The miraculous powers of modern calculation are due to three inventions : the Arabic Notation, Decimal Fractions and Logarithms. - Florian Cajori

Fermat died with the belief that he had found a long-sought-for law of prime numbers in the formula <math>2^{2^n} + 1 =</math> a prime, but he admitted that he was unable to prove it rigorously. The law is not true, as was pointed out by Euler in the example <math>2^{2^5} + 1 =</math> 4,294,967,297 = 6,700,417 times 641. The American lightning calculator Zerah Colburn, when a boy, readily found the factors but was unable to explain the method by which he made his marvellous mental computation.

The history of mathematics is important also as a valuable contribution to the history of civilization. Human progress is closely identified with scientific thought. Mathematical and physical researches are a reliable record of intellectual progress.

In 1735 the solving of an astronomical problem, proposed by the Academy, for which several eminent mathematicians had demanded several months' time, was achieved in three days by Euler with aid of improved methods of his own... With still superior methods this same problem was solved by the illustrious Gauss in one hour.