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other mathematiciansQuanta Magazine
•78% Informative
The Riemann hypothesis is a statement about a central formula in number theory.
It says that for some complex numbers, the zeta function is equal to zero .
The new proof automatically leads to better approximations of how many primes exist in short intervals on the number line.
In 1940 , Albert Ingham established an upper bound on the number of zeros whose real part is not equal to 1/2 .
The most important zeros to cap were those with a real part of exactly 3/4 .
Larry Guth , an expert in harmonic analysis, was at the same conference as Maynard .
Guth and Maynard rewrote their problem so that it was now about the largest eigenvalue of their matrix.
The new work has allowed mathematicians to shorten the intervals in which they can get good estimates.
Guth likened it to playing with a Rubik ’s Cube; sometimes you have to undo previous moves and make everything look worse before finding a way to get more colors in the right place.
Guth 's expertise as a harmonic analyst rather than a number theorist made it possible.
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