Hyman Levy's father was Marcus Levy (born in Russia about 1862) who was a picture frame maker and dealer in paintings in Edinburgh. His mother was Minna Levy (born in Germany about 1864) who was a draper. Hyman had two older siblings: Joseph (born about 1885), Fanny (born about 1887), and several younger siblings: Sophia (born about 1892), Millie (born about 1894), Morris (born about 1895), and David (born about 1897).
Hyman Levy was the third of eight children in the orthodox Jewish family. The actual date of his birth seems a little hard to determine, given as 7 March in Who's Who and one has to assume that Levy himself supplied this information. Yet Barnard in  claims that although 7 March appears on his birth certificate this is incorrect and his actual date of birth was 28 February.
Levy attended George Heriot's School in Edinburgh, then entered the University of Edinburgh to study mathematics and physics. He graduated from Edinburgh in 1911 with an M.A. with First Class honours and then won a Ferguson Scholarship, a 1851 Exhibition and a Carnegie Research Fellowship which enabled him to undertake research at the University of Göttingen.
In 1914 when World War I broke out, Levy was in Göttingen working with Hilbert and Runge. Escaping from Germany, he returned to England where he worked at the University of Oxford with A E H Love until 1916. In 1916 Levy was honoured by being elected a fellow of the Royal Society of Edinburgh. Then, between 1916 and 1920, he worked as a member of the aeronautics research staff of the National Physical Laboratory.
Levy left the National Physical Laboratory in 1920 and became an assistant professor of mathematics at the Royal College of Science of the Imperial College of Science and Technology, London. He was promoted to Professor of Mathematics three years later, then, in 1946, he became Head of the Mathematics and Mechanics Department. Under his leadership the Department expanded greatly and he also provided leadership to the whole of the Royal College of Science, being its Dean from 1946 to 1952. His contributions to Imperial College are noted in :-
His presence in the council chamber will be remembered by many colleagues for his remarkable gift of quick appreciation and sensible comment; and his regular attendance at student gatherings, either as a lecturer or after dinner speaker, an art at which he excelled, will be long remembered with affection by generations of students.
In 1954 Levy retired and became Professor Emeritus but he agreed to continue to act as head of the mathematics department at Imperial College for one further year until 1955.
Levy's main work was in numerical methods, numerical solution of differential equations, finite difference equations and statistics. As Barnard writes in :-
He published books on these topics long before their importance, later taken for granted, was recognised in Britain.
Among Levy's most important mathematical books was Aeronautics in Theory and Experiment (1918) which was :-
... perhaps the earliest text covering, at advanced level, the whole theory of aeroplane design and operation...
Among other mathematical works he published were Numerical Studies in Differential Equations (1934), Elements of the Theory of Probability (1936), and Finite Difference Equations (1958). However, Levy was more than a mathematician. He was a philosopher of science and also a political activist who :-
... strongly influenced by poverty and degradation he saw around him in childhood, ... devoted his life to the idea that science should be used to provide the basis of a full life for all humanity.
He expounded his materialistic philosophy in a number of books, the first being The Universe of Science (1932). He was a political activist in the Labour Party in the 1920s. His advice was followed and the Labour Party set up a Science Advisory Committee which Levy chaired from 1924 to 1930. In 1931 he moved further to the political left, becoming a member of the British Communist Party. He visited Moscow in 1956 as a member of a British Communist Party Delegation with the remit of investigating :-
... reports that Jewish writers, artists and intellectuals had been tortured and killed and Jewish culture suppressed.
The persecution of Jewish intellectuals in Russia which he found in the investigation appalled Levy. Rather than resign from the British Communist Party, Levy attacked the leadership of his own Party demanding to know whether they had been aware of the treatment of the Jews in Russia. He wrote an exposure in the communist weekly World News in January 1957. Later that year he published a book Jews and the National Question. A review by a leading member of the British Communist Party stated (see ):-
With this book Levy finally parts company with Marxism.
Then in 1958 he was expelled from the Communist Party.
Levy had also suffered family problems because of his Jewish upbringing. In 1918 he married Marion Aitken, the daughter of the headmaster of a school in Selkirk. Marion was a devout Presbyterian and this caused a breakdown of relations between Levy and his own family. The marriage produced one daughter and two sons.
A strong supporter of the London Mathematical Society during his career in London, Levy served the Society on its Council from 1929 to 1933, being vice-president of the Society during 1931-32.
He is described in  as follows:-
With the soft Scottish accent that he retained throughout his life, Levy's warmth, human kindness, and ready wit won him many friends and much respect amongst those who strongly disagreed with his politics.
In  the author writes:-
Neither in his mathematics nor his political interests was Levy content merely to study and write; he strove to express his views wherever possible in speech and action.
Article by: J J O'Connor and E F Robertson