# Raj Chandra Bose

### Quick Info

Hoshangabad, Madhya Pradesh, India

Fort Collins, Colorado, USA

**Raj Chandra Bose**was an Indian mathematician and statistician who worked in America. He best known for his work in design theory, finite geometry and the theory of error-correcting codes.

### Biography

**Raj Chandra Bose**was born in Hoshangabad, a town in central India, but he was brought up in Rohtak, a town in Haryana state in northwestern India. His father, Protap Chandra Bose, had served as a doctor in the British army before becoming a doctor in the town of Rohtak. Protap Chandra Bose's first wife died without any children being born, and he then married Ushangini Mitra from the town of Hoshangabad who had met while visiting his sister who lived in that town. Raj Chandra, the eldest of his parents' four children, was born in Hoshangabad since his mother had returned to her parents' home to have her first child. His brother was born in 1905 and his three sisters were born in 1907, 1910 and 1914. It was a happy childhood but one in which he was expected to work hard at his academic studies. His father was ambitious for his eldest son and pushed him hard. Anything other than top of the class was considered a failure so, for example, when Raj Chandra only came second in the geography examination in the eighth grade his father demanded that he learn the geography textbook by heart - something which he did not find too hard since he had a photographic memory.

After completing his schooling at the Government High School in Rohtak, Bose entered the Hindu College in Delhi in April 1917. He had caught influenza at the time he was sitting the scholarship examinations for the Punjab University and failed to gain a high enough rank for a scholarship. His happy childhood and rewarding time studying at the Hindu College came to a tragic end in October 1918 when his mother died in the worldwide influenza epidemic. This epidemic, also called the Spanish influenza epidemic, killed millions throughout the word with over 12 million people dying in India alone. Despite the loss of his mother, Bose came first in the 1919 Intermediate Examination at the Punjab University. In January 1920 Bose's father died from a stroke and he was left as the eldest in the family with all the responsibility that gave yet little money to either educate himself or look after the family. He arranged for cousins to live rent free in his family home in Rohtak in exchange for looking after his brother and sisters. In 1921 his brother completed his schooling and Bose brought him and his sisters to Delhi where they all lived in a single room. He made some money tutoring but times were exceptionally difficult especially when he gave up tutoring before his final B.A. examinations in 1922 to enable him to prepare properly:-

Only a few days were left for his B.A. examination. Raj Chandra Bose was lost in his books. But his sister came with a problem. There was hardly any food left in the house. It was an urgent problem but nothing new. In the past three years he had faced one crisis after another. ... he remembered that there were still some medicines, including a bottle of quinine, in his father's medicine chest. It was soon after World War I and medicines were scarce and costly in India. A bottle of quinine fetched him a handsome amount. The crisis was overcome. Raj Chandra took his B.A. examination and passed it successfully.Bose wanted to continue his studies, but now the family had no income and even if he won a scholarship it would not start for some months. He was fortunate to be offered a one-year teaching position at St Stephens High School and also received a scholarship to take a Master's degree in Applied Mathematics at the Hindu College. His brother was also a student but took on private coaching to help with the family finances. However Bose's teaching job prevented him attending most of the lectures for the MA courses up to April 1923 when his position at St Stephens High School came to an end. As a consequence, although he came top in the MA examinations of 1924, he was not given a First Class degree. He tried unsuccessfully to get a teaching position in a Delhi College and for a year the family had to survive on his, and his brother's, income from coaching. However, Bose now had some good luck, although one would have to say that in many ways he had created his own luck with the quality of his coaching [1]:-

Now my fortunes took another turn. Seth Kedarnath Goenka, whose younger brother I was coaching, was so pleased with my work that he agreed to support me for as long as I needed, in Calcutta, where I wanted to study pure mathematics. I thus came to Calcutta in 1925. My sisters remained with my brother, who now had a steady job. Here I had the good luck to catch the attention of Professor Shyamadas Mukherjee, a very fine geometer of the old school. His main interests at that time were non-Euclidean geometry, $n$-dimensional geometry and global properties of convex curves. He gave me a room in his house and free use of his library. He also secured a good coaching job for me so that I no longer needed any help from Seth Kedarnath.After the award of an MA in Pure Mathematics, First Class, in 1927, Bose remained in Calcutta (its official name today is Kolkata) working as a research associate from January 1928 to December 1929. He was guided by Shyamadas Mukherjee and studied geometry. After the position ended he spent a couple of months out of work before being appointed as a lecturer in mathematics at Asutosh College in Calcutta. It was hard work, yet so poorly paid that he had to supplement his income coaching. Finding time to undertake research was hard but he continued to work on geometry and published

*On the number of circles of curvature perfectly enclosing or perfectly enclosed by a closed convex oval*in 1932. He married Sandhya Lata Datta, the daughter of a district judge, in September 1932. In December 1932 he had another stroke of good fortune when he was approached by P C Mahalanobis who offered him a part-time post at the Indian Statistical Institute which had been set up in Calcutta in 1931. Part-time meant working on Saturdays throughout the year and full-time during the summer and Pujah vacations. He began to read papers whose titles were on a long list that Mahalanobis had given him. From 1935 he had a full-time position at the Indian Statistical Institute as did Samarendra Nath Roy who had been appointed to a part-time post a few months after Bose. They quickly became the best of friends and collaborators.

Examples of his papers over the first few years he worked at the Indian Statistical Institute are:

*On the exact distribution and moment-coefficients of the*$D^{2}$

*-statistics*(1936), (with P C Mahalanobis and S N Roy)

*Normalization of variates and the use of rectangular coordinates in the theory of sampling distributions*(1936), (with S N Roy)

*Distribution of the studentized*$D^{2}$

*-statistic*(1938),

*On the construction of balanced incomplete block designs*(1939), and (with K R Nair)

*Partially balanced incomplete block designs*(1939). In January 1940 he left the Institute to become a lecturer in the Department of Mathematics at the University of Calcutta. In 1941 he became a lecturer in the newly established Department of Statistics at the University of Calcutta and also rejoined the Indian Statistical Institute in a part-time capacity. Mahalanobis was the first head of the Department of Statistics but, in 1945, he gave up this position and Bose became the Head. Despite publishing a host of outstanding papers, Bose had never taken a doctorate and, in order to become a professor, he now required to rectify that. He submitted his papers with a covering Introduction and, after R A Fisher had examined the work, he was duly awarded a doctorate in 1947.

Invitations came for Bose to spend time as a visiting professor in the United States. He gave a course of lectures at the Virginia Polytechnic Institute at Blacksburg in the summer of 1947, then spent two semesters of 1947-48 at the University of North Carolina at Chapel Hill. Then he taught a 1948 summer course at the University of California at Berkeley. He returned to Calcutta in August 1948 with offers of permanent professorships at the University of North Carolina and at the University of Illinois at Urbana. He was then offered the Hardinge professorship and Head of the Department of Mathematics at the University of Calcutta. From this collection of tempting offers he chose the University of North Carolina at Chapel Hill, taking up his professorship there in March 1949. One year later, he was joined at Chapel Hill by his former colleague Samarendra Nath Roy. To obtain an overview of his contributions we quote from [5]:-

Bose made important contributions to