Leon graduated from London in 1940 and began work on an M.Sc. However the war meant that students from King's College were sent to Bristol University and it was there that he completed his Master's degree. In 1942 he was appointed to Sheffield University and, except for short spell at Manchester and Bristol (working with Heilbronn), he was to spend the rest of his career at Sheffield (where he was to work unsupervised for a Ph.D. which was awarded in 1949).
Mirsky had three main areas of research.
- The theory of numbers, where he studied r-free numbers, i.e. numbers not divisible by the r th power of any integer. He obtained analogues of Vinogradov's result on the representation of an odd integer as the sum of three primes, the Goldbach conjecture on the representation of an even integer as the sum of two primes, and the twin primes conjecture.
- Linear algebra, where he wrote his famous text An introduction to linear algebra (1955) and went on to publish 35 papers on the topic. In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements.
- Combinatorics, where he also wrote an important book Transversal Theory and he developed ideas coming from Hall's theorem:-
A finite family of sets has a system of distinct representatives if and only if the union of every k sets of the family contains at least k elements .
... bears witness to Mirsky's gift for exposition; his hallmark was elegance combined with clarity.Mirsky's talent for teaching was clearly related to his gifts as a writer and is described in  as follows:-
Leon was a born teacher. He welcomed the challenge of presenting a whole theory or just one proof in a logical, efficient, clear and elegant manner. ... His lectures ... were highly individual performances. There was never any hint of familiarity with his audience and Leon always wore a gown to emphasize the formality of the occasion. On the other hand, the alert student could spot a succession of jokes all made with an entirely straight face and no change of tone.He believed that mathematics research should not be a solitary occupation, but firmly believed in collaborating with others :-
He was particularly eager to share ideas at research level and firmly believed that research should always be a cooperative rather than competitive venture.Outside mathematics Mirsky had a wide variety of interests :-
His knowledge of literature, history and philosophy was wide and, in some areas, almost professional. Many of his former colleagues will miss the stimulus of conversations with him on these and a host of other subjects.
Article by: J J O'Connor and E F Robertson
Click on this link to see a list of the Glossary entries for this page