Abstract algebra: useless

[Anonymous No.9846403]

I know: Group theory gets used in quantum mechanics and elsewhere in physics, but the group theory used is trivial. E.g., never hear of Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc. For group representations,you need to know very little about group theory to do group representations (I wrote my undergrad honors paper in it). Heck, I wrote a paper on multidimensional, distribution-free hypothesis tests based on groups of measure-preserving transformations, and the group theory needed was trivial. Similarly for the use of group theory in ergodic theory, ODE, and integer linear programming. Groups are nice, but really need to know only about 10 pages of the basics and can pick it up in an hour whenever need it. Or, you want group theory to attack Rubik's cube?

Yes, Hamming used some finite field theory in error correcting codes: Now that work and a dime won't cover a 10 cent cup of coffee. Instead, coding theory has moved on. Yes, yes, I know, from A. Wiles we finally have a proof of Fermat's last theorem; other than Wiles, who made any money with that?

Algebraic geometry is building expensive houses on-spec that stand empty too long. There's just no significant promise of return on investment there, or elsewhere in abstract algebra. E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.

US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics, shrinking departments, mathematicians who'd swap their Ph.D. for an electrician's license, and the technology world putting mathematics on the back burner if not in the trash. Can cover nearly all abstract algebra in 1 word: Useless.

[Anonymous No.9846409]

>>9846403
Agreed fully, but proper mathematical analysis is not applied math. And yet it is supremely useful and meaningful.
Algebra and number theory are where the undergrad kiddies play around on their little baby jungle gym. People who continue to do it past the first few years of graduate school and don't only algebraic topology purely as a tool for studying topological spaces are not mathematicians, they are manchildren.

[Anonymous No.9846502]

>b-b-but muh rich structure
>muh Sn

[Anonymous No.9846563]

IT's true, people who specialize in analysis are usually much more alpha.
The deeper you go into algebra the more cucked you tend to be.

[Anonymous No.9846584]

Great to know, I fucking hated my abstract algebra course but loved analysis. Thanks /sci/ :)

[Anonymous No.9846629]

Linear Algebra ⊂ Abstract Algebra

/thread

[Anonymous No.9846640]

>>9846403
>I know: Group theory gets used in quantum mechanics and elsewhere in physics, but the group theory used is trivial. E.g., never hear of Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc. For group representations,you need to know very little about group theory to do group representations (I wrote my undergrad honors paper in it). Heck, I wrote a paper on multidimensional, distribution-free hypothesis tests based on groups of measure-preserving transformations, and the group theory needed was trivial. Similarly for the use of group theory in ergodic theory, ODE, and integer linear programming. Groups are nice, but really need to know only about 10 pages of the basics and can pick it up in an hour whenever need it. Or, you want group theory to attack Rubik's cube?
>Yes, Hamming used some finite field theory in error correcting codes: Now that work and a dime won't cover a 10 cent cup of coffee. Instead, coding theory has moved on. Yes, yes, I know, from A. Wiles we finally have a proof of Fermat's last theorem; other than Wiles, who made any money with that?
>Algebraic geometry is building expensive houses on-spec that stand empty too long. There's just no significant promise of return on investment there, or elsewhere in abstract algebra. E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.
>US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics, shrinking departments, mathematicians who'd swap their Ph.D. for an electrician's license, and the technology world putting mathematics on the back burner if not in the trash. Can cover nearly all abstract algebra in 1 word: Useless.
stale pasta

[Anonymous No.9846684]

I don't understand the "pure mathematics has no applications" meme. We know. We don't care. That's why we have a distinction between pure and applied mathematics. If you want "useful" math, then become an engineer. I must warn you, though, it's soul-crushingly boring.

[Anonymous No.9846727]

>>9846629
>vector space? what's that? Oh you mean a module over a field.
>Linear map? What's that? Oh you mean a functor

[Anonymous No.9846765]

>>9846684
>We know
That's not true at all. Just something math majors say to girls to sound artisitic and profound.

[Anonymous No.9846766]

>>9846727
A functor and a linear map is not the same.

[Anonymous No.9846775]

>>9846684
That's an artificial divide (dare i say social construction lol) that is at most a century old.
Mathematicians of the previous centuries appreciated the beauty and fun of math problems and constructions just as they found beauty in its applicability to the real world and its ability to compute things or predict events.
The idea that really valuable math should be completely turned inwards is very recent, and proves to be pretty bad incentive for math departments being awarded grants.

[Anonymous No.9846786]

>>9846684
Reminder that the best mathematicians in all of history also studied physics.

[Anonymous No.9846789]

>>9846786
especially Grothendieck

[Anonymous No.9846796]

>>9846789
Not amongst the greats.

[Anonymous No.9846819]

>>9846403
sorry that you lack the mathematical maturity to understand the importance of group theory

[Anonymous No.9846874]

>>9846403
Engineer here, we're starting to use Algebraic Topology as an alternative to solving PDEs for multiphysics problems

http://www.discretephysics.org/en/

[Anonymous No.9846996]

>>9846403
I dare you to prove that there is no general solution in radicals to fifth degree or higher polynomials without using group and field theory. I literally dare you because I've never seen that done and it would be pretty sweet.

