Albert Turner Bharucha-Reid

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13 November 1927
Hampton, Virginia, USA
26 February 1985
Atlanta, Georgia, USA

Albert Bharucha-Reid was an American mathematician who worked on probability theory, Markov chains, and statistics.


Albert Bharucha-Reid was given the name Albert Turner Reid and only changed Reid to Bharucha-Reid after his marriage. We shall, however, for simplicity use the name Bharucha-Reid throughout this biography. He was the son of William Thaddeus Reid and Mae Elaine Beamon. William Reid, born on 19 January 1887 in Abdingdon, Virginia, was an electrician working at the Hampton Institute who married Mae Elaine Beamon in Hampton, Virginia, on 26 October 1921. Mae Beamon had been born on 7 August 1894 in Hampton, Virginia. They lived in Elizabeth City, Virginia. William and Mae Reid had three children: William Micajah Reid (born 27 September 1924 in Elizabeth City, Virginia); Cora M Reid (born about 1925/26); and Albert Turner Reid, the subject of this biography. Albert was given the name Turner because he was related to Charles Henry Turner (1867-1923), the first African American to receive a Ph.D. in zoology from the University of Chicago, who published over 70 papers and made important advances in zoology, particularly in understanding insect behaviour.

In 1930, when Albert was two years old, the family were living at Chesapeake, Elizabeth City, Virginia. They were still at the same address ten years later, and at this time Albert was in 7th grade of Elementary School. Bharucha-Reid graduated from George P Phenix High School in Hampton, Virginia, a school for African Americans created by the Hampton Institute, in 1944 and then for a time attended Howard University in Washington D.C. followed by the Hampton Institute. In 1945 he registered for military service and completed a Draft Card. At that time he was living at home in Hampton, Elizabeth City, Virginia, with his father. Aged 18, he is described as a student, 136 lbs, light brown complexion, brown eyes, brown hair and 5 ft 10 ins in height.

After this, he studied mathematics and biology at Iowa State University, graduating with a B.S. in 1949. Up to this time he had been interested equally in mathematics and biology, probably influenced by his famous relative Charles Henry Turner, but when he continued his studies at the University of Chicago in 1950 his mathematical interests were definitely moving towards statistics and probability. While undertaking research on mathematical biology, probability and statistics at Chicago, Bharucha-Reid also worked at a Research Assistant in Mathematical Biology at the University. He published papers such as On the diffusion of metabolic intermediates (1951), A suggested chain process for radiation damage (1951), A Probability Model of Radiation Damage (1952), Note on Diffusion, Controlled Reactions (1952), Note on the growth of bacterial populations (1952), On Stochastic Processes in Biology (1953). In these papers, he is described as being a U. S. Public Health Service Research Fellow on the Committee on Mathematical Biology at the University of Chicago. The 1953 paper begins:-
The purposes of this article are: (i) to discuss the role of the theory of stochastic processes in the methodology of mathematical biology, (ii) to present a review of some work dealing with the application of stochastic processes in biology, and (iii) to encourage, perhaps, other workers to utilise the theory of stochastic processes in formulating mathematical models of various biological phenomena.
His paper An age-dependent stochastic model of population growth (1953) has the same affiliation as above.

He remained at Chicago until 1953 but chose not to complete his Ph.D. and instead moved to a position as a research associate in mathematical statistics at Columbia University in 1953. In December 1953 he attended the 113th Annual Meeting of the American Statistical Association in Washington, D.C. and presented the paper Stochastic Processes and the Study of Growth Phenomena. He gives the following Abstract:-
This paper is divided into three parts: (1) Introduction, (2) Construction of stochastic models, and (3) Statistical inference in stochastic models. In Part 1 we discuss the deterministic and stochastic approaches to the study of growth phenomena; and give an introduction to the theory of branching stochastic processes as developed by Bellman and Harris. We consider in Part 2 the construction of various stochastic models for growth using the above theory. Models for birth, birth-and-death, and mutation processes are discussed. The use of these formal models in the study of epidemics and rumour spread, as well as in the study of bacterial growth, is pointed out. In Part 3 we discuss problems of estimation and testing associated with stochastic growth processes. Previous work is reviewed, and some recent investigations on sequential decision problems for branching processes is discussed.
On 5 June 1954 Albert Reid married the Indian Rodabe Phiroze Bharucha (born 15 June 1930) in Cook County Illinois, and, shortly after that time, changed his name from Reid to Bharucha-Reid. We note that Rodabe also changed her name to Bharucha-Reid and she was awarded a doctorate by Wayne State University in 1972 for her thesis Organized behavior under stress. Albert and Rodabe Bharucha-Reid had two children, Kurush Feroze Bharucha-Reid and Rustam William Bharucha-Reid (born 1967). We note that Kurush Bharucha-Reid, born on 29 March 1955, became an intelligence and special operations expert in the United States Army, serving with great distinction. He died on 26 May 2010 at the age of 55.

