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A Million-Dollar Matrix
The Redheffer matrix has been included in the MATLAB Gallery for many years, but, until now, I didn’t know much about it. The Riemann Hypothesis is subject of one of the Clay Mathematics Institute Millenium Prizes that are worth one million
dollars each.
If we could find an n-by-n Redheffer matrix
\[ \texttt {R = gallery(`redheff',n)} \]
with a determinant that satisfies
\[ \texttt {det(R) > sqrt(n)} \]
it would be worth a million dollars.
For over 100 years, mathematicians believed that such an n might exist. This is the story of Redheffer matrices, the Mertens conjecture, five different ways to compute n, and the proof that a prize-winning matrix does not
exist.
https://blogs.mathworks.com/cleve/2024/10/22/mobius-mertens-and-redheffer