Why is the Yorke-Kaplan conjecture still unresolved?

  • Context: MHB 
  • Thread starter Thread starter Joppy
  • Start date Start date
  • Tags Tags
    Conjecture
Click For Summary
SUMMARY

The Yorke-Kaplan conjecture remains unresolved due to the existence of potential flaws in proofs from the 1980s, which have not been definitively addressed. Discussions highlight that while sources like MathWorld reference a proof, they fail to clarify any errors associated with it. The conjecture's complexity may stem from pathological cases that complicate its validation. Thus, the conjecture continues to be a topic of interest in mathematical circles.

PREREQUISITES
  • Understanding of mathematical conjectures and proofs
  • Familiarity with the history of mathematical research, particularly from the 1980s
  • Knowledge of pathological cases in mathematical analysis
  • Ability to interpret mathematical articles and papers, such as those found on MathWorld
NEXT STEPS
  • Research the history and implications of the Yorke-Kaplan conjecture
  • Study the concept of pathological cases in mathematics
  • Explore the details of proofs related to the Yorke-Kaplan conjecture from the 1980s
  • Review articles and papers on MathWorld for additional context and references
USEFUL FOR

Mathematicians, researchers in dynamical systems, and students interested in unresolved mathematical conjectures will benefit from this discussion.

Joppy
MHB
Messages
282
Reaction score
22
I read somewhere that this was proved sometime in the 80's, but that same source didn't mention that the proof was wrong. Of course I would cite the source but I can't find it again.. Does anyone know of any specific reason why this is still a conjecture?

I realize that for these sorts of measures there is often some pathological or special case getting in the way. Is that what is happening here?

Thanks :).
 
Mathematics news on Phys.org
The MathWorld article fits your description (mentions that it was "proved" in the 1980's, but does not mention a flaw in the proof), but I'm not sure if that's what you were thinking of.
 
Ackbach said:
The MathWorld article fits your description (mentions that it was "proved" in the 1980's, but does not mention a flaw in the proof), but I'm not sure if that's what you were thinking of.

Thanks Ackbach! I'm not sure it's the same article.. but I should have checked at MathWorld anyway since there is a nice paper trail there :). Thanks again.
 

Similar threads

Graduate Is the Collatz Conjecture Finally Close to a Proof?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Shinichi Mochizuki's ABC Conjecture and Replication Crisis in Maths
  • · Replies 33 ·
2
Replies
33
Views
8K
Graduate Is the Collatz Conjecture's Behavior Predicted by Binary Representations?
  • · Replies 1 ·
Replies
1
Views
3K
MHB Is massively collaborative mathematics possible in forums?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Quantum Interest Conjecture and negative energy-density
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Why doesnt Bertrand's postulate imply Legendre's conjecture?
  • · Replies 20 ·
Replies
20
Views
12K
Graduate Approximating the reals by rationals (Littlewood's Conjecture)
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Erdos conjecture on arithmetic progression
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Math/Science Books that grow on you
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Meaning of "passage to the quotient"?
  • · Replies 3 ·
Replies
3
Views
991