Mathematician:Johann Peter Gustav Lejeune Dirichlet

Mathematician

German mathematician who worked mainly in the field of analysis.

Credited with the first formal definition of a function.

Demonstrated that Fermat's Last Theorem holds for $n = 5$.

Married Rebecka Mendelssohn, the youngest sister of Fanny Mendelssohn and Felix Mendelssohn.

Nationality

German, although born in what was then part of the French empire.

History

• Born: 13 Feb 1805, Düren, French Empire (now Germany)
• 1855: Succeeded Gauss in professorship at Göttingen.
• Died: 5 May 1859, Göttingen, Hanover (now Germany)

Theorems and Definitions

Definitions

• Dirichlet Beta Function

• Dirichlet Character in Number Theory, specifically:
  • Dirichlet Series (Analytic Number Theory)
  • Dirichlet L-function

• Dirichlet Conditions (for Fourier Series)
• Dirichlet Convolution (Number Theory and Arithmetic Functions)
• Dirichlet Density (Number Theory)

• Dirichlet Distribution (Probability Theory)
  • Generalized Dirichlet Distribution
  • Dirichlet Process

• Dirichlet Eigenvalue
• Dirichlet Eta Function (Number Theory)
• Dirichlet Form

• Dirichlet Function
  • Modified Dirichlet Function (also known as the Thomae Function or small Riemann function)

• Dirichlet Kernel (Functional Analysis, Fourier Series)

• Dirichlet Tessellation (also known as a Voronoi Diagram) and hence:
  • Dirichlet Cell
  • Dirichlet Polygon

• Latent Dirichlet Allocation (Statistics)

Definitions of concepts named for Johann Peter Gustav Lejeune Dirichlet can be found here.

Theorems

• Theorems named Dirichlet's Theorem:
  • Dirichlet's Approximation Theorem (Diophantine Equations)
  • Dirichlet's Theorem on Arithmetic Sequences (Number Theory, specifically prime numbers)
  • Dirichlet's Unit Theorem (Algebraic Number Theory and Ring Theory)
  • Dirichlet's Theorem for 1-Dimensional Fourier Series, also known as Fourier's Theorem, for Joseph Fourier

• Dirichlet Boundary Condition (Differential Equations)
• Dirichlet Divisor Problem (currently unsolved) (Number Theory)

• Dirichlet Integral (Integral Calculus)

• Dirichlet's Principle:
  • Dirichlet's Box (or Drawer) Principle (also known as the Pigeonhole Principle or Letterbox Principle) (Combinatorics)
  • Dirichlet's Principle for Harmonic Functions (Mathematical Physics)

• Dirichlet Problem (Partial Differential Equations)
• Dirichlet Stability Criterion (Dynamical Systems Theory)
• Dirichlet's Test for Uniform Convergence (Analysis)

• Class Number Formula (Analysis)

Results named for Johann Peter Gustav Lejeune Dirichlet can be found here.

Publications

• 1863: Vorlesungen über Zahlentheorie

Critical View

The story was told that young Dirichlet had as a constant companion on all his travels, like a devout man with his prayer book, an old, worn copy of the Disquisitiones Arithmeticae of Gauss.

-- Heinrich Franz Friedrich Tietze

Dirichlet was not satisfied to study Gauss's Disquisitiones once or several times, but continued throughout his life to keep in close touch with the wealth of deep mathematical thoughts which it contains by perusing it again and again. For this reason the book was never put on the shelf but had an abiding place on the table at which he worked. Dirichlet was the first one who not only fully understood this work, but also made it accessible to others.

-- Ernst Eduard Kummer

Also known as

Usually referred to as Peter Dirichlet.

The Johann is often ignored or forgotten even when specifying his name more fully: Peter Gustav Lejeune Dirichlet.

Sources

• John J. O'Connor and Edmund F. Robertson: "Johann Peter Gustav Lejeune Dirichlet": MacTutor History of Mathematics archive

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Dirichlet, Peter Gustav Lejeune (1805-59)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.28$: Dirichlet ($\text {1805}$ – $\text {1859}$)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Dirichlet, Peter Gustav Lejeune (1805-59)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Dirichlet, Peter Gustav Lejeune (1805-59)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Dirichlet, Peter Gustav Lejeune (1805-59)