What are some insightful quotations about topology?

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SUMMARY

This discussion centers on insightful quotations about topology, highlighting notable contributions from various thinkers. Hermann Weyl emphasizes the conflict between topology and abstract algebra in mathematics. Edward Witten discusses the invariance of topology in Einstein's general relativity, while Jacques Lacan presents a complex view on the implications of topology in understanding the "Other." Additionally, historical perspectives are provided through quotes from Leibniz and Mark Twain, illustrating the evolution of thought surrounding the concept of topology.

PREREQUISITES
  • Understanding of basic mathematical concepts, particularly in topology.
  • Familiarity with Einstein's general relativity and its implications on space.
  • Knowledge of historical figures in mathematics, such as Hermann Weyl and Leibniz.
  • Awareness of philosophical interpretations of mathematical concepts, as discussed by Jacques Lacan.
NEXT STEPS
  • Explore the foundational principles of topology in mathematics.
  • Research Einstein's general relativity and its relationship with topology.
  • Investigate the works of Hermann Weyl and their impact on modern mathematics.
  • Study the philosophical implications of topology as presented by figures like Jacques Lacan.
USEFUL FOR

Mathematicians, philosophers, students of topology, and anyone interested in the intersection of mathematics and philosophy will benefit from this discussion.

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Can anyone tell me a good quotation about topology?
 
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"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.
 
This is interesting, but I need another one, for which the subject is just about topology.
 
http://www.brainyquote.com/quotes/keywords/topology.html
 
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I found this, but this is true in any situation (for example BH formation)?

"In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything."
(Edward Witten)

And what about the Plank scale?
 
Ed Whitten? Try quoting someone smart!
 
I don't understand this one:

A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one sex as Other, as absolute Other, what does the most recent development in topology allow us to posit?

(Jacques Lacan)
 
There is a delicious quote at the beginning of each chapter of Glen Bredon's book "Topology and Geometry". Here is a good one. It is Leibniz talking about topology before topology:

"I believe that we lack another analysis properly geometric or linear which expresses location directly as algebra expresses magnitude." -- Leibniz, 1679, Letter to Huygens

Here is one by Mark Twain:

"A round man cannot be expected to fit in a square hole right away. He must have time to modify his shape." -- Mark Twain

Who has another good one?
 

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