Which math field is growing the fastest now?

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Discussion Overview

The discussion revolves around the growth and relevance of various fields in mathematics, particularly focusing on statistics, chaos theory, and point-set topology. Participants explore whether certain areas are experiencing significant discoveries or if they have become stagnant.

Discussion Character

  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant mentions a claim from a math teacher regarding statistics and chaos theory being the field with the most potential for discoveries.
  • Another participant argues that research is ongoing in many fields, including Calculus of Variations and Geometric Measure Theory, suggesting that discoveries can occur wherever there is interest and expertise.
  • Some participants assert that certain fields, like point-set topology, may be considered stagnant or auxiliary, with little contemporary relevance.
  • There is a suggestion that concepts like nets and filters in topology could be revisited and integrated into other mathematical contexts, such as Riemann-Stieltjes integration.
  • One participant expresses the view that point-set topology is increasingly aligned with set theory in modern discussions.

Areas of Agreement / Disagreement

Participants express differing views on the vitality of various mathematical fields. While some believe that certain areas are stagnant, others maintain that research continues across all disciplines. No consensus is reached regarding which fields are growing or declining.

Contextual Notes

Some claims about stagnation in specific fields depend on subjective perceptions and may not reflect broader trends in mathematical research. The discussion includes varying definitions of what constitutes a "stagnant" field.

kramer733
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So my math teacher (who has a honours in math) said that his friend who's doing her phd on math told him (yes that's a lot of he says she says) that the field that's going to have the most discoveries is in statistics because of "chaos theory". Is this true? So does this mean that calculus, algebra have stagnated? Is there nothing else to discover?
 
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There is research going on in all fields. See Calculus of Variations and Geometric Measure Theory, Homotopy Theory, etc. Perhaps Chaos Theory is special, but research is done where the person is interested and has a good background in; there are always things to discover.
 
Actually, there are fields that are stagnant' tapped out, and are now at best
auxiliary. Point-set topology is one of them. Talk to anyone today about Lindeloff
spaces, metrizability, etc., and they will look at you as saying: what.?, or , why
would anyone care.?
 
Bacle said:
Actually, there are fields that are stagnant' tapped out, and are now at best
auxiliary. Point-set topology is one of them. Talk to anyone today about Lindeloff
spaces, metrizability, etc., and they will look at you as saying: what.?, or , why
would anyone care.?

I think nets & filters could be added to that list, but I think nets should make a comeback. Prob 2H in Kelley's topology text could be part of a course on Riemann-Stieltjes integration. I think they've always been done in topology because nets & filters are equivalent but I don't seen why nets couldn't be done right after the Riemann integral, as if to say "see how much easier it is with nets?"
 
Last edited:
My impression is that point-set topology becomes more of set theory now days
 

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