“The Riemann Hypothesis is the most imporant Unsolved Problem in mathematics.” It has not been totally solved, but there has been meaningful progress made by Claude AI. The prompting human was a software engineer who, after being rebuffed by Claude’s “that’s a 150-year old problem, I’m not going to do that”, simply replied, “believe in yourself” and various other positive encouragement, leading to the progress. So it’s not just the progress but also the mechanism for AI.
Harmonic series when power is 1. Basel series when power is 2. Zeta function when power is 3. (Geometric series would be a fixed denominator but having a varying exponent, so 1/2^x) Geometric asymptote found by 1 / 1-(common ratio, which is 2 (of the 2^x term). Asymptotes are the limits caused by terms including infinity. Euler said consider the geometric series for primes.
“Geometric series for power of primes”
True statement: Every natural number greater than 1 can be written uniquely as a product of prime numbers, up to reordering.
Example:
60 = 2 × 2 × 3 × 5
This is called the Fundamental Theorem of Arithmetic — also called unique prime factorization.
“The Periodic Table of the Numbers consists of the Primes; everything else is made out of them.” 46:05 in