enough, but I noticed a tendency to split the autistic realm of number theory into two distinct fields (analytic and algebraic), and I wondered if specializing in one of those is mostly determined by one's cognitive inclination, or rather by a practical choice, i.e. a specific range of problems a mathematician is interested in and chooses to specialize accordingly, but said mathematician could have been equally competent on the other side had he chosen to be.

>>9103184
Any mathematician worth his salt should be knowledgeable about all different fields, because any problem worth studying requires a great deal of interdisciplinary mathematics.

>>9103184

In analysis you work within one or a few related algebraic structures like a vector space of a function space and you figure out the properties within.

In algebra you work with many more algebraic structures and you work at a higher abstraction level.

>>9103311

Lol no. I never need to touch statistic or probability ever again. Stop talking about of your ass, brainlet.

>>9103303
If you want to answer questions like "find all the integers with x property" (like for example all lattice points in an elliptic curve) then you want algebraic. If you want to answer questions like "About how many integers are there in this set" (like for example about how many prime numbers are there smaller than 69968382832) then you want to go analytic.

In simpler terms, if you want to count numbers then you go analytic. If you want to find structure in numbers then you go algebraic.

So you specialize in what you care, but also in what you are good at. If you just happen to be better at analysis than algebra (like happened to Terence Tao) then you go analytic so that you can exploit your skill and become famous.

>>9103316
Case in point: a mathematician not worth his salt.

>>9103316
Brainlet