An interesting read! Unfortunately the author omits the mindblowing (at least for me) proof of why the series Z(s) = 1 + 1/(2^s) + 1/(3^s) + 1/(4^s) + ... i

An interesting read! Unfortunately the author omits the mindblowing (at least for me) proof of why the series Z(s) = 1 + 1/(2^s) + 1/(3^s) + 1/(4^s) + ... is equal to the infinite product over the terms "1/(1-p^(-s))", with one term for each prime number p. This proof does not need a lot of math [1], and if you know the formula for a geometric series, you can also "prove it" by hand-waving: Each term in the product is a geometric series, and if you multiply all these series out, the result is a sum over all possible permutations of prime-factored numbers (well, the inverses of them). Since each natural number has exactly one such represnetation, it's effectively a sum over all 1/(n^s). Of course, you need some rigor to show that you are actually allowed to rearrange terms of an infinite product of inite sums like that... [1]: https://en.wikipedia.org/wiki/Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function#Proof_of_the_Euler_product_formula https://en.wikipedia.org/wiki/Proof_of_the_Euler_product_for...