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Tagged with conjectures soft-question
8 questions
78
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9
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Mathematical conjectures on which applications depend
What are some examples of mathematical conjectures that applied mathematicians assume to be true in applications, despite it being unknown whether or not they are true?
63
votes
7
answers
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Theorems demoted back to conjectures
Many mathematicians know the Four Color Theorem and its history: there were two alleged proofs in 1879 and 1880 both of which stood unchallenged for 11 years before flaws were discovered.
I am ...
59
votes
7
answers
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How closed-form conjectures are made?
Recently I posted a conjecture at Math.SE:
$$\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx\stackrel{?}{=}\frac{\pi}{2}(\mu^2-\nu^2),$$
where $J_\mu(x)$ and $Y_\mu(x)$ ...
- 6,819
20
votes
4
answers
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Can anything deep be said uniformly about conjectures like Goldbach's?
This is a soft question sparked by my curiosity about the intrinsic depth of Goldbach-like conjectures as perceived by current experts in number theory. The incompleteness theorem implies that, if our ...
- 2,912
18
votes
3
answers
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Is it a reasonable way to write a research article assuming truth of a conjecture?
I have found a conjecture in a research article (published in a good journal) on number theory, which is not well known but very reasonable. Let me be clear that, there is no counter-example that vote ...
- 930
8
votes
3
answers
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The resolution of which conjecture/problem would advance Mathematics the most? [closed]
This is an impossibly broad question, and makes the unwarranted assumption that Mathematics is a uniform field. It might make more sense to ask the same question restricted to, say, Mathematical Logic,...
3
votes
0
answers
234
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Uses of excluded middle on a conjecture that can be rewritten constructively with this trick
An interesting proof technique is to use the law of excluded middle on a conjecture. There are proofs using LEM on the Riemann hypothesis for example.
Constructively this is disallowed (if you can ...
- 6,353
2
votes
2
answers
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Easy to explain conjectures that are still unsolved [duplicate]
Mathematics has many open conjectures which are ridiculously hard to even understand. But this is not always the case. An example is:
Collatz conjecture.
I would like to see some more examples. So ...