# Gauss and Germain

Carl Friedrich Gauss (1777–1855) lived in Göttingen and was one of the greatest matheamticians of all time. He worked in many areas, ranging from complex numbers (the ‘Gaussian number plane consisting of numbers of the form a + bi, where i2 = −1) to statistics (the ‘Gaussian distribution’) and electricity. He gave the first satisfactory proof that every polynomial equation has a complex root, and in number theory he initiated the study of congruences and proved the law of quadratic reciprocity.

Gauss also investigated which regular polygons can be constructed with ruler and compasses alone, proving that a regular n-gon can be so constructed when n is a power of 2 times a product of different Fermat primes of the form 2k + 1 (where k is a power of 2); such polygons include an equilateral triangle, a regular pentagon and a regular polygon with 17 sides (as shown on the East German stamp).

In the predominantly male world of late 18th-century university mathematics, it was difficult for talented women to become accepted. Discouraged from studying the subject, they were barred from universities or the membership of academies. One mathematician who had to struggle against such prejudices was Sophie Germain (1776–1831).

Sophie Germain’s main contributions to mathematics were in number theory and the study of elasticity. In  number theory she obtained several new results on Fermat’s last theorem, xn + yn = zn, proving in particular that, if n is any prime number less than 100, then there are no positive integer solutions if x, y and z are mutually prime to one another and to n. In elasticity she developed a general theory of vibrations of a curved surface. Her work subsequently provided the basis for the modern theory of elasticity.

In order to gain acceptance, Germain wrote to Lagrange and Gauss with her mathematical discoveries, under the male pseudonym of M. Le Blanc. Both Lagrange and Gauss were very impressed with her work, and continued to correspond with her.

[East Germany 1977; France 2016; Germany 1955, 1977; Nicaragua 1994]

Published/edited: 28/04/2015