Richard Rado FRS (28 April 1906 – 23 December 1989) was a German-born British mathematician whose research concerned

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. He was Jewish and left Germany to escape Nazi persecution. He earned two PhDs: in 1933 from the

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

, and in 1935 from the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to study at

Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...

. After he was awarded the scholarship, Rado and his wife left for the UK in 1933. He was appointed Professor of Mathematics at the

University of Reading The University of Reading is a public research university in Reading, Berkshire, England. It was founded in 1892 as the University Extension College, Reading, an extension college of Christchurch College, Oxford, and became University College, ...

in 1954 and remained there until he retired in 1971.

Contributions

Rado made contributions in

and

including 18 papers with

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

. In graph theory, the

Rado graph In the mathematics, mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a Countable set, countably infinite graph that can be constructed (with probability one) by choosing independently at random for eac ...

, a countably infinite graph containing all countably infinite graphs as induced subgraphs, is named after Rado. He rediscovered it in 1964 after previous works on the same graph by

Wilhelm Ackermann Wilhelm Friedrich Ackermann (; ; 29 March 1896 – 24 December 1962) was a German mathematician and logician best known for his work in mathematical logic and the Ackermann function, an important example in the theory of computation. Biograph ...

, Erdős, and

Alfréd Rényi Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest to A ...

. In

combinatorial set theory In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom ...

, the

Erdős–Rado theorem In partition calculus, part of combinatorial set theory, a branch of mathematics, the Erdős–Rado theorem is a basic result extending Ramsey's theorem to uncountable sets. It is named after Paul Erdős and Richard Rado. It is sometimes also a ...

extends

Ramsey's theorem In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (sa ...

to infinite sets. It was published by Erdős and Rado in 1956. Rado's theorem is another Ramsey-theoretic result concerning systems of linear equations, proved by Rado in his thesis. The Milner–Rado paradox, also in set theory, states the existence of a partition of an ordinal into subsets of small order-type; it was published by Rado and E. C. Milner in 1965. The

Erdős–Ko–Rado theorem In mathematics, the Erdős–Ko–Rado theorem limits the number of Set (mathematics), sets in a family of sets for which every two sets have at least one element in common. Paul Erdős, Chao Ko, and Richard Rado proved the theorem in 1938, but d ...

can be described either in terms of set systems or

hypergraph In mathematics, a hypergraph is a generalization of a Graph (discrete mathematics), graph in which an graph theory, edge can join any number of vertex (graph theory), vertices. In contrast, in an ordinary graph, an edge connects exactly two vert ...

s. It gives an upper bound on the number of sets in a family of finite sets, all the same size, that all intersect each other. Rado published it with Erdős and Chao Ko in 1961, but according to Erdős it was originally formulated in 1938. In

matroid In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms ...

theory, Rado proved a fundamental result of transversal theory by generalizing the Marriage Theorem for matchings between sets ''S'' and ''X'' to the case where ''X'' has a matroid structure and matchings must match to an independent set in the matroid on ''X''. The Klarner–Rado Sequence is named after Rado and David A. Klarner.Klarner-Rado Sequence
Michigan State University, MSU Librarie

Awards and honours

In 1972, Rado was awarded the

Senior Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Stat ...

Contributions

Awards and honours

References

Further reading