Not sure about hardest, but the typical consensus is that it's humanity's 2nd most important unsolved math problem after
P versus NP (I was taught about that one at university and I'm still clueless there). I'd say of all the million dollar Millennium Prize Problems, the Riemann hypothesis is the one that
looks the easiest (deceptively of course). I don't know if many other people were introduced to complex numbers in high school, but by
Euler's formula the function can be expressed in terms of log, sine and cosine instead anyway. So I think it doesn't require much above a high school level of math to explore the problem. I could go into more detail sometime if anyone likes.
I do a bit of sloppy programming to visualise things, mostly partial sums of the Dirichlet eta function. It shares all the zeros of the Riemann zeta function, but is easier to calculate as it converges nicely in the zone of interest.
The most insight I've gained is by using the imaginary part of
s as my x-axis. Here's an example where I set the real part of
s to 0.5, only include the prime terms of the series (the 2nd, 3rd, 5th, 7th, 11th etc.), and calculate the real part of the partial sum to get my y values. So the ups and downs of the lines in my image equate to moving horizontally in your video. I draw each iteration a bit further down the screen to see them progress. What's interesting is that the positions of the zeros show up (as prominent dips) without me even presenting the imaginary part of the sum at all:
As to how the problem relates to the prime numbers, that's something even I find difficult to wrap my head around.
Earthcubed wrote:
doing that thing where he drags the guts of his premise across sandpaper for their entire intestinal length before wiping his keyboard with it
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