What are strange , obscure , ignored fields of mathematics?

AI Thread Summary
The discussion revolves around identifying mathematical fields that are perceived as "dead" or lacking active research. Participants express skepticism about the classification of K-theory and Morse Theory as dead, emphasizing their relevance, particularly in areas like string theory. There is a consensus that some fields, such as foliations and fractals, have seen diminished activity since the 1970s, although recent interest has been rekindled due to non-commutative geometry. The conversation also touches on the status of category theory, which is deemed popular, and highlights that high school algebra and constructive geometry are considered outdated, with little to no new research emerging. General topology is mentioned as another field experiencing a decline in research output, suggesting it may be nearing a state of resolution despite some obscure unsolved problems remaining.
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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