Mathematician:Joseph Liouville

Mathematician

Active in the fields of number theory, complex analysis, differential geometry, topology, mathematical physics and astronomy.

Proved the existence of transcendental numbers.

Contributed the Sturm-Liouville theory to the field of mathematical physics, in collaboration with Charles Sturm.

Pioneered the study of fractional calculus.

There are several theorems named after him, all in different areas of mathematics and physics.

Nationality

French

History

• Born: 24 March 1809, Saint-Omer, France
• Died: 8 September 1882, Paris, France

Theorems and Definitions

• Liouville Function
• Liouville Number
• Liouville's Constant
• Liouville-Neumann Series (with Carl Gottfried Neumann)
• Liouville-Roth Constant (with Klaus Friedrich Roth)
• Liouville-Green Method of Approximations (with George Green), also known as the LG Method, or the WKB Method (after Gregor Wentzel, Hendrik Anthony Kramers and Léon Nicolas Brillouin)
• Sturm-Liouville Theory (with Jacques Charles François Sturm)

• Liouville's Lemma, concerning diophantine approximations
• Liouville's Theorem:
  • Liouville's Theorem (Complex Analysis)
  • Liouville's Theorem (Conformal Mappings)
  • Liouville's Theorem (Differential Algebra)
  • Liouville's Theorem (Differential Equations)
  • Liouville's Theorem (Hamiltonian Mechanics)
  • Liouville's Theorem (Number Theory): a Liouville number is transcendental

Results named for Joseph Liouville can be found here.

Definitions of concepts named for Joseph Liouville can be found here.

Publications

• 1836: Founded the mathematics journal Journal de Mathématiques Pures et Appliquées (also known as Journal de Liouville)
• 1846: Published the works of Évariste Galois.

Sources

• John J. O'Connor and Edmund F. Robertson: "Joseph Liouville": MacTutor History of Mathematics archive

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.29$: Liouville ($\text {1809}$ – $\text {1882}$)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Liouville, Joseph (1809-82)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Liouville, Joseph (1809-82)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Liouville, Joseph (1809-82)