What are some insightful quotations about topology?

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In summary, topology and abstract algebra have been seen as opposing forces in the world of mathematics. However, according to Hermann Weyl, they both play important roles in shaping individual disciplines. Edward Witten emphasizes the stability of topology in contrast to the changing nature of space in Einstein's general relativity. Jacques Lacan's musings on topology and the Other raise questions about the role of topology in defining identity. Finally, Leibniz's early thoughts on topology and Mark Twain's humorous take on fitting into different shapes offer further insight into the subject.
  • #1
mersecske
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Can anyone tell me a good quotation about topology?
 
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  • #2
"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.
 
  • #3
This is interesting, but I need another one, for which the subject is just about topology.
 
  • #4
http://www.brainyquote.com/quotes/keywords/topology.html [Broken]
 
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  • #5
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?
 
  • #6
Ed Whitten? Try quoting someone smart!
 
  • #7
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)
 
  • #8
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?
 

1. What is topology?

Topology is a branch of mathematics that studies the properties of a space that are preserved under continuous deformations, such as stretching or bending, but not tearing or gluing.

2. How is topology used in science?

Topology is used in a variety of scientific fields, including physics, biology, and computer science. It can be used to study the shape and structure of objects, analyze networks and systems, and understand how objects interact with each other.

3. What are some examples of topological concepts?

Some examples of topological concepts include connectivity, compactness, and continuity. These concepts are used to describe the properties of a space and how objects can be transformed within that space without changing its fundamental structure.

4. What is the importance of studying topology?

Studying topology allows us to better understand the fundamental properties of spaces and how objects behave within them. This knowledge has practical applications in fields such as physics and engineering, and can also lead to new discoveries and insights in mathematics itself.

5. How does topology relate to real-world problems?

Topology has many real-world applications, including analyzing and designing transportation networks, studying the properties of materials, and understanding the behavior of complex systems such as the human brain. It can also be used to solve problems in data analysis and optimization.

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