### Charles Hermite was a famous French mathematician who worked on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra in the nineteenth century. He was always more interested in advanced subjects than his curriculum, and while still in secondary school, he published two noteworthy papers. He went on to École Polytechnique to study mathematics, but he had to quit the next year due to a malformation in his right foot that caused him to use a cane. At the age of twenty-four, he completed his baccalauréat and license after five years of independent study. In the meantime, he began writing letters to famous mathematicians, detailing his results. Despite his incredible research, he only had a few publications to his name, disseminating the majority of his findings through letters, short notes, and course lectures, which served as the foundation for additional research by other mathematicians. He was a great teacher as well, having been appointed professor of analysis at both the École Polytechnique and the Sorbonne. He was always cheerful, despite his deformities, splitting his time between his family, teaching, and study.

## Childhood and Adolescence

Charles Hermite was born in Dieuze, in the north-eastern part of France, on December 22, 1822. Ferdinand Hermite, his father, was an engineer by training but a natural artist. He briefly worked in a salt pit before marrying Madeleine nee Lalleman and afterwards managing his in-drape law’s business.

Ferdinand and Madeleine had a total of seven children, with Charles being the sixth. He had two sisters and four brothers. Charles was born with a deformity in his right foot that made it difficult for him to move. His parents were quite concerned about the abnormality since they knew it would prevent him from pursuing a career later in life. Charles, on the other hand, was in a good mood and took it all in stride.

When Charles’ family moved to Nancy in 1828. Despite his parents’ lack of interest in their children’s education, they sent them all to top schools, with Charles being accepted to Collège de Nancy.

Charles Hermite traveled to Paris after graduating from Collège de Nancy, where he first studied at Lycee Henri IV. He was significantly influenced by César-Mansuète Despretz, with whom he studied physics. He did not stay here for long, however, and moved to Lycée Louis-le-Grand in 1840.

He studied mathematics at Lycée Louis-le-Grand with Louis Richard, who had previously taught Évariste Galois. Despite the fact that he had entered the institution with the goal of studying for the École Polytechnique admission exam, his focus soon began to wane.

He began reading the writings of prominent mathematicians such as Euler, Gauss, and Lagrange under Richard’s guidance. ‘Disquisitiones arithmeticae’ by Gauss and ‘Traité sur la résolution des équations numériques’ by Lagrange were among the works the eighteen-year-old read. He did not, however, abandon his purpose.

In 1841-1842, he began studying with Eugène Charles Catalan in order to prepare for the entrance examination at École Polytechnique. Simultaneously, he began original mathematical study, publishing his first paper in the Nouvelles Annales de Mathématiques, a French mathematical journal, in 1842.

Hermite took the entrance exam for École Polytechnique in 1842. However, due to his extracurricular studies, he only just passed his exam and finished in 68th place on the list. In the same year, he enrolled at the institution.

He began to devote more time to extracurricular studies at École Polytechnique as well, focusing on Abelian functions, which were of significant interest to European mathematicians at the time. It led to his meeting with a well-known mathematician named Joseph Louisville.

Because of his disfigurement, Charles Hermite was ordered to leave École Polytechnique in 1843. École was a military academy, and Hermite was deemed physically inadequate because he walked with a cane.

He was allowed to continue his studies at École when several powerful professors intervened on his behalf; nonetheless, he was granted certain very tight limitations, which he found unacceptable. As a result, he dropped out of École and studied privately for the following five years, completing his baccalauréat and license exams in 1847.

Between 1843 and 1848, Hermite had a remarkably prolific era. Despite the fact that he was still an undergraduate with no formal education, he began to be admired by well-known mathematicians for his research effort.

He initiated correspondence with Carl Gustav Jacob Jacobi, a German mathematician who made significant contributions to mathematics, in January 1843. During this time, Hermite wrote him at least six letters.

He discussed his work on Abel’s theorem in his first letter to Jacobi. In his second letter, he discussed the transformation of elliptic functions, which he wrote in August 1844. The remaining four letters dealt with number theory.

