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Charles Hermite

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Charles Hermite was a significant French mathematician of the 19th century. He specialized in several complex branches of mathematics. These included analysis, number theory, and algebra. His work helped solve deep puzzles about how numbers and equations behave. One of his most famous achievements was a proof involving a special number called e. This number is the base of the natural logarithm. By proving its nature, he changed how mathematicians viewed certain types of numbers.

Charles Hermite circa 1887
Charles Hermite circa 1887

Hermite's mathematical journey began with a struggle against unfair rules. He was born in Dieuze, Moselle, on December 24, 1822. He had a deformity in his right foot that affected his gait. In 1842, he was admitted to the École Polytechnique. This was a very famous military academy for science and engineering. However, the school would not let him continue his studies because of his foot. They tried to impose strict conditions on him. Hermite refused to accept these terms and quit the school. He spent the next five years studying privately to earn his degree. He eventually passed his baccalauréat examinations in 1847.

During his years of private study, Hermite built strong connections. He befriended many eminent mathematicians of his time. These included Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville. These friendships helped him grow as a thinker. He even married Louise Bertrand, the sister of Joseph Bertrand, in 1848. His talent was recognized very early in his career. In July 1848, he was elected to the French Academy of Sciences. This is a very prestigious group for scientists. He later became a professor at both the École Polytechnique and the University of Paris.

Hermite made many specific contributions to the field of algebra. In 1842, he published a proof regarding the Abel–Ruffini theorem. This theorem concerns the impossibility of finding algebraic solutions for certain equations. Specifically, it looks at equations of the fifth degree. He also worked deeply with Abelian and elliptic functions. He corresponded with Carl Gustav Jacob Jacobi about these topics. This work helped create a complete edition of Jacobi's mathematical writings. In a series of papers between 1858 and 1866, Hermite showed how to find roots for quintic polynomials. He did this by using elliptic integrals.

Another major area for Hermite was the theory of invariants. He developed this theory at the same time as Arthur Cayley and James Joseph Sylvester. During this work, Hermite discovered the law of reciprocity. This is a fundamental idea in higher algebra. In 1873, he reached a massive milestone in number theory. He became the first person to prove that the number e is transcendental. A transcendental number is a number that is not the root of any non-zero polynomial equation with rational coefficients. This means e cannot be produced by simple algebraic steps. His methods were so strong that Ferdinand von Lindemann used similar techniques in 1882. Lindemann used them to prove that pi is also transcendental.

Later in his life, Hermite shifted his focus toward calculus. He became very interested in the theory of linear differential equations. This is a branch of math used to describe how things change over time. He successfully found solutions to a specific type of math problem called Lame's equation. His career was filled with many honors and titles. He was promoted to grand officer in the French Legion of Honour on his 70th birthday. He was also an honorary member of the Manchester Literary and Philosophical Society. His influence reached far beyond the classrooms of Paris.

Charles Hermite died in Paris on January 14, 1901. He was 78 years old at the time of his death. Before he died, he suffered from asthma and poor sleep. His legacy remains visible in many different places today. Some mathematical properties are named directly after him. Even astronomers have found a way to honor his memory. There is a crater named the Hermite crater located near the Moon's north pole. This serves as a permanent mark of his importance to science and discovery.

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