Ismail Jacobus Mohamed


Born: 27July 1930 in Barkley East, Eastern Cape, South Africa
Died: 6 July 2013 in Johannesburg, South Africa

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Ismail Mohamed's parents were Ismael Mohamed and Rose Johanna Fortuin but they were divorced before Ismail was five years old. Ismael Mohamed worked for a tyre company but became a shopkeeper with a small general store in Bloemfontein where he remained for the rest of his life. Let us first explain the name of the subject of this biography. His birth certificate reads "Ismail Mohamed" and he was known by this name at school, his mother called him "Ismail Jacobus" while his family and close friends called him "Josef."

We follow [2] and [4] closely in parts of the biography we give below (correcting errors we found in those texts) but we have added a fair amount of material.

Mohamed's early school years were spent in Barkley East where his mother worked as a cook for white families. When World War II broke out, she lost her job and, since there was high unemployment, they moved together to Aliwal North. When Mohamed was twelve years old his mother left for Johannesburg to look for employment there leaving Mohamed with his maternal grandmother, Katrina. After Rose had made a home in Doornfontein, Mohamed joined her.

His mother's family were devout members of the NG Sending Kerk [a Mission Church] and were regular attenders. Mohamed, however, was sent to St Joseph's Catholic School for his schooling and, impressed by the nuns' teaching, he was baptised into the Roman Catholic church. English was the language of instruction at St Joseph's School and Mohamed had problems with the language. This caused him to fail his examinations and his education was further hindered when he contacted a fever, the result of the harsh conditions he was living in, and was isolated in hospital for five months.

After recovering from the fever he attended the Eurafrican Training Centre, which was a five kilometre walk away from the family home in Radio Springs. He then went to a secondary school in Vrededorp, Johannesburg, graduating in 1949. His performance at this school was excellent and he topped his class, showing exceptional abilities at mathematics. This performance was all the more remarkable since he had to work scrubbing and polishing floors and gardening for white families to earn money for the school fees. One of the white families, realising that Mohamed was skilled at mathematics had him teach the subject to their children [1]:-

He grew up surrounded by racism and discrimination and his experiences and those of others around him moulded him into a fierce opponent of apartheid.
Taking a job as a painter and builder's mate in 1950, he earned sufficient to let him enrol at the University of the Witwatersrand in 1951. Again he showed his mathematical abilities, obtaining a B.Sc. in Mathematics and Physics in 1953, and a First Class Honours Degree in Mathematics in the following year. In 1955 he was appointed as a mathematics teacher at William Hills High School in Benoni, Transvaal, but he had more educational ambitions, enrolling as a part-time M.Sc. student at the University of the Witwatersrand at the same time having been awarded a Shell Postgraduate Bursary. In 1957 he was awarded a Shell Postgraduate Scholarship to study mathematics at Queen Mary College, University of London, England.

Mohamed sailed on the Arundel Castle from Durban, South Africa, arriving in Southampton, England, on 27 September 1957. For a while he worked as an assistant lecturer at the University of Wales, Cardiff. He planned to marry Ellen Kathleen Rygaardt (born 5 July 1938), one of his former students at William Hills High School, and she sailed from Durban to Southampton on the Carnarvon Castle, arriving on 12 September 1958. She gave her occupation as Laboratory Assistant, and she stated that she intended permanent residence in England giving her address as 86 Bethune Road, London N16. They were married early in 1959 and were living at 7 Brownswood Road, Stoke Newington, London in 1959, at 51 Gloucester Drive, Stoke Newington, in 1960, and in the Seven Sisters Road, Tottenham West in 1961. Ellen Mohamed found employment as a Laboratory Technician and simultaneously studied at the Paddington Technical College where she earned a diploma in Chemical Technology. In 1961 they had their first child, a daughter Elaine, in London. They had problems obtaining a visa for Elaine to travel to South Africa with them when they returned to South Africa and their other four children, Andrew, Jennifer, Ivor and Ingrid, were born in Africa.

In 1960, Mohamed was awarded his M.Sc. from Witwatersrand for his thesis On certain generalisations of equations in groups and the number of solutions while in 1960 he completed his Ph.D. in Mathematics in Group Theory at University of London. His thesis was entitled On Series of Subgroups Related to Groups of Automorphisms, and his thesis advisor had been Kurt Hirsch. In a paper he published in the Proceedings of the London Mathematical Society in 1963, he writes:-

These results are extracted from my thesis for the degree of Ph.D. in the University of London (1960). I take this opportunity to express my gratitude to Professor K A Hirsch for his help and encouragement in supervising this research. I thank the University of the Witwatersrand, Johannesburg, and the Shell Petroleum Company of South Africa for financial assistance received.
A second paper, On the Class of the Stability Group of a Subgroup Chain was published in 1964, also containing results from his thesis and having an identical acknowledgement as his first paper.