Now let us give a comment on the name change to Bharucha-Reid. Albert Bharucha-Reid attended the Third Berkeley Symposium on Mathematical Statistics and Probability, December 1954 and July-August 1955 and presented the paper On the Stochastic Theory of Epidemics. His name on the paper in the published Proceedings is given as A T Bharucha-Reid and the affiliation Columbia University. He and his wife, and first child took a flight from New York to Bombay, India, on 12 June 1956, however, and gave their names as Albert Reid, Rodabe Reid and Kurush Reid. When they returned, flying from Bombay to Idlewild Airport, New York on 7 October 1956 they gave their names as Albert T Bharucha-Reid and Rodabe P Bharucha-Reid.

When Bharucha-Reid was undertaking the research for the paper On the Stochastic Theory of Epidemics mentioned above, he was supported by funds provided under Contract AF 18(600)-939 with the USAF School of Aviation Medicine, Randolph Field, Texas.

You can read the Introduction to that paper and the Abstracts of other early papers by Bharucha-Reid, at THIS LINK.

His paper Generating functions and the semigroup theory of branching Markov processes (1958) written jointly with Herman Rubin has the note:-
Work supported by the Office of Ordnance Research, U.S. Army, under Contract No. DA- 04-200-ORD-651.
This 1958 paper has the address, University of Oregon, but a note to say that his current address was Mathematical Institute, University of Wrocław, Wrocław, Poland. Bharucha-Reid had left Columbia University in 1955 and worked as an Assistant Research Statistician at the University of California, Berkeley for the year 1955-1956 before taking up the appointment of Instructor at the University of Oregon in 1956. He was a Fellow of the Polish Academy of Sciences, 1958-1959, which is the period when he was at the University of Wrocław in Poland.

In addition to his academic work and work for the U.S. Army, he worked on a United States Air Force project researching stochastic theory of epidemics. We note that on 27 August 1958 and again on 11 August 1959 he flew with the Military Air Transport Service from the United States Air Force base at Burtonwood, England to Newark, New Jersey, USA.

Promoted to Assistant Professor Mathematics at the University of Oregon, he remained there until 1961 when he was appointed as Associate Professor of Mathematics at Wayne State University. He remained at Wayne State University, Detroit, Michigan, until 1981 but spent time at various other institutions. He was Professor Applied Mathematics at the Institute for Mathematics Sciences, Madras, (now Chennai) India (1963-1964), Professor of Mathematics at the Research Center, University of Wisconsin, Madison (1966-1967), and at the Georgia Institute Technology (1973-1974). Other roles he had during these years included being a Member of the Graduate Record Examination Board, Princeton, New Jersey (1978-1982) and on the Board of Governors of Cranbrook Institute Science, Bloomfield Hills, Michigan (1977-1980).

