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, the base of natural logarithms, is transcendental—a landmark result that showed e cannot be the root of any non-zero polynomial equation with integer coefficients. Born in Dieuze, Moselle, on 24 December 1822, Hermite had a deformity in his right foot that affected his gait throughout his life. He was the sixth of seven children; his father worked in the drapery business of his mother’s family while also pursuing art. The family moved to Nancy in 1828. Hermite attended secondary school in Nancy and later in Paris at Collège Henri IV and Lycée Louis-le-Grand, where he studied 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 excellence. After a year of preparation with mathematician Eugène Charles Catalan, he was admitted in 1842. However, because of his deformed foot, the school refused to let him continue after one year. Despite efforts to regain admission under strict conditions, Hermite 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 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. From 1862 to 1873 he lectured at the École Normale Supérieure, and in 1869 succeeded Jean-Marie Duhamel as professor of mathematics at both the École Polytechnique and the University of Paris, where he remained until his death. He was made a grand officer of the French Legion of Honour on his 70th birthday. Hermite 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. He was the sixth of seven children; his father worked in the drapery business and as an artist. Hermite attended Collège de Nancy, then Collège Henri IV and Lycée Louis-le-Grand in Paris, where he read works by Lagrange and Gauss. He was admitted to the École Polytechnique in 1842, but the school barred him from continuing after one year due to his deformed foot. He refused the administration’s strict conditions for readmission and left without graduating. After five years of private study, during which he befriended mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, he earned his baccalauréat in 1847. He married Bertrand’s sister, Louise, in 1848. That year he returned to École Polytechnique as répétiteur and examinateur d'admission, and was elected to the French Academy of Sciences. He contracted smallpox in 1856, and through the influence of Augustin-Louis Cauchy and a nun who nursed him, he resumed practicing his Catholic faith. From 1862 to 1873 he lectured at the École Normale Supérieure, and in 1869 succeeded Jean-Marie Duhamel as professor of mathematics at both the École Polytechnique (until 1876) and the University of Paris, where he remained until his death. On his 70th birthday he was promoted to grand officer in the French Legion of Honour. He was elected an honorary member of the Manchester Literary and Philosophical Society in 1892. In his final days he suffered from asthma, weak appetite, and poor sleep, and died in Paris on 14 January 1901.
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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