While studying in London, Mohamed joined the Labour Party and worked with British Trade Unions trying to strengthen the socialist aspect of the Labour Party. His thinking here was that a more socialist Britain would force change in South Africa.

After the award of his Ph.D. in 1960, Mohamed was appointed as an assistant lecturer at Queen Mary College, University of London. The Sharpeville Massacre occurred on 21 March 1960. Demonstrators against the pass laws gathered outside the Sharpeville police station leading to the police opening fire and killing 69 of the black protestors. The Mohameds watched the television pictures of the massacre in London and felt they had to return to support the antiapartheid movement. Offered an appointment at the University of the Witwatersrand, he declined the offer of a permanent position at the University of London and, in September 1961, they returned to South Africa. The 1963 and 1964 papers we mentioned above have the address University of the Witwatersrand.

Mohamed spent the years 1961-64 trying to carry out his job as a mathematician and in parallel he put great energy into working for human rights. He worked with the African People's Democratic Union of South Africa attempting to promote social change through non-collaboration and boycotts. The African People's Democratic Union of South Africa, however, failed to recruit sufficient support and collapsed. It was a frustrating time and he accepted a lectureship at Birkbeck College, University of London, at the end of 1964. The University of Zambia was founded in 1965 and Mohamed was offered a senior lectureship in mathematics. He accepted and the University opened to students and teaching began on 12 July 1966. Although not in South Africa he maintained contacts with those in South Africa working for the rights of those in the black townships. He taught South African students and through them learned of the on-going political situation in the country.

In 1968 Mohamed's joint paper with Hermann Heineken, A Group with Trivial Centre Satisfying the Normalizer Condition, was published. This paper was a very important one and had a major impact on the development of group theory. The authors proved the following theorem:-

For each prime p there is a metabelian p-group G with trivial centre, such that every proper subgroup of G is nilpotent and subnormal.
We will not explain here what these technical terms mean, and suggest that if the reader is unfamiliar with group theory they ignore the rest of this paragraph. This result solved at least four open problems. It showed (i) A group satisfying the normalizer condition need not be hypercentral, (ii) A group with all its proper subgroups nilpotent and subnormal need not be nilpotent, (iii) The direct product of two groups satisfying the normalizer condition need not satisfy the normalizer condition, and (iv)  If all subgroups of a group are subnormal, there need not be a bound on the defects of these subgroups. The first three questions had been posed by Aleksandr Kurosh while the fourth had been posed by Jim Roseblade. In the paper the authors give the following acknowledgement:-
We would like to thank Professor P Hall and Dr J E Roseblade for many comments on the subject which were a great help in the construction of this group.
In 1968 Mohamed moved to a senior Lectureship in the Department of Mathematics of the University of Botswana, Lesotho and Swaziland which was in Maseru, Lesotho, Southern Africa. He was rapidly promoted to Reader and then to Professor. He published two further papers with Hermann Heineken. In 1972 they published Groups with Normalizer Condition in which they constructed further examples of groups similar, but different, to those of their 1968 paper. Their other joint paper was Non-nilpotent groups with normalizer condition (1973). Mohamed had published a single author paper Non-nilpotent groups with normalizer condition in 1973 which was the text of a talk he had given on his work with Heineken.

Although his career had progressed extremely well at the University of Botswana, Lesotho and Swaziland, nevertheless, he longed to return to South Africa and make a positive contribution in supporting human rights there. He applied for a position at the University of the Witwatersrand, the university from which he had received his first degrees. There was no doubt as to his exceptional mathematical abilities and his record. He received, however, the following response from the deputy Vice-Chancellor of the University [4]:-

One can see that to appoint you in a permanent position of authority over white students and junior white staff would be to wound the very heart of Baaskap [white supremacy] and that there are limits to which we can go to offend a government.
In 1975 Mohamed accepted a position as Professor and Head of the Department of Mathematics at the University of the Western Cape. He joined with colleagues arguing against Apartheid education. In June 1976 there were uprisings in Soweto and Mohamed urged the black staff of the university to join the students in protest. In July of 1976 he delivered an address at a South African Students Organisation arguing against Apartheid education. He was detained and held in Victor Verster Prison in Paarl for around 15 weeks without being charged. Mohamed was released in December 1976 and, because of his detention, his university appointment was terminated. After a period during which Mohamed and his family suffered considerable hardship, he was offered a position as Associate Professor of Mathematics at the University of the Witwatersrand which he accepted.