Ronald Mickens gave a talk [14] in 2013 giving insights into Bharucha-Reid's life and family, professional career, and research areas. His Abstract is as follows:-
Albert Turner Bharucha-Reid had a distinguished career in both pure and applied mathematics. His many contributions to research, student training and mentoring, and academic and professional leadership were acknowledged by various honours and awards he received throughout his life. His first book, 'Elements of the Theory of Markov Processes and Their Applications', provided one of the first concise introductions to the area of probabilistic analysis and for many years was successful as a textbook and guide for self-study. He published more than seventy papers and authored seven books on topics in the stochastic theory of epidemics, Markov process, random integral and polynomial equations, and computational methods. His last book, with M Sambandham, 'Random Polynomials', was published posthumously in 1986. ... Of both great interest and significance is the fact that he never received the formal doctoral degree in mathematics.
Bharucha-Reid published two different types of books. There were his monographs such as Elements of the Theory of Markov Processes and Their Applications (1960), Random Integral Equations (1972) and (with Masilamani Sambandham) Random Polynomials (1986). He begins the Preface to the first of these as follows:-
My purpose in this book is twofold: first, to present a nonmeasure-theoretic introduction to Markov processes, and second, to give a formal treatment of mathematical models based on this theory which have been employed in various fields. Since the main emphasis is on applications, this book is intended as a text and reference in applied probability theory.
You can read a longer extract from the Preface and extracts from several reviews of the book at THIS LINK.

He begins the Preface to Random Integral Equations as follows:-
At the present time the theory of random equations is a very active area of mathematical research; and applications of the theory are of fundamental importance in the formulation and analysis of various classes of operator equations which arise in the physical, biological, social, engineering, and technological sciences. Of the several classes of random equations which have been studied, random integral equations (and random differential equations formulated as integral equations) have been studied rather extensively. This book is intended as an introductory survey of research on random integral equations and their applications.
You can read a longer extract from the Preface and extracts from two reviews of the book at THIS LINK.

The book with Masilamani Sambandham was published a year after Bharucha-Reid died. The Publisher's Description contains the following:-
The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials.
You can read the full Publisher's Description and extracts from three reviews of the book at THIS LINK.

The second type of book that Bharucha-Reid published consisted of long articles written by experts in their fields. He edited two such books, the first being the three volume work Probabilistic Methods in Applied Mathematics (1968, 1970, 1973) and the second being Probabilistic Analysis and Related Topics (1978, 1979, 1983). Bharucha-Reid explains his aims with these series in the Preface to the first of these books. Here is an extract from this Preface:-
Within recent years research in stochastic processes, functional analysis, and numerical analysis has led to the development of powerful methodological tools for the applied mathematician; and there is considerable evidence that applied mathematicians are indeed using the results of research in the above fields to formulate theories and study more realistic mathematical representations of concrete natural phenomena. This present serial publication, which will be published in several volumes at irregular intervals, is devoted to the role of modern probability theory, in particular the theory of stochastic processes, in the general field of applied mathematics.
For a longer extract from this Preface and short extracts from reviews of both books, see THIS LINK.

We gave details above of Bharucha-Reid's career up to 1981. Ronald Mickens gives some information on the final years of his life in [13]:-
He went to the Georgia Institute of Technology in 1982 and to Atlanta University in 1984. At the time of his death he was director of the Center for Computational Sciences at Atlanta University. ... During his last months at Atlanta University, Bharucha-Reid was very active in several aspects of the physics program. In particular, he made direct contributions to the new research thrusts in computational and plasma physics. Two of his final papers were in fact concerned with the numerical solution of a random singular integral equation appearing in crack problems and the effect of random loading on the mechanics of fatigue and crack growth in structures.
Following his early death at the age of 57, several tributes have been paid. For example, in 1994 the National Association of Mathematicians inaugurated the NAM Albert Turner Bharucha-Reid Lecture Series. The first lecture, Gronwall Inequalities for Weak Solutions of Nonlinear Systems with Applications to the Navier-Stokes Equations, was given at Morris Brown College, Atlanta, by Tepper Gill of Howard University. Tepper Gill had been one of Bharucha-Reid's Ph.D. students.

In [23] Jasmine Talley explains about the Albert Turner Bharucha-Reid Collection of his papers:-
Through his professional correspondence, we see that he advanced the research in his field of probability theory, as well as in physics. He collaborated with other mathematicians and scientists all over the world and kept close tabs on their careers. In addition, he frequently requested the writings and manuscripts from colleagues and granted requests for his own writings and publications. He served as a visiting professor and lecturer at many institutions including the University of Wisconsin and the Institute of Mathematical Sciences in Madras, (now Chennai) India. Dr Bharucha-Reid also mentored at least thirteen Ph.D. students. Because of his stature in the field of mathematics, many professionals and students sought out his expertise and advice or his recommendation for professorship positions at universities around the world. He was awarded an honorary doctorate of science from Syracuse University in 1984.

