Charles Hermite
French mathematician who proved e is transcendental.
Charles Hermite was a French mathematician whose work spanned analysis, number theory, and algebra. He is most celebrated for proving that the number e is transcendental, a major milestone in mathematics. Born on 24 December 1822 in Dieuze, Moselle, he was the sixth of seven children. His father worked in the family drapery business while also pursuing art, and the family relocated to Nancy in 1828 when the business moved. Hermite had a deformity in his right foot that affected his gait throughout his life. He attended secondary school at Collège de Nancy, then in Paris at Collège Henri IV and Lycée Louis-le-Grand, where he read works by Joseph-Louis Lagrange on numerical equations and Carl Friedrich Gauss on number theory. He aimed to enter the École Polytechnique, a military academy known for mathematical rigor, and studied for a year under mathematician Eugène Charles Catalan to prepare for the difficult entrance exam. Admitted in 1842, he was forced to leave after one year because the school would not accommodate his deformed foot. Despite efforts to regain admission under strict conditions, he refused and left without graduating. For five years he studied privately, befriending mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, and earned his baccalauréat in 1847. He married Bertrand’s sister, Louise, in 1848. That year he returned to the École Polytechnique as a répétiteur and examinateur d’admission, and was elected to the French Academy of Sciences. After contracting smallpox in 1856, he resumed his Catholic faith, influenced by Augustin-Louis Cauchy and a nursing nun. He lectured at the École Normale Supérieure from 1862 to 1873, then succeeded Jean-Marie Duhamel as professor of mathematics at both the École Polytechnique and the University of Paris, remaining at the latter until his death. He was made a grand officer in the French Legion of Honour on his 70th birthday. He died in Paris on 14 January 1901, aged 78, after suffering from asthma, poor appetite, and sleeplessness.
- field
- Mathematics
- nationality
- French
- known_for
- Proof of the transcendence of e
Lore & Background
Hermite was born in Dieuze, Moselle, with a deformity in his right foot that impaired his gait throughout his life. He was the sixth of seven children; his father worked in the drapery business and also pursued a career as an artist. The family relocated to Nancy in 1828 due to the drapery business. For his secondary education, Hermite attended the Collège de Nancy, followed by the Collège Henri IV and the Lycée Louis-le-Grand in Paris. During this time, he studied writings by Joseph-Louis Lagrange on numerical equations and Carl Friedrich Gauss on number theory. He sought admission to the École Polytechnique, a military academy, and after a year of preparation under the tutelage of Eugène Charles Catalan, he was admitted in 1842. However, the school barred him from continuing after one year because of his deformed foot. He attempted to regain admission under strict conditions but refused to accept them and left without graduating. He spent five years studying privately, befriending mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, and earned his baccalauréat in 1847. He married Bertrand's sister, Louise, in 1848. That same year, he returned to the École Polytechnique as a répétiteur and examinateur d'admission, and was elected to the French Academy of Sciences.
Reader's Guide
This built on Liouville's prior work and opened the door for Lindemann's later proof of the transcendence of π. Hermite also proved that π² and therefore π are irrational, though he did not prove π transcendental. He proved that eigenvalues of Hermitian matrices are always real, generalizing Cauchy's result. His work on elliptic and Abelian functions, including correspondence with Jacobi, was included in Jacobi's complete works. Later in life, he studied linear differential equations and found solutions to Lamé's equation. His legacy includes the Hermite crater on the Moon and numerous mathematical concepts named after him.
Did You Know?
- Hermite was forced to leave École Polytechnique after one year because of a deformity in his right foot.
- The Hermite crater near the Moon's north pole is named after him.
Frequently Asked Questions
What is Charles Hermite most famous for?
He is best remembered for proving that the number e is transcendental, meaning it cannot satisfy any polynomial equation with rational coefficients. This result is widely regarded as a landmark achievement in the history of mathematics.
Which mathematical fields did Charles Hermite contribute to?
His work spanned analysis, number theory, and algebra, making him one of the more broadly influential mathematicians of his era.
Why is Charles Hermite's proof about e considered so important?
Before his result, it was unclear whether e might be algebraic like many other well-known constants. By establishing its transcendence, Hermite settled a long-standing open question and opened the door to further breakthroughs in transcendental number theory.
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