/sci/ - Science & Math

There was a time when Number Theory was the answer to this question,

Geometric topology

algebra

>>6740729
practical applications in the future for sophisticated math?
Aside from software development and information securities, not really.

though it is highly accurate when applied.
Until the next breakthrough in mechanical computation where mathematics will lay out the groundwork for its logic. Math fails to subjugate the physical world adequately, or atleast the way we apply modern algebra.

The question is, is the evolution of mathematics and physics not mutual? I mean, what does math mean when it is not applied to something in the real world anyway, extra fun puzzles for autistic adults?

>>6740734
Pretty sure it's used in string theory.

>>6740739
>what does math mean when it is not applied to something in the real world anyway, ...?
Every math "thing" still has to be encoded in a physical system (eg mathematicians' brains) in order for us to talk about it. So, in a way, higher mathematics is still a set of natural patterns manifesting in reality. Of course, that doesn't mean that every piece of mathematics is necessarily "meaningful", or "deep"...
From this point of view higher maths is very similar to abstract phylosophy, like Hegel's analitic phylosophy or something like that

>>6740729
Mathfag here. When I go back to uni, one of my classes will be algebra. We will follow closely the book 'a first course in advanced algebra' by john fraleigh.

From just a casual glance at the book it seems to be all about groups and set does this have or lead to any applications?

Its worth mentioning that I really dont care if all Math has any applications. I just enjoy doing it.

Inner product spaces of infinite dimension and/or with a non-canonical inner product.

>>6740819
Abstract Algebra, specifically the topics you mentioned, have an insane amount of applications. More than many branches of mathematics. This is the case for most of the stuff you will study as an undergrad.

>>6740745
>has no practical applications and is unlikely to have any in the future?

>>6740820
B-but QFT?

>"dude math is useless when will we ever use it?"
>"please give me examples of when we will use this math"
>computers don't count though

Physicist here.

I'm sure we'll find SOME way to use all this shit,

infinite graph theory. just useless-

>>6741026
Infinite rings, groups, semi-groups, monoids, magmas, automata, semi-automata, etc.. can all be modeled with infinite graphs.

Pics related, cayley graphs of free groups.
http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox#A_sketch_of_the_proof
http://duluth.umn.edu/~ddunham/notices/paper.html
http://berstein.wordpress.com/2011/02/01/bridsons-universe-of-finitely-presented-groups/

Some more general info on graphs of groups (cayley graphs), these are studied in geometric group theory.
http://terrytao.wordpress.com/2010/07/10/cayley-graphs-and-the-geometry-of-groups/

Geometric group theory is a subset of Algebraic graph theory.
http://en.wikipedia.org/wiki/Algebraic_graph_theory

Then of course to any monoid there corresponds an automata and similarly semi-groups and semi-automata. Both of which can be graphed with state diagrams (pretty much the same thing as the cayley diagrams above).

Set theory is probably the easy answer. Cant think of a way large ordinals have anything to do with reality.

>>6740729
We're only now finding uses for shit discovered in the 1800s. No, there is nothing in mathematics that can conclusively be said to never be useful.

>>6740978

>>6742346
>finding uses for shit discovered in the 1800s
like what? im intrigued

>>6742344
sorry to disapoint
http://en.wikipedia.org/wiki/Constructive_solid_geometry

>>6742385

Euclid's constructions in geometry were purely theoritcal and "useless" until 1800 years later where telescopes where good enough to get better information on stars and real-life geometry problems became harder.

Number theory from a couple centuries back was useless until computers started needing it.

Matrix theory was developed on its own and purely for theory, applications in physics were discovered later

Calculus. That's the hardest topic in math, but when am I ever going to use it? Never.

>>6740734
It's used in modern physics

>>6740820
That's used in babby level quantum mechanics

>>6742754
retard

>>6742763
>babby
baby

>>6742754
>The worst b8
1/10, please kill yourself

are fourier transforms just a way to encode numbers to their multipliers and back to shrink bits needed or does it have other applications too?

>>6742763
Modern physics that will never have any application to the real world.
>>6740729
Motives.

>>6740820

Signals analysis.

>>6742873
Be careful not to fall for it.

>>6742864
How about detecting pulsars in cosmic radiation?

Differential equations. Pure mental masturbation.

>>6742837
>baby
babby

>>6740729
https://en.wikipedia.org/wiki/Ramsey_theory

>>6742913
Are you having a giggle mate?

When you come to think about it Goldbach's conjecture has really no fucking purpose.

Topos theory

come at me

>>6742864
It's used in signal analysis. Pic related from a class on extracellular recordings in the nervous system.

There's also software to extract the fourier transforms out of a picture so that you can filter out thermal noise rays from a microscopy image for example.

>>6742913
1/10 for trying

>>6740731
This is such a hard concept to explain to people.

>>6740729
>inb4 triple integrals
You stupid?

