IdiotsOpposite
Boom, headshot.
A couple of questions, anyone may answer (I don't care what people call themselves, it's their accomplishments that matter more):
First, what's your Erdos number?
Second, I'd like to go back to Reimann's zeta function and the zeros. I've read a little about this (Marcus Du Sautoy's Music of the Primes) and I really don't understand it.
The way it was described in the book (assuming I remember it correctly!!), the zeros are areas of a complex landscape that are i distant from the y axis and never cross the line. The problem everyone was working on was finding a prove that no zero was ever off the line through i. Reimann's housekeeper burned many of his personal documents after he died, so any proof that he had figured out must be rediscovered.
Can you explain to me how that graphs of the zeta in polar coordinates relates to my description above? Again, I'm probably mangling parts of this - so I apologize if the question is ill-formed or a frustrating waste of mathematical times
The Zeta function! My favorite function of all, and the focus of the book I was reading. First, it's important to note that there are two categories of zeroes for the Riemann Zeta function. The first are called trivial zeros, and occur at every negative even integer. -2, -4, -6, etc. The others are called non-trivial zeroes, and so far as we know, they all seem to be on the critical line Re(s) = 1/2. Now, the Riemann Zeta function exhibits some symmetry around this critical line thanks to the functional equation. If there's some zero between 1/2 < Re(s) < 1 and Im(s), then there's going to be an equivalent zero, with Im(1-s)! Couple this with the fact that the Riemann Zeta function's zeroes are also symmetric over the real line, this means that any zero that does not lie on Re(s)=1/2 will imply the existence of 3 other zeros that also do not lie on Re(s)=1/2. But that's not important now, is it? I sort of completely lost track of what question you were asking.All right, so the function in polar coordinates I put up is a polar representation of Zeta(1/2 + i t), which would normally be represented as a complex number x+iy, is shown using the polar representation of complex numbers instead. Using this representation, every time the function that's moving around in its series of circles crosses the point (0,0), that's a zero of the Zeta function. I can't remember the exact wording, but I believe that there's a proof that if the Zeta function makes a complete circle WITHOUT crossing the point (0,0), then the Riemann Hypothesis will be disproven. I'll have to look that up when I get home.
At Waterloo what made people cry were first year "weeding out" courses like linear algebra. My brain really liked combinatorics for some reason, it just *made sense*.
