What are strange , obscure , ignored fields of mathematics?

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SUMMARY

This discussion centers on the perception of "dead" fields in mathematics, specifically highlighting Calculus of Variations, Morse Theory, and K-theory as areas with perceived low activity. Participants argue against the notion that K-theory is dead, emphasizing its relevance to string theory. Other fields mentioned include foliations and fractals, which have seen renewed interest due to non-commutative geometry. General topology is also noted as a declining area with fewer research papers being published.

PREREQUISITES
  • Understanding of K-theory and its applications in string theory.
  • Familiarity with Morse Theory and its significance in topology.
  • Knowledge of non-commutative geometry and its impact on mathematical research.
  • Basic concepts of general topology and its historical context in mathematics.
NEXT STEPS
  • Research the latest developments in K-theory and its applications in modern physics.
  • Explore the current state of research in Morse Theory and its implications.
  • Investigate the role of non-commutative geometry in revitalizing interest in foliations and fractals.
  • Examine the historical evolution and current trends in general topology.
USEFUL FOR

Mathematicians, researchers, and students interested in niche areas of mathematics, particularly those exploring less active fields and their historical significance.

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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