Fields with least amount of geometry/topology?

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Discussion Overview

The discussion revolves around identifying mathematical fields that have minimal connections to geometry and topology. Participants explore various branches of mathematics and their relationships to these concepts, as well as interpretations of the term "fields."

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that the simplest field could consist of a single number, such as 0, while others propose fields with two numbers, like modulo 2.
  • There is a misunderstanding about the term "fields," with one participant interpreting it as professions, mentioning veterinary medicine.
  • Participants clarify that "Abstract Algebra" is generally considered distinct from topology and geometry, although connections may still exist.
  • One participant questions what mathematical area could be entirely devoid of connections to geometry or topology, suggesting number theory and abstract probability theory as potential candidates, provided certain conditions are met.
  • Another participant mentions that mathematical logic might also be a field with minimal ties to geometry and topology.

Areas of Agreement / Disagreement

Participants express differing views on which fields have minimal geometry/topology connections, with no consensus reached on specific fields or the extent of their connections.

Contextual Notes

Some assumptions about the definitions of fields and the extent of connections to geometry and topology remain unresolved, leading to varied interpretations and suggestions.

tgt
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Which fields are they? Maybe a ranking if you can give one.
 
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The simplest field I can think of consists of one number 0. The next simplest consists of two numbers (0 and 1) using modulo 2 for addition. After this things get more complicated.
 
I had thought the question was about fields of work or professions! Veterinary medicine came to mind.
 
fields (non mathematical term) in maths.
 
tgt said:
fields (non mathematical term) in maths.

As far as I know, Sally Field has a very minimal amount of geometry/topology in her work. I think there was a scene of her doing some algebra in an episode of Gidget.
 
A little bit more seriously, "Abstract Algebra" as a general field is usually distinguished form Topology/geometry. Other forms of mathematics typically include some algebra and some topology.
 
HallsofIvy said:
A little bit more seriously, "Abstract Algebra" as a general field is usually distinguished form Topology/geometry. Other forms of mathematics typically include some algebra and some topology.

But still it's very related in a way since one can define geometry in terms of algebraic concepts. What is something that is so far from topology and geometry that there is not the slightest connection?
 
What is something that is so far from topology and geometry that there is not the slightest connection?

It is very hard to find a branch of mathematics that has absolutely no connection to geometry or topology, particularly since you don't think abstract algebra is not far enough away. I could suggest number theory but then the pythagorean theorem might turn you off. Also abstract probability theory could qualify, as long as you don't use Borel fields for sigma fields.
 
mathman said:
It is very hard to find a branch of mathematics that has absolutely no connection to geometry or topology, particularly since you don't think abstract algebra is not far enough away. I could suggest number theory but then the pythagorean theorem might turn you off. Also abstract probability theory could qualify, as long as you don't use Borel fields for sigma fields.

So maybe analysis related stuff? How about mathematical logic?
 

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