>>6743589
Phenomenological QFT? idk

>>6742837
>>6742920
hahahahahaha

>>6740819

groups have big applications in artificial intelligence

>>6742864
>>6743629
Also used by popular tools like:
- The music visualization thingies, from the simple equalizer lights to more complex ones,
- Recognition, like Shazam,
- Image compression (well technically, it uses wavelet transforms instead of Fourier transforms, but that's a very similar principle),
- etc.

>>6742864
Fourier transforms are literally one of the most useful things mathematicians brought up so far (if you can even say so). It really is ubiquitous in all kinds of quantitative sciences. It's really fundamental.

>>6743953
>- Image compression (well technically, it uses wavelet transforms instead of Fourier transforms, but that's a very similar principle),
Well technically, JPEG uses discrete cosine transform and JPEG2000, which nobody really uses anyway uses wavelet transforms.

>>6740745

thats the joke

>>6743677
Could you please explain it to me? Wikipedia does a shit job at explaining this.

>>6745222
https://www.youtube.com/watch?v=cG3sfrK5B4E

3:15

>>6745233
Uhh. I was talking about Number Theory, but thanks I guess. Interesting video.

>>6745248
Well it has to do with number theory & set theory

https://www.youtube.com/watch?v=or0QpAfOoZE

hello thread

topological tensor group number theory

>>6747075
You're a faggot

>>6740729
banach tarski
only Jesus knows how to apply it

>>6747107
Just looked that up. Thanks.
Its basically the "Jesus feeds 5000" story

>>6740819
There are plenty of chemistry and physics applications of group theory, since group theory is essentially the study of symmetry (think of a group as the set of symmetries of some object). So to each molecule you can associate a group, etc. and study properties of the molecule via the group. Basically anywhere that there's symmetry there's an application of group theory.

>>6742754
yeh mebe in the 1700s when isaac first invented it

>>6747862
Newton wrote Principia Mathematica around 1685


>mfw Newton wasn't even the first to use calculus

>>6743677
What is cryptography?

The number theory provides a means of removing meaning from something by applying specific algorithms to encrypt data, number theory is used to do it.

>>6740729
What do you mean you knew b4 triple integrals? Those are used for volume

>>6742754
Well that's used in... oh, everything.

The answer is none.

The modularity theorem, declaring that all elliptical curves are inherently modular seemed simply theoretical until Andrew Wiles used it and l-functions to prove Fermat's last theorem, which has wide ranging implications for number theory, matrix math, cryptography, etc.

To say that any theoretical subject matter in math will never have any practical applications, is to pretend to know the scientific and technological progress in the future. Simply a close minded assumption.

Riemann geometry seemed novel until it was proved that our spacetime is not Euclidean in nature, Riemann geometry is the basis for General Relativities field equations.

Every theoretical footstep in math is paving the way for practical applications once its fully understood.

/thread.

>>6742754
Fuck you.

>>6747996
this

>>6740729
Audio Fractal Engineering possibly.

It's just repeating a note or tone wavelength beside another with the same wavelength while decreasing the tone of the latter continuously and playing another when it reaches about zero dB.

> differential equations
Dumb bitch, it has enormous applications in physics and finance

I guess TOPOLOGY, ALGEBRAIC TOPOLOGY, SET THEORY AND MEASURE THEORY Have not direct applications in anything

binary

differential equations
linear algebra
double integrals
triple integrals (this is still being developed)

weird advanced abstract algebra stuff, like the monster group and shit like that

>>6748087


Assuming you even know what algebra is.

Because abstract algebraic descriptions of manifolds could not possibly describe a 3 dimensional spacetime, such as ours, right?

It is easy to deem theoretical algebra as arbitrary, especially when you believe that algebra is manipulating equations and nothing else.

>>6748099
I never said it was arbitrary. Also, i didn't say algebra in general is detached from reality and useless, that's nonsense.
>..algebra is manipulating equations and nothing else
Well, algebra IS the manipulation of symbols, the study of the properties of these symbols and their transformations, but these things mean something only insofar as they stand for something physical. You know, you can "use" math to multiply apples or to describe fields in space time or something, but it's not at all clear that that's ultimately what's really going on. We use math mostly as an approximation tool. There's no math that describes the universe on all scales, for all i know-
And assuming that algebra has some deep value to it just because it is "abstract" is just nonsense to me.
Anyway, that's not the point of the thread, it seams. The monster group seems pretty divorced from reality to me- any counter argument for that would be interesting though

>>6742754
I thot that was algebra???

>>6748194
http://en.wikipedia.org/wiki/Monstrous_moonshine

>conjectured relation with quantum gravity.

>>6742776
hahaha, easily the best response that could have been said.

>>6748084
>being this dense

>>6740734
it is used in topological optimization, a hot topic in engineering.

>tfw your peers and family mock you for being a pure mathematician
>tfw someone asks what practical applications your field of research has and you can't think of any on the spot
>tfw you remember all of them as soon as that someone leaves

>>6748065
dumb bitch dumb bitching a dumb bitch.

>>6740820
>what is signal processing, detection, probability, quantum mechanics, and information geometry?

>>6749929