**Pierre-Laurent Wantzel**(1814-1848) by A de Lapparent appeared in

*École Polytechnique: Livre du Centenaire*, 1794-1894

**1**(1895), 133-135. We give here an English translation of article, which of course was originally written in French:-

### Pierre-Laurent Wantzel (1814-1848)

Wantzel, in the eyes of the world, is forgotten. His premature death did not allow him the place in the Institute that he deserved. The day after his death, Mr de Saint-Venant dedicated to him, in the *Annals of Terquem and Gerono* (Nouvelles Annales de Mathématiques), several emotional pages; but no biographical dictionary has deigned to recognize that notice; the colleagues of Wantzel have, for the most part, disappeared from this world, and today mathematicians know only what magnificent hopes were given the beginnings of this geometrician, who left to the école Polytechnique and the world of science a luminous trace, unfortunately resembling the meteors in the sky that vanish as soon as they are glimpsed.

Born June 5, 1814, Pierre-Laurent Wantzel was taught by a mere elementary school teacher. At the age of 12, he entered the School of Arts and Trades (l'École des Arts et Métiers de Chàlons), where he demonstrated such a disposition for Mathematics that his instructors sent him to Paris in 1828. There he took classes at the coll6ge Charlemagne, and, in 1829, Reynaud appreciated him enough to not only allow him to correct proofs of the new edition of his *Arithmetic* but to also introduce in that volume a demonstration concerning the square root which was suggested by the young editor. In 1831, the first prize of French dissertation from the Collège Charlemagne was awarded to him, and better yet, first prize in Latin dissertation, acquired in an open contest, attested with splendour to the universality of Wantzel's aptitude. The following year, after other successes of the same magnitude, won in the area of sciences, he entered his first year at the École Polytechnique, at the age of 18, dazzling his colleagues by the superiority of his mind, as he charmed them with the frankness and nobility of his character. Rarely has a student left more brilliant memories. Having been "in Wantzel's class" was the sort of honour one liked to show off.

Design, for which he cared little, kept him from keeping his entrance ranking. Nonetheless, he became a student-engineer of Bridges and Roads, and in 1837 asked for a leave in order to devote himself exclusively to science. In accordance with this desire, the Director General, Mr Legrand, was too wise to not retain a man of such worth; therefore he named Wantzel an engineer in 1840, attached him to the School of Bridges and Roads in 1844, in the capacity of professor of applied mechanics. As well, the École Polytechnique had previously welcomed Mr Wantzel, in 1838, as professor of analysis. He was also charged with specialized classes in various preparatory schools and became, in 1848, an admissions examiner, and was recognized for the stunning brilliance with which he performed these duties, as he was for the lucidity and brilliance of his exposition. Wantzel's first publication, prior to his entering École Polytechnique was in 183 1, and concerned the theorems relative to radicals. Later there appeared, in 1837, research on problems of Geometry. He proved, for the first time the impossibility (already affirmed, but not demonstrated, by Gauss) of obtaining, with rule and compass, the duplication of a cube or the trisection of an angle. We also owe to him a note on the curvature of elastic rods, several works on the flow of air, pursued in concert with Mr de Saint-Venant; finally, in 1848, an important posthumous note on the rectilinear diameters of curves. It was he who first gave the integration of differential equations of the elastic curve

But the masterpiece of Wantzel was his work on incommensurable numbers, a study admirable for the simplicity and clarity of its method and for the beauty of the results obtained. It was in these works that he achieved the exact measure of what was expected of him. Unfortunately Wantzel did not know how to concentrate his efforts. Overly numerous occupations, a too-large faculty of improvisation, a vivacity of emotions which ranged from black humour to enthusiasm, training in Philosophy, History, Music and debate, all of these kept him from turning his beautiful and generous intelligence in one precise direction. In addition, excessive and poorly regulated work had affected his health. The profoundly regrettable measure with which he performed his duties as examiner was the final blow, and he died in 1848, consoled by hopes of a profoundly religious soul, but leaving with his friends, and with science, irreparable regrets.

A de Lapparent