@lionjim. You could soon be a millionaire
- Thread starter BW Lion
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I think if s=1, the series diverges. Not sure about values for s>1
(I'm not Jim but I did stay at a Holiday Inn Express before)
(I'm not Jim but I did stay at a Holiday Inn Express before)
That's "Dr.John Urschel".Calling John Urschel, calling Mr . John Urschel..................................
If s=1 it’s a harmonic series, diverges. (This is something that is taught in Calc 3.) It converges for every other complex s. The headline is a bit misleading, as “solving the problem” means that one has to prove that if the series sums to zero then either s is a negative integer or s=.5 + yi, y real. It has been a big deal since it was #8 in Hilbert’s list of 23 problems he made in 1900 (wiki page follows).
This problem is way above my pay grade, sorry. (I’m an algebraist by training, anyway.)
Goldbach’s Conjecture, mentioned in the article, is easier for the layman to understand: every even integer greater than 2 is the sum of two primes. For example, 4 = 2+2, 6 = 3+3, 8 = 3+5, etc. Prove it. (It’s been an open question since at least 1742.) This is also a million dollar question.
Hilbert's problems - Wikipedia
I guess this is the place and time to mention Godel’s Incompleteness Theorems: given any consistent system of axioms there will always be statements which cannot ever be proved one way or the other. Hilbert’s Problem 1: Resolve the Continuum Hypothesis, is one of them. (Paul Cohen proved, in 1963, that this could never be resolved.) Goldbach’s Conjecture could very well be this sort of animal: it’s almost certainly true (no one believes it is not true), but it’s possible that it is something whose proof does not exist within the axioms we use. There has been a whole lot of work by some very very smart people trying to prove Goldbach (after all, prove it and you’ll get a million dollars and eternal fame), and it’s very possible that no proof exists.If s=1 it’s a harmonic series, diverges. (This is something that is taught in Calc 3.) It converges for every other complex s. The headline is a bit misleading, as “solving the problem” means that one has to prove that if the series sums to zero then either s is a negative integer or s=.5 + yi, y real. It has been a big deal since it was #8 in Hilbert’s list of 23 problems he made in 1900 (wiki page follows).
This problem is way above my pay grade, sorry. (I’m an algebraist by training, anyway.)
Goldbach’s Conjecture, mentioned in the article, is easier for the layman to understand: every even integer greater than 2 is the sum of two primes. For example, 4 = 2+2, 6 = 3+3, 8 = 3+5, etc. Prove it. (It’s been an open question since at least 1742.) This is also a million dollar question.
Hilbert's problems - Wikipedia
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