Hans Adolph Rademacher was a German

Germany

Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, known for work in mathematical analysis

Mathematical analysis

Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

 and number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

.

Biography

Rademacher received his Ph.D. in 1916 from Georg-August-Universität Göttingen; Constantin Carathéodory

Constantin Carathéodory

Constantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...

 supervised his dissertation. He was dismissed from his position at the University of Breslau by the Nazis in 1933 due to his public support of the Weimar Republic

Weimar Republic

The Weimar Republic is the name given by historians to the parliamentary republic established in 1919 in Germany to replace the imperial form of government...

, and emigrated from Europe in 1934.

After leaving Germany, he moved to Philadelphia and worked at the University of Pennsylvania

University of Pennsylvania

The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...

 until his retirement in 1962; he held the Thomas A. Scott Professorship of Mathematics

Thomas A. Scott Professorship of Mathematics

The Thomas A. Scott Professorship of Mathematics is an academic grant made to the University of Pennsylvania. It was established in 1881 by the railroad executive and financier: Thomas Alexander Scott.-Recipients:*Ezra Otis Kendall, 1881 – 1899...

 at Pennsylvania from 1956 to 1962. Rademacher had a number of well known students, including George Andrews, Paul T. Bateman

Paul T. Bateman

Paul Trevier Bateman is an American number theorist, known for formulating the Bateman–Horn conjecture on the density of prime number values generated by systems of polynomials and the New Mersenne conjecture relating the occurrences of Mersenne primes and Wagstaff primes.Bateman received his Ph.D....

, and Theodor Estermann

Theodor Estermann

Theodor Estermann was a mathematician, working in the field of analytic number theory.He was born in Neubrandenburg, Germany. His doctorate, completed in 1925, was supervised by Hans Rademacher. Heini Halberstam, Klaus Roth and Robert Charles Vaughan were Ph.D. students of his.-External links:*...

.

Research

Rademacher performed research in analytic number theory

Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...

, mathematical genetics

Genetics

Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....

, the theory of functions of a real variable

Real analysis

Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...

, and quantum theory

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Most notably, he developed the theory of Dedekind sum

Dedekind sum

In mathematics, Dedekind sums, named after Richard Dedekind, are certain sums of products of a sawtooth function, and are given by a function D of three integer variables. Dedekind introduced them to express the functional equation of the Dedekind eta function. They have subsequently been much...

s.

Awards and honors

With his retirement from the University of Pennsylvania, a group of mathematicians provided the seed funding for The Hans A. Rademacher Instructorships, and honored him with an honorary degree as Doctor of Science.

See also

• Rademacher complexity
  Rademacher complexity
  In statistics and machine learning, Rademacher complexity, named after Hans Rademacher, measures richness of a class of real-valued functions with respect to a probability distribution....
  
  
• Rademacher function
• Rademacher sum
• Rademacher–Kolmogorov theorem
• Rademacher–Menchov theorem
• Rademacher's series
• Rademacher distribution
• Rademacher's theorem
  Rademacher's theorem
  In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the following: If U is an open subset of Rn andis Lipschitz continuous, then f is Fréchet-differentiable almost everywhere in U In mathematical analysis, Rademacher's theorem, named after Hans Rademacher, states the...
  
  

External links