References (show)

  1. The Albert Turner Bharucha-Reid Lecture, National Association of Mathematics.
  2. Albert Turner Bharucha-Reid, Prabook.
  3. R Coleman, Review: Probabilistic Analysis and Related Topics, Vol. 1, by A T Bharucha-Reid (ed.), Journal of the Royal Statistical Society. Series A (General) 143 (1) (1980), 79-80.
  4. D A Dawson, Review: Random Integral Equations, by A T Bharucha-Reid, SIAM Review 16 (2) (1974), 266-268.
  5. R Durrett, Review: Probabilistic Analysis and Related Topics, Vol. 3, by A T Bharucha-Reid (ed.), American Scientist 75 (3) (1987), 322.
  6. R P Eddy, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, Mathematics of Computation 15 (75) (1961), 304-306.
  7. R Fikes, Albert T Bharucha-Reid (1927-1985), BlackPast.
  8. J Gani, Review: Probabilistic Analysis and Related Topics, Vol. 1, by A T Bharucha-Reid (ed.), International Statistical Review / Revue Internationale de Statistique 48 (2) (1980), 231.
  9. W M Gilbert, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, Econometrica 32 (3) (1964), 457.
  10. R H Glendinning, Review: Random Polynomials, by A T Bharucha-Reid and M Sambandham, Journal of the Royal Statistical Society. Series A (General) 150 (3) (1987), 281.
  11. G J, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, The Incorporated Statistician 11 (2) (1961), 126-128.
  12. J B Lathrop, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, Operations Research 11 (2) (1963), 290-293.
  13. R E Mickens, Albert Turner Bharucha-Reid, Physics Today 38 (12) (1985), 93.
  14. R E Mickens, Albert Turner Bharucha-Reid, Joint Mathematics Meetings, American Mathematical Society (9 September 2013).
  15. D W Miller, Review: Probabilistic Methods in Applied Mathematics, Vol. 1, by A T Bharucha-Reid (ed.), Management Science 16 (1), Theory Series (1969), 141.
  16. P A Moran, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, Journal of the Royal Statistical Society. Series A (General) 124 (1) (1961), 94-95.
  17. B Nicolaneko, G Papanicolaou and D Stevens, Review: Probabilistic Methods in Applied Mathematics, Vol. 2, by A T Bharucha-Reid (ed.), American Scientist 59 (1) (1971), 119.
  18. L Peccati, Review: Probabilistic Methods in Applied Mathematics, Vols. 1-3, by A T Bharucha-Reid (ed.), Giornale degli Economisti e Annali di Economia, Nuova Serie 34 (11/12) (1975), 808-809.
  19. M S, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, Population (French Edition) 17 (1) (1962), 181.
  20. G Samal, Review: Random Polynomials, by A T Bharucha-Reid and M Sambandham, Bull. Amer. Math. Soc. 21 (1) (1989), 182-183.
  21. R Spangenburg, D Moser and D Long, Bharucha-Reid, Albert Turner, African Americans in Science, Math, and Invention, A to Z of African Americans (Infobase Publishing, 2014), 13-14.
  22. R Syski, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, SIAM Review 5 (2) (1963), 173-174.
  23. J Talley, Albert T Bharucha-Reid Papers, Amistad Research Center (17 July 2017).
  24. G Weiss, Review: Elements of the Theory of Markov Processes and Their Applications, by A T Bharucha-Reid, Science, New Series 132 (3435) (1960), 1244.
  25. G H Weiss, Review: Probabilistic Methods in Applied Mathematics, Vol. 1, by A T Bharucha-Reid (ed.), SIAM Review 11 (1) (1969), 96-98.
  26. S W Williams, Albert Turner Bharucha-Reid, Mathematicians of the African Diaspora, The Mathematics Department, State University of New York at Buffalo (2008).

Additional Resources (show)

Honours (show)

Honours awarded to Albert Bharucha-Reid

  1. Bharucha-Reid lectures
  2. Claytor-Woodard lecturer 1984

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update November 2019