The proof that the number e is transcendental stands as a definitive achievement in the mathematical career of Charles Hermite. Born in Dieuze in 1822, he overcame significant physical challenges to become a central figure in 19th-century analysis, number theory, and algebra, leaving behind a profound legacy of theorems and special functions that remain foundational to modern science.
Academic Formation and Challenges
Hermite entered the Lycée Louis-le-Grand in 1840 after prior study at the Lycée Henri-IV. His ambition to attend the École polytechnique was initially realized in 1841, though his tenure lasted only until 1842. A physical deformity in his foot caused the administration to restrict his continued attendance, prompting him to depart without graduating. He pursued private study for several years, ultimately earning his Bachelor of Science in 1847.
Twenty questions, eight minutes on the clock, and a percentile measured against everyone who has taken it. No sign-up.
Take the IQ test →Institutional Contributions
His professional career was deeply embedded in the French academic establishment. He returned to the École polytechnique as an instructor in 1848, maintaining a position there until 1876. He also held a lectureship at the École Normale Supérieure from 1862 until 1869. That same year, he began his tenure at the University of Paris, where he remained until 1897. In 1890, he served as president of the French Academy of Sciences.
Advances in Algebra and Analysis
Hermite made significant strides in the field of elliptic functions and invariants. In 1854, he introduced the concept of an orthogonal matrix. By 1855, he proved that eigenvalues of Hermitian matrices are always real, expanding upon earlier work by Cauchy. His research also encompassed Hermite polynomials and the cubic Hermite spline. His collaborative efforts with peers like Arthur Cayley and James Joseph Sylvester helped shape the theory of invariants.
Transcendence and Final Years
The year 1873 proved pivotal, as Hermite published his proof regarding the transcendence of e and the irrationality of pi. These findings utilized rigorous methods that influenced later researchers like Ferdinand von Lindemann. In his later years, he focused on calculus and the theory of linear differential equations, including solutions to Lamé's equation. He died in Paris in 1901 and is buried at Montparnasse Cemetery.
Fast facts
- Born: 1822, Dieuze, France
- Died: 1901, Paris, France
- Academic degree: Bachelor of Science
- President of the French Academy of Sciences: 1890
- Notable work: Hermite polynomial
- Burial site: Montparnasse Cemetery
- Award: Grand Officer of the Legion of Honour
Questions readers ask
What is the Hermite–Lindemann Theorem?
It is a mathematical result concerning the transcendence of numbers, specifically derived from Hermite's work on the transcendence of e.
Did Hermite graduate from the École polytechnique?
No, he left the institution in 1842 without graduating due to conflicts regarding his physical deformity.
Achievements
- Commanders Grand Cross of the Order of the Polar Star
- Notable work: Hermite polynomial
- Notable work: Hermite–Lindemann Theorem
- Notable work: Hermite distribution
- Notable work: Hermite interpolation
- Held posts at École Normale Supérieure, University of Paris and École polytechnique
- Fields: algebra, number theory and mathematics
.jpg)