Pretty good intro at
http://www.math.jhu.edu/~wright/RH2.pdf
when you're a bit more sober (... or maybe not ...)
Riemann Hypothesis ...
- Thread starter MartinQ
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Pretty good intro at
http://www.math.jhu.edu/~wright/RH2.pdf
when you're a bit more sober (... or maybe not ...)
Couple of "simple" ones I came across recently ...
* Numbers which appear in both the triangular number and square number sequences can be found "easily" by looking at the continued fraction approximation to sqrt(2).
* The well known pythagoras ratios 3:4:5, 5:12:13, 7:24:25, ... have circles that lie inside them of radius 1, 2, 3, ... respectively.
mjr
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Not a problem with statistics. In fact, one of the key tests of normality is to squint a bit at the graph, then if it doesn't look normal, drink some vodka and repeat. The number of shots consumed is the degree of normality. This is the Kolmogorov Smirnoff test.
Wiles wrote the modern statement of the B S-D conjecture.
These are relatively short works. A famous proof in group theory after more than a century of cumulative work which was believed at the time to he the pinacle was 1200 pages. Shortly after it was finished it was discovered that something had been missed out of the other proofs
. The entire proof is so long that there isn't agreement about how many thousands of pages it is.
Fermat's book must have some big margins!Wiles wrote the modern statement of the B S-D conjecture.
These are relatively short works. A famous proof in group theory after more than a century of cumulative work which was believed at the time to he the pinacle was 1200 pages. Shortly after it was finished it was discovered that something had been missed out of the other proofs
Profpointy
Legendary Member
I thought you'd get the prize for disproving it too. And if it's false your proof could be a single number
Nope, only proof.
I've got my counter example written here on a bit of paper but it's rather complex.
Don't think complex numbers are allowed. Only real integers please.
I thought the conjecture was that all non trivial zeroes of the zeta function were of the form xi+0.5, in which case finding a zero outside of that line would disprove the conjecture. Is that not the case?
Sounds about right, I was talking about Fermat's problem statement, rather than the solution / conjecture which is part of the solution, no matter how interesting it is.
But I didn't mean for you to think about it too much :-)
Reminds me of one of the Saturday evening BBC programs Atlantis ~5 years ago with Pythagoras, Hercules & Jason. On one of the episodes they were lost and were looking at various different paths back home. I think it was Pythagoras who said "those routes (roots) look a bit complex to me". Would be nice to think it was one of those in jokes, but it may just be me ...
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nickyboy
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With the right amount of Bourbon you'd be in there with your own proof
40%
Yep, I thought your post refered to Riemann's hypothesis, not to Fermat's.Yes. A counter example of the Reimann Hypothesis would be a complex number (hence my "joke"
A counter example to Fermat's Last Theorem (not sure how we got onto that) would have to be a real integer, but we know there aren't any, as proved by Andrew Wiles.
https://www.dropbox.com/s/qj9qha156eyvt0b/2018-The_Riemann_Hypothesis.pdf?dl=0
test on it tomorrow ...
test on it tomorrow ...
nickyboy
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Time to hit the bourbon