These works had such an impact on Jacobi that he included excerpts from them not only in his own ‘Opuscula,’ but also in Crelle’s Journal. Hermite also collaborated with Joseph Liouville at this time, making substantial contributions to Liouville’s work.

## Career of Charles Hermite

Charles Hermite began his career as a répétiteur and examinateur d’admission at École Polytechnique in 1848, six years after he was asked to leave. He established that doubly periodic functions can be represented as quotients of periodic complete functions the same year.

He submitted a memoir to the Académie des Sciences in 1849, in which he applied Augustin-Louis Cauchy’s residue techniques to doubly periodic functions. Despite the fact that both Cauchy and Charles-François Sturm provided excellent reports, the report could not be released due to a priority issue with Liouville.

Hermite began working on the theory of quadratic forms in the early 1850s, which required him to research invariant theory. In the process, he discovered a reciprocity law for binary forms, leading to the creation of the theory of transformations in 1855. ‘Sur quelques applications des fonctions elliptiques’ was published the same year.

In 1858, he demonstrated that elliptic functions could be used to solve a fifth-degree algebraic equation. It is one of his most important works, and it has made him well-known.

École Polytechnique created the job of maître de conférence specifically for him in 1862, and he was appointed to it. He was hired as an examinateur de sortie et de classement there in 1863. He was also a lecturer at the École Normale Supérieure from 1862 until 1873.

Charles Hermite became professor of analysis at École Polytechnique in 1869 and stayed there until 1876.

He was also appointed to the Faculty of Sciences of Paris in 1869, where he remained until his death.

In the 1870s, he began working on problems involving approximation and interpolation once more. He established that ‘e’ is a transcendental number in 1873. In the same year, he wrote ‘Cours d’Analyse de l’École Polytechnique Première Partie,’ his second important book.

Continuing to work, he made a number of modest discoveries that established the groundwork for future research by other mathematicians. In 1882, Felix Lindemann, a mathematician, obtained the transcendence of by extending Hermite’s demonstration that ‘e’ is a transcendental number.

Hermite’s contribution to mathematics is undeniably more than meets the eye. This is mostly due to his propensity of publicizing his findings via letters, short notes, and courses.

He continued to lecture in addition to his studies, releasing ‘Cours professé à la Faculté des Sciences’ in 1891. ‘Correspondance,’ published posthumously in 1905, is his last piece to be published during his lifetime.

## Major Projects of Charles Hermite

Charles Hermite is most known for his work on algebraic equations of the fifth degree, published in 1858. Despite the fact that such equations cannot be solved using radicals, he demonstrated that they can be solved using elliptic functions, thus establishing a new branch of algebra. Later, he applied the findings to quadric form class number relations.

## Achievements & Awards

Hermite was elected to the Académie des Sciences in Paris on July 14, 1856.

He was appointed to grand officer of the Legion of Honour in 1892.

## Personal History and Legacy

Louise Pauline Arsène Bertrand, sister of fellow mathematician Joseph Louis François Bertrand, married Hermite in 1848. Isabelle Caroline Ferdinande Forestier née Hermite and Marie Picard nee Hermite were their two daughters.

Hermite contracted smallpox in 1856. Augustin-Louis Cauchy was a tremendous moral support for him during his illness. Hermite returned to the Roman Catholic fold and became a royalist under his influence, a belief he retained till the end.

In 1897, Hermite announced his retirement from the workforce. Three years later, on 14 January 1901, in Paris, he died at the age of 78.

Hermite polynomials, Hermite’s differential equation, Hermite’s formula of interpolation, and Hermitian matrices are among the mathematical entities that bear his name.

## Estimated Net Worth

Charles Hermite net worth is unknown.

## Trivia

“But to call Hermite a logician!” remarked Henri Poincaré, one of Hermite’s most famous students. Nothing could be further from the truth in my opinion. Methods constantly seemed to appear out of nowhere in his thoughts.”