**Philip Stein**was the son of Solomon Zebulin Stein (c. 1854-1909) and Soroh Leah Malnik (c. 1853-1930). The family were Jewish. Solomon and Soroh were married on 21 November 1974 in Vorna, Lithuania. Philip was the brother of Minnie Stein (born 1882 and went on to marry Harry Shore), Bessie Stein (born 1883 and went on to marry Isaac Schock), Rachel Stein (who went on to marry Benjamin Abraham Davis), and Dinah Stein (born 1890 and went on to marry Max Grodzinski). We have given 25 January 1890 as Philip Stein's birth day, since this is the date he used for his date of birth. However, he did not know the actual date. He wrote about this fact when he wrote about his youth [3]:-

In 1897 the Stein family emigrated to Cape Colony in South Africa. Although Cape Colony had been British, it had become independent in 1872 (it is now part of South Africa). Stein attended the Normal College Boy's High School in Cape Town and was awarded a minor bursary of £10 tenable for one year in the School Higher Examination of 1905. After graduating in 1906, he studied at the South African College in Cape Town. At this stage the South African College, although teaching at university level, did not have university status and so could not award degrees. Stein sat the matriculation examination for the South African College in 1906 and was awarded a minor exhibition of £20 tenable for one year. In 1909, while at the South African College, Stein won the Ebden Scholarship. This scholarship, to the value of £200 per annum, allowed him to study abroad for three years. He entered Caius College, Cambridge and spent the three years financed by the scholarship studying the Mathematical Tripos. Returning to South Africa, Stein had a number of different posts before being appointed to the University Technical College of Natal in Pietermaritzburg.I was born in Lithuania on the estate of a Polish noble. The place was called Germeneitz, and it was near the village of Švėkšna, which also belonged to this noble. My official birthday is the twenty-fifth of January1890. ... I do not know my actual birthday to within six months. My mother was ill at the time of my Bar Mitzvah, so there was no celebration to fix the day into my memory. This day is anyway within six months of my actual birthday. ... I still remember Germeneitz in Shvekshna. We lived in Germeneitz until I was about seven. My mother leased the cattle(milk)from the Noble's bailiff. The cattle were tended and herded by the Noble's peasants. We had milk and sold it in Švėkšna. Some years ago she bought the crop of the Noble's orchard. Švėkšna was very near the Prussian border and my mother used to take the fruit into Prussia and retail it in the market at Memel or Konigsburg. ... In Germeneitz we lived at one end of a terrace of cottages. The others were occupied by the Noble's peasants. These peasants must have had young children, for before going to Švėkšna to Cheder, I didn't stir far from the house. In the winter anyway I was rarely allowed out of the home at all. I can nevertheless still picture the place in my mind. It was in a hollow. The orchard was on one side of a cove, and there was also a hill on the other side covered by moss. I would wander into the orchard and pick berries or apples, depending on whether or not the fruit in that year was ours. I would climb up on the hill and then roll down. ... Shvekshna was practically a Jewish village. There were some Germans who lived on the outskirts. I suppose these were small traders of craftsmen. But essentially it was a purely Jewish village. There was a village square. On one side was a church, a fine brick building. But whether it was Greek Orthodox or Roman Catholic I do not know. I think the latter, as the Lithuanians are Roman Catholic. On the other side there were shops and inns whose customers were mainly Lithuanian peasants. These peasants brought their wares to the market and then, I am sorry to say, usually went on to the inns and spent the proceeds on cheap vodka. It was the restriction on the sale of drink that led to their emigration. From the square there was a lane leading off to a smaller square in which the places of worship for the Jews were situated.

W Natal Roseveare was appointed as the first professor of mathematics at the newly founded University Technical College of Natal in Pietermaritzburg in August 1910. From its foundation the College [2]:-

Roseveare wrote a number of papers including:... enjoyed some measure of independence in that ... its own teaching staff now participated in constructing the syllabi and examined their own students, with the advice of external examiners, instead of assisting them in 'spotting' questions that were set and marked by remote strangers. In addition, within a few years it was authorised to conduct graduation ceremonies in Pietermaritzburg ...

