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/sci/ - Science & Math

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7334688 No.7334688 [Reply] [Original]

Is there something more inane than topology and functional analysis. The entire field is basically definitions after definitions. Has something interesting ever come into existence because of this shit?

>> No.7334694

I'm not sure about advanced topology, but basic topology helps a lot in proving theorems of other fields that would be really complex to prove without topological results. For instance, you take a property you want to prove on a structure, you show that this property is conserved by some functions, you apply that function to your structure, which yields a much simpler structure on which you easily prove your property, and topology allows you to take that simple result and port it back to the original structure on which you wanted to prove it, basically for free. It's awesome.

>> No.7334708

Topology is were theorems in analysis go to heaven and become definitions

>> No.7334728
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7334728

Just saying that this is literally the most dry stuff I have ever tried to self-study. I went carefully through the first 30 pages of the textbook, realized what it was, then flipped through the next 500 pages only to see that it never stops being the same shit. I think one has to suffer from some serious form of autism to seriously enjoy this.

>> No.7334738

>>7334728
You aren't cut our for math.

>> No.7334746

>>7334738
I know; I'm more of a physicist. I just tried to enjoy our sister field a bit .

>> No.7334760
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7334760

>>7334746
Yeah there's no real connection between topology and physics.

>> No.7334918

>>7334760
I thought everything cool in physics with regards to wormholes, quantum spacetimes etc was heavily connected to topology?

>> No.7335075
File: 78 KB, 1280x720, let me tell you why that's bullshit.jpg [View same] [iqdb] [saucenao] [google]
7335075

>didn't get through point-set topology
>didn't get to the juicy algebraic topology

>didn't get through analysis
>didn't get to the juicy Hilbert spaces and operator theory

>crying on the internet for your ineptitude

>>7334760
>Yeah there's no real connection between topology and physics.
Hilariously wrong. Topology classifies defects in spin systems and predicts phase transitions in condensed matter theory (Schwartz 1991); topology is literally the backbone of constructive quantum field theory (Baez, Segal, Zhang 2014) ; topology of the phase space of a quantum dynamical system is connected to eigenstate degeneracies (Chowdhury 2003).
Actually fact check before you spew bullshit at unsuspecting physics undergraduates.

>> No.7335077

>>7335075
One could of course assume that anon was being sarcastic, considering the choice of image.

>> No.7335078

>>7335077
>curvature of spacetime
That choice of image is more differential geometry. I'm talking pure topology.

>> No.7335081

>>7334688
Look up topological insulators. Some basic rules of topology applied to wave functions and their phase have led to the predictions of "topologically protected" surface states in some condensed matter systems, and the subsequent discovery of it.