With this new position Mohamed lived in Newclare, Johannesburg, and began working to support his local community. In July 1980, his son Andrew who had just turned 17, fled the country with a group of friends, escaping into exile, but some of his friends were arrested and the Mohameds became involved in the long trial that ensued. The Security Police told the Mohameds that their son had been killed attempting to cross the border. In fact he had not been killed but they only discovered this after two years. The Mohameds' eldest daughter, Elaine, was detained in 1981 and charged with furthering the aims of the South African Communist Party in 1982. The family went through a tense period, during her seven month solitary confinement and trial. She was convicted to five years imprisonment, which was suspended.

In May 1980 South Africa made cosmetic changes to the government but these made little difference since black South Africans were still denied citizenship. In August 1983 the United Democratic Front was founded and Mohamed, who missed this event through ill health, was elected a Vice-President. He said [4]:-

We reject the government's attempts to co-opt sections of the oppressed into entrenching apartheid. We demand the right for all people to rule and share fairly in the wealth and resources of our country. We shall write our own constitution based on the Freedom Charter.
Let me [EFR] now introduce some personal memories. In 1983 my colleague Colin Campbell and myself announced a major conference, Groups St Andrews 1985, to be held in St Andrews in July-August 1985. Our plenary speakers were four leading group theorists; we mention in particular, Gilbert Baumslag, a South African working at the City University of New York, and Jim Roseblade who we mentioned above when discussing the Heineken-Mohamed groups. Mohamed wrote to us saying he wished to attend Groups St Andrews 1985 and we invited him to lecture to the conference. On 18 February 1985 Mohamed was arrested along with other leaders of the United Democratic Front so could not attend Groups St Andrews 1985. During the conference I was approached by some participants who wanted to write to the South African government arguing for Mohamed's release as a prisoner of conscience and wanted to invite other conference participants to sign their letter. I had a worry about this for I had no idea what Gilbert Baumslag's political views were and I had no wish to offend him. I spoke to him explaining about the letter and Gilbert fully supported it and wished to add his signature in support of Mohamed. The letter was sent off signed by around 300 of the world's leading group theorists. I doubt if it had any impact but the trial of United Democratic Front members collapsed (some of the State's evidence was suspect) and all were released by June 1986.

On 20 December 1986 Mohamed and his family hurriedly left South Africa after being warned that they were no longer safe at home. Mohamed was due sabbatical leave and he spent time in both London and in the United States until July 1987. His daughter Jennifer was advised not to return to South Africa and remained abroad. While in the United States he delivered the paper 'Rights and Concerns in Conflict in South Africa' at the National Academy of Sciences in Washington DC in 1987.

Pieter Willem Botha served as Prime Minister and then President of South Africa. Although he made some concessions to political reform, his administration continued the ban on the African National Congress and other such organisations. Botha suffered a stroke in early 1989 and pressure was put on him to resign as President which he did in February 1989. Frederik Willem de Klerk became President and in his first address to parliament he stated that all apartheid laws would be repealed and the ban on the African National Congress, the United Democratic Front, and other such organisations would be lifted. Eventually after discussions and continued violence by both sides, a fully democratic election was held on 27 April 1994. Mohamed was elected as an African National Congress Member of Parliament.

Mohamed served three terms as a member of parliament before retiring in 2009. His contributions were many, particularly in helping produce a Green Paper on Science and Technology, arguing for increased spending on Science and Technology, and chairing the Science and Technology committee.

For his remarkable achievements, Mohamed received several honours. In 1985 the University of Lesotho awarded him an honorary D.Sc., the citation recognising his struggle for social justice and his remarkable mathematical contributions. He was unable to receive the degree in person for he was on trial in South Africa. After his election to parliament, the University of the Witwatersrand awarded him an honorary degree [1]:-

In recognition of his contribution to mathematics, his tireless work on behalf of the underprivileged people of South Africa, and his lifetime campaign against apartheid, the University of the Witwatersrand, with a deep sense of pride, confers on one of its distinguished graduates, Ismail Jacobus Mohamed, the degree of Doctor of Laws honoris causa.
The report of his death in [3] ends by giving these details:-
Mohamed died on 6 July after an illness. He is survived by his wife, Ellen, five children and five grandchildren. He will be buried at the Heroes Acre at Croesus, Newclare, at 9.30 a.m. after a church service at St Anthony's Catholic Church in Coronationville.
The South African Government website reported [5]:-
President Jacob Zuma will on Saturday, 13 July 2013, attend the funeral service of the late former Member of Parliament and Wits University Mathematics Professor Ismail Mohamed in Johannesburg.

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


List of References (5 books/articles)

Mathematicians born in the same country

Additional Material in MacTutor

  1. Entry in the list of African men PhDs

Other Web sites
  1. Mathematical Genealogy Project
  2. MathSciNet Author profile
  3. zbMATH entry

Main Index Biographies index

JOC/EFR May 2019
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School of Mathematics and Statistics
University of St Andrews, Scotland

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