** Mathematics** is the study of

The real part (red) and imaginary part (blue) of the critical line Re(s) = 1/2 of the Riemann zeta-function.Image credit: |

The ** Riemann hypothesis**, first formulated by

The Riemann hypothesis is a *s*). The Riemann zeta-function is defined for all *s* ≠ 1. It has zeros at the negative even integers (i.e. at *s*=-2, *s*=-4, *s*=-6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:

*The real part of any non-trivial zero of the Riemann zeta function is ½*

Thus the non-trivial zeros should lie on the so-called **critical line** ½ + *it* with *t* a *i* the

The Riemann hypothesis is one of the most important open problems in contemporary mathematics; a $1,000,000 prize has been offered by the

The ** Lorenz attractor** is an iconic example of a

- ...that
Euler found 59 moreamicable numbers while for 2000 years, only 3 pairs had been found before him? - ...that there are
6 unsolved mathematics problems whose solutions will earn you one million US dollars each? - ...that there are different sizes of
infinite sets inset theory ? More precisely, not all infinitecardinal numbers are equal? - ...that every
natural number can be written as the sum offour squares ? - ...that the
largest known prime number is nearly 25million digits long? - ...that the set of
rational numbers is equal in size to the set ofintegers ; that is, they can be put inone-to-one correspondence ?

The ** Mathematics WikiProject** is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's

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