Pierre Wantzel

Pierre Laurent Wantzel (5 June 1814 to 21 May 1848) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge. In a paper from 1837 he proved that doubling the cube and trisecting the angle are impossible with compass and straightedge, and in the same paper he solved the problem of which regular polygons are constructible: a regular polygon is constructible if and only if the number of its sides is the product of a power of two and any number of distinct Fermat primes, so that the sufficient conditions given by Carl Friedrich Gauss are also necessary. These problems had been sought for thousands of years, particularly by the ancient Greeks, but Wantzel's work was neglected by his contemporaries and essentially forgotten.