Grand Challenges
Applying the MS Pilot framework to some of the deepest questions in science and philosophy.
Riemann Hypothesis
"How do prime numbers hide their patterns?"
Intuitive Explanation
Prime numbers seem random, but the Riemann Hypothesis suggests they follow a deep, hidden 'music' or pattern related to the zeros of a specific mathematical function. Cracking it would unlock profound secrets about the nature of numbers.
A Vector-Based Approach
We can treat the distribution of primes and the values of the Riemann zeta function as two distinct, high-dimensional vectors. By applying Dimensional Analysis, we can search for a geometric transformation (a 'rotation' or 'projection') that maps one vector onto the other, revealing the hidden structure that connects them.
Algorithmic Pathway
The proposed algorithmic recipe to reframe the problem.
Vector Definition
Define the distribution of prime numbers up to a limit N as a vector (V_primes) and the locations of non-trivial zeta function zeros as another vector (V_zeros).
Primes -> V_primes, Zeros -> V_zerosComparative Analysis
Measure the 'distance' or 'correlation' between the two vectors. A high correlation would suggest a deep structural relationship, as predicted by the hypothesis.
correlation(V_primes, V_zeros)Creative Synthesis
Attempt to generate a function (F) that transforms the zero vector into the prime distribution vector, effectively creating a predictive model for primes.
F(V_zeros) ≈ V_primes