What are strange , obscure , ignored fields of mathematics?

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Discussion Overview

The discussion revolves around identifying strange, obscure, or ignored fields of mathematics. Participants explore various mathematical areas that may be considered less active or "dead," including theoretical and historical perspectives.

Discussion Character

  • Debate/contested
  • Exploratory

Main Points Raised

  • Some participants suggest fields like Calculus of Variations, Morse Theory, and k-theory as potentially "dead" areas of mathematics.
  • Others challenge the notion that k-theory and Morse Theory are inactive, arguing that k-theory is of significant interest to string theorists.
  • A participant mentions a lack of recent work on foliations and fractals, suggesting they may be obscure, while another counters that these fields have seen renewed interest due to non-commutative geometry.
  • General topology is mentioned as a field that appears to be declining in research activity, with some claiming it is "solved" despite having obscure unsolved problems.
  • Constructive geometry is noted as a field that may be considered dead, with its problems now addressed by Galois theory.
  • One participant humorously notes that high school algebra has not seen research papers for centuries, implying it is also a "dead" field.

Areas of Agreement / Disagreement

Participants express a range of opinions on the activity level of various mathematical fields, with no consensus on which fields are truly "dead." Some argue against the characterization of certain fields as inactive, while others support the idea that specific areas have seen a decline in research.

Contextual Notes

Participants acknowledge that the classification of a field as "dead" may depend on definitions and perspectives regarding research activity and interest. There is also uncertainty about the current state of research in some areas, with references to historical developments and the frequency of published papers.

Samardar
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Any Ideas? That are outside the mainstream?
 
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You a hippie or something?
 
I would actually be very interested in knowing about this as well. From what I've come across, the most dead fields seem to be Calculus of Variations, Morse Theory, and k-theory.
 
ahsanxr said:
You a hippie or something?

:smile: That actually made me laugh out loud.
 
Oriako said:
I would actually be very interested in knowing about this as well. From what I've come across, the most dead fields seem to be Calculus of Variations, Morse Theory, and k-theory.

K-theory, Morse Theory dead? I believe you are quite mistaken.
 
Functor97 said:
K-theory, Morse Theory dead? I believe you are quite mistaken.
"The most dead", from what I've seen... I could be hugely mistaken, I just can't think of any other fields of math that would be less active (or have less researchers in them) or whatever it is that drops the frequency of published papers.
 
Oriako said:
"The most dead", from what I've seen... I could be hugely mistaken, I just can't think of any other fields of math that would be less active (or have less researchers in them) or whatever it is that drops the frequency of published papers.

K theory is of vital interest to string theorists. It is by no means a "dead" topic.
 
Foliations, Fractals? Haven't seen much work on foliations since Thurston and not much on fractals beyond recreation. No clue how obscure you mean though. There aren't really obscure fields that haven't been researched into anymore. Granted, if there was one, most mathematicians would jump at the opportunity to be a pioneer in the field.

Perhaps the most 'dead' fields would be ones that have been practically cleaned out.
 
Foliations and fractals have gotten a lot of renewed interest in them in the past couple of decades due to non-commutative geometry.
 
  • #10
^ In particular (not sure about fractals), I haven't seen much work in foliations since the '70s, on Thurston and Haefliger's publications. I'm not too sure if there are any recent developments within the 2000's.
 
  • #11
Can anyone think of any others? Is Category theory really popular?
 
  • #12
Oriako said:
I would actually be very interested in knowing about this as well. From what I've come across, the most dead fields seem to be Calculus of Variations, Morse Theory, and k-theory.

LOL at thinking K-theory is dead :biggrin:
 
  • #13
  • #14
micromass said:
LOL at thinking K-theory is dead :biggrin:
Oops! Well now I know not to believe what I hear from one person who is also an undergraduate XD.

@Anonymous217: Which fields have been so well studied that there is not much left to do?
 
  • #15
The most dead part of mathematics is high school algebra . there have been no research papers in this field since centuries
 
  • #16
A field which is dead is something like "constructive geometry". Given a figure, can we construct it with ruler and compass. Such a problems are now easily solved by Galois theory and I have no knowledge of research papers from that area. That doesn't mean that Galois theory is dead however.

General topology is a dying field, in my opinion. There are less and less research papers from that area. We can say that general topology is "solved". There are some unsolved problems, but they are rather obscure...
 

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