/sci/ - Science & Math » Thread #13398844

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Weyl on Topology & Algebra

Anonymous Fri 16 Jul 15:02:31 2021 No.13398844 View Reply Original Report

Quoted By: >>13398854 >>13398856 >>13399171 >>13399194 >>13400130

>In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics.
- Hermann Weyl

What did he mean by this?

Anonymous

Anonymous Fri 16 Jul 2021 15:05:19 No.13398854 Report

Quoted By: >>13398958

>>13398844
Is that him? Wow, he is a chinlet just like me! How inspiring.

Anonymous

Anonymous Fri 16 Jul 2021 15:06:05 No.13398856 Report

Quoted By: >>13399110

>>13398844
Topology pretty, creative, fructifying.

Algebra ugly, demented, poisonous.

He foresaw the coming of the category theory and algrebaist tranny plague.

Anonymous

Anonymous Fri 16 Jul 2021 15:41:09 No.13398958 Report

Quoted By:

>>13398854
https://archived.moe/sci/thread/13388087/

Anonymous

Anonymous Fri 16 Jul 2021 16:26:43 No.13399110 Report

Quoted By: >>13399720

>>13398856
So has algebra won? Or are there any geometric competitors?

Anonymous

Anonymous Fri 16 Jul 2021 16:29:53 No.13399120 Report

Quoted By: >>13399198 >>13399720

There is no geometry without algebra. However vivid your imagination, at the end of the day, if you're doing geometry, be it euclid's or modern differential geometry, you're going to be writing down finitary algebraic expressions, equations, numbers. This is the domain of algebra. Through algebra we come to learn about shapes.

Anonymous

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Anonymous Fri 16 Jul 2021 16:31:43 No.13399123 Report

Quoted By:

Ad maiorem Diaboli gloriam, I guess!

Anonymous

Anonymous Fri 16 Jul 2021 16:45:51 No.13399171 Report

Quoted By:

>>13398844
If you are interested in philosophy, think of the contrasting views between Heraclitus (all is flux) and Parmenides (all is one). Algebra and geometry similarly occupy opposite ends of the conceptual spectrum—the first exists in time, comprising a system of rule-based derivations, while the latter is immediately perceptible, existing ideally.

Anonymous

Anonymous Fri 16 Jul 2021 16:51:44 No.13399194 Report

Quoted By:

>>13398844
Did you guys know that Weyl cucked Schrodinger?

Anonymous

Anonymous Fri 16 Jul 2021 16:53:16 No.13399198 Report

Quoted By: >>13399214

>>13399120
I would argue that rather than one being derivative of the other, the two demonstrate a conceptual synergy. The number sense on which algebra depends is spatially derived (think of the number line that we all subconsciously revert to, or the way we even learned about numbers in the first place)— check out Dehaene’s work if you are skeptical.

Anonymous

Anonymous Fri 16 Jul 2021 17:00:13 No.13399214 Report

Quoted By:

>>13399198
(Cont.) And geometry doesn’t win, either, since geometry alone can’t account for a world that is constantly changing. Only algebra, which involves change by its nature (algebra is Arabic for ‘the reunion of broken parts’), can do so. So it’s only through breaking the world into discrete elements that we can identify what is distinctly continuous and spatial. I may be wrong though, and welcome contrary opinions.

Anonymous

Anonymous Fri 16 Jul 2021 18:54:05 No.13399524 Report

Quoted By:

Bump

Anonymous

Anonymous Fri 16 Jul 2021 20:05:03 No.13399720 Report

Quoted By: >>13399989

>>13399110
Machine learning will replace most of mathematics and it will use mostly geometric methods to do so.
>>13399120
You can do geometry with a compass and ruler, you can’t do algebra without heavy metals in utero.

Anonymous

Anonymous Fri 16 Jul 2021 21:30:20 No.13399989 Report

Quoted By:

>>13399720
>Machine learning will replace most of mathematics
Explain or provide a source?

Anonymous

Anonymous Fri 16 Jul 2021 22:14:55 No.13400130 Report

Quoted By:

>>13398844
The distinction is pointless in modern mathematics since spaces and structures are equivalent concepts now.

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