[Anonymous No.9847039]

>>9846996
>I dare you to prove that there is no general solution in radicals to fifth degree or higher polynomials without using group and field theory. I literally dare you because I've never seen that done and it would be pretty sweet.
see pic related for a topological proof

[Anonymous No.9847046]

>>9846403
I found group theory really dry when I did it too desu - the sort of person who enjoys it also writes their name inside their gym kit in case they lose it

[Anonymous No.9847053]

>>9847039
Sweeeeet, thanks man

[Anonymous No.9847054]

>>9846502
the muh Sn made me laugh in this because I thought that the whole time reading theorems from the book

[Anonymous No.9847172]

>>9846874
Why have I not heard of this?

[Anonymous No.9847192]

>>9846874
Wait, are you that guy that was talking about a "new computational method" in /engi/?

[Anonymous No.9847293]

>>9846403
absolutely based and redpilled

[Anonymous No.9847303]

Theoretical pure math is useless, in a few years everything will be taken over by machine learning i.e. statistics and optimization

[Anonymous No.9847308]

>>9846874
>last update: 16th April 2014

[Anonymous No.9847618]

>>9846766
t. doesnt know cat theory

[Anonymous No.9847628]

>>9846403
>Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc
>Finite groups
People don't know these theorems because most work is done on infinite groups. Including group theory research itself.

>Algebraic geometry is building expensive houses on-spec that stand empty too long.
Nigger what? We use AG in symbolic math packages so that most results can be used by anyone.

>E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.
This happens in most research fields. The literature is just too vast for any researcher to be read up on all of it.

>US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics,
I don't think this is true. For example the DoD funded the geometrics langlands which is the largest grant ever awarded to mathematicians in human history. I would appreciate any statistics to the contrary though.
>shrinking departments,
There are too many departments for the current economy. Less faculty is inevitable, but I'm willing to bet the number of faculty has been increasing steadily if you check the LBS.
>mathematicians who'd swap their Ph.D. for an electrician's license,
This is true for engineers as well, what's your point?
>and the technology world putting mathematics on the back burner if not in the trash.
Again, this is not true. Many frontier results are being used in optimization, equation solvers, simulators, graphics processing techniques etc. etc.
>Can cover nearly all abstract algebra in 1 word: Useless.
True. Because it's fundamentally abstract, it's not of use unless you actually relate it to something tangible; such as computations. This is some that is done all the time. And many modern results in AG and AT are used in computations.

[Anonymous No.9847629]

>>9847628
>quotesniping copypasta
why?

[Anonymous No.9847631]

>>9846563
Even functional analysis techniques are proving inferior to modern AT and AG methods. GTFO with your primitive sticks and stones shit.

>>9846874
What the fuck, this is just another way to describe FEM.

[Anonymous No.9848245]

>>9847629
FOR THE GLORY OF AUTISM!!
that's why anon

[Anonymous No.9848284]

>>9847631
AT and AG methods? Sorry, undergrad brainlet here, I roughly know what functional analysis is about but what are AT and AG methods?

[Anonymous No.9848497]

>>9848284
algebraic topology/geometry AKA nothing important

[Anonymous No.9848513]

>>9848497
Careful now. You might trigger some autist to post links to arXiv papers describing hypothetical "applications" of AT/AG.

[Anonymous No.9848537]

>>9848513
*grabs you by the throat*

[Anonymous No.9848670]

>>9848513
Algebraic topology has become fundamental in modern research in quantum physics and fluids.

[Anonymous No.9848803]

Combinatorics?

[Anonymous No.9848950]

>>9848537
so what important problems has topological data analysis solved? what interesting results has it produced?

[Anonymous No.9849569]

>>9848513
>hypothetical "applications" of AT/AG.
They aren't hypothetical anymore, it's starting to be applied everywhere in fundamental libraries these days.

I'm a researcher in optimization theory and algorithm development. My work uses AT and almost no analysis, and the algorithms I developed are proving better than previous generations' on any benchmarks I've tested.

Other than my own work you can see some more basic applications like solvers using homotopy method, which are also very powerful.

Symbolic math packages almost all use AG.

Like others have said most gauge theories in modern physics uses both AT and AG.

It's important and powerful fields.

[Anonymous No.9849638]

>>9846996
>>9847039
1. you are just moving the goal posts, nobody gives a shit about expressing the solutions of polynomial equations with radicals, because you can just represent them with real numbers, thanks to the bisection method, or Newton's method
2. Topologists absolutely, and universally dunk on algebraists

[Anonymous No.9850352]

>>9849638
You're not wrong desu. Solving them with numerical methods is usually faster too.

[Anonymous No.9852241]

>>9850352
it is ALWAYS faster you fucking brainlet

[Anonymous No.9852304]

>>9846796