The Forgotten Mathematician

Pierre Wantzel was born in 1814 on the 5th of June in Paris. His father was a professor of mathematics at École speciale du Commerce after serving in the army. Due to this Pierre started his life with a natural love for mathematics. He attended school at his home town of Ecouen where he demonstrated this love. When he was only 9 years old his teachers would turn to him for help when judging the difficulty of problems. His love and skills for mathematics was realized by his parents when they sent him to École des Arts et Métiers de Châlons. He was surprisingly 12 years old he went there, and this was far younger than most.   His teacher was the well-known Étienne Bobillier, a mathematician known for his works on polar curves and algebraic surfaces. This helped kinder his mathematical skill, but it did not last long because in 1827 the school was reformatted. This was because France itself was facing revolts and other political issues. The school was reformed to become less academic, and this caused Pierre to take his studies elsewhere.

In 1828 he traveled to the Collège Charlemagne to continue his studies and receive language coaching. He later married the daughter of language coach, but before this he accomplished many feats of genius including editing a second edition book by Reynauld, Treatise on arithmetic, at only 15 in 1829. This book featured a method for finding square roots that was never proved. He proved the method, and in doing so he received the first prize for dissertation from his college. Later on he took the entrance exam to École Polytechnique and the science section for École Normale. He placed first in both of these, something never before achieved. Furthering his education he traveled to Ponts et Chaussées, an engineering school, but did not stay long. He remained there for a year until 1835 where he journeyed to the Ardennes. Following a similar pattern he later traveled to Berry after only a year at the Ardennes. After studying engineering he decided that teaching mathematics was his true dedication. In order to achieve this he took a leave from his occupation, and went to become a lecturer for a school from his past, École Polytechnique. He later became a professor of applied mathematics at École des Ponts et Chaussées but not before becoming an engineer in 1841. Continuing with his true interests he began teaching classes on not only mathematics but physics as well. He continued his educational career becoming the entrance exam examiner In 1843. He was not confined by his university, however, as he traveled around Paris to many schools teaching there too.

The tools of Pierre Wantzel. Image: Mcgill via Wikimedia Commons.

Pierre achieved fame when he published what would become his most important works. These were on the subject on radicals, and solving equations and they were dubbed as some of the most famous problems of the time. Publishing them in Liouville’s Journal he was the first to prove that it was impossible to duplicate a cube and trisect an angle with a ruler and compass. Gauss had originally stated that it was impossible but offered no proof. This is what Pierre accomplished in his 1837 paper where he traces the solution back to cube roots, something that proves impossible to do with those tools. This was built off of the work of others, yet it still went beyond what had been previously done. Continuing his works Pierre delved into equations, and from this he created new proofs of algebraic equations deemed impossible. These were solved not by providing a solution but proving they were impossible to solve. He revised a proof of Abel’s theorem in 1845, stating that it was impossible to solve any equations where the exponent n is greater than 5. He also added details to many vague solutions on the subject these solutions were proposed by famous mathematicians such as Ruffini. Pierre published over 20 works throughout the course of his life a few of these branch out into the field of physics, specifically dealing with extreme pressure differences.

Pierre was a strong man who focused on his work so much that he sacrificed his sleep and meals to do so. Pierre Wantzel did not live out his life fully as he overworked himself. He relied on coffee and opium to continue his lifestyle, and this ultimately resulted in his demise. In 1848 at the age of 33 he died and the world lost a great mind. Overall his works were very important yet were not remembered as well as others. This is commonly attributed to the classical nature of the problem he is famous for. Several other mathematicians mentioned the problem yet they have given no proof. Max Simon’s work from 1906 does mention Pierre’s, but it was published as a supplement to another work rather than as its own. Another reason is his early death. Due to his potential yet little time to achieve true greatness he is less known. Sadly he was not elected as a member of the Académie des Sciences. His achievements were great and if he had lived longer he would have achieved much more.