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other mathematiciansQuanta Magazine
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84% Informative
The Riemann zeta function is one of the most central functions in number theory.
Mathematicians had been trying for centuries to prove the irrationality of ( 3 ) But for most other numbers it remains frustratingly hard to prove.
Researchers have shown how to broaden Apéry 's approach into a much more powerful method.
Many mathematicians take an Occam’s -razor point of view: Unless a number should be rational, it probably is not.
Leonhard Euler proved that e is irrational, but the status of many simple numbers, such as + e or ( 5 ), remains a mystery.
In an irrationality proof, you want your sequence of fractions to rule out ever-larger denominators.
Few numbers meet this standard more thoroughly than the values of the Riemann zeta function and the allied functions known as L-functions.
In addition to its role in number theory, L(x) makes unexpected cameos in geometry.
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