Fermat's Last Theorem (formulated in the 17th century) has recently been proved by Andrew Wiles. This essay is a summary of the historical attempts to prove or disprove the theorem. Fermat himself proved the theorem in the case when the exponent is four. It took over 100 years more until Euler proved the case when the exponent is three. Through the years, many mathematicians erroneously believed that they have succeeded in proving the general case of Fermat's Last Theorem. Although they failed they developed new mathematics, for example a new kind of complex number -- the cyclotomical integers (introduced by Ernst Kummer), the existence of regular and irregular primes and arithmetic geometry.