*A chapter on algebra*(1903),

*On convergence of series*(1905),

*On 'Circular Measure' and the product forms of the sine and cosine*(1905),

*Expansions of trigonometrical functions*(1905), and

*Expansions of functions in general*(1905). Stein joined the staff at the Technical College when he was appointed as a lecturer in 1920. Earlier that year he had married Lily Rollnick, a daughter of Wolf Vulf Rollnick and Chaya Johanna Hurwitz, on 15 February 1920 in South Africa. They had three children: Sylvester Roman Stein (born 25 December 1920 in Cape Town, he became a writer, journalist, actor and anti-apartheid campaigner), Zena Stein (born 7 July 1922 in Durban, she became a epidemiologist and anti-apartheid campaigner married to Mervyn Susser), and Wilfred Donald Stein (born in Durban on 26 November 1931, he studied in South Africa, England and the USA and became Professor of Biophysics at the Hebrew University of Jerusalem).

Up to this point Stein was not a research mathematician and he had never studied for a doctorate. Roseveare encouraged Stein to undertake research and, in 1926, he took leave of absence from the Technical College and went, with his family, to the University of Cambridge in England. At Cambridge, J E Littlewood was his thesis advisor and he undertook research on the theory of functions. He was awarded his doctorate in 1931 for two dissertations: 1. *On Equalities For Certain Integrals In The Theory Of Picard Functions*; and 2. *On The Asymptotic Distribution Of The Values Of An Integral Function*. While undertaking research at Cambridge he produced to results which appeared in his paper *On a theorem of M Riesz* (1933). It is this paper [1]:-

Ralph Fowler, who made important advances in astronomy, had worked on statistical mechanics in the 1920s. He had come across a problem concerning trigonometric functions which had applications to statistical mechanics and he had posed the problem to J E Littlewood. While Stein was at Cambridge, J E Littlewood had told him about the problem and Stein solved it in a highly satisfactory way. His solution appears in the paper... by which he is best known to workers in the theory of functions of real and complex variables. This gives a proof of the fundamental result of Marcel Riesz on which the theory of conjugate functions inL_{p}spaces depends. The proof involves an ingenious use of Green's formula and is still the most elegant proof of the theorem: for this reason it is frequently quoted in the literature and has served as a model for arguments, in particular those of Donald Spencer, generalizing the Riesz inequality.

*On the real zeros of a certain trigonometric function*(1935).

Continuing to work at the University Technical College of Natal, Stein began to collaborate with his colleague R L Rosenberg in the late 1940s. Rosenberg was interested in problems in numerical analysis and their collaboration led to their joint paper *On the solution of linear simultaneous equations by iteration* (1948). The authors acknowledge that they "are indebted to Dr Olga Taussky for advice on some points." In fact Olga Taussky-Todd [1]:-

Lionel Cooper, the author of [1], attended the South African College School in Cape Town from 1924 to 1931. In his final year at school, Cooper took the examinations for university entrance conducted by Philip Stein of the University of Natal. Stein said that Cooper's mathematics paper was the best he had ever seen. Lionel Cooper writes about Stein [1]:-... writes that this paper is now a classic. As a result of this Stein visited the National Bureau of Standards and there wrote three papers 'The convergence of Seidel iterants of nearly symmetric matrices'(1951), 'A note on bounds of multiple characteristic roots of a matrix'(1952)and 'Some general theorems on iterants'(1952). ... In the1960's Professor Olga Taussky-Todd suggested further problems to Stein; these are not yet completely solved, but he gave a partial solution of one in 'On the ranges of two functions of positive definite matrices'(1965)and wrote another much quoted paper with Allen Pfeffer, 'On the ranges of two functions of positive definite matrices'(1967), a former student of John Todd. This is concerned with the problem of Lyapunov stability of matrices.

His active mathematical life continued for many years after his retirement: he taught for some years in the University of Makerere and also for a period in University College, Cardiff. Stein was an excellent and conscientious teacher and a force stimulating mathematics at all levels in South Africa for the many years of his active life. His quiet humour, his liberal outlook and his general reasonableness will be remembered by his many friends.

**Article by:** *J J O'Connor* and *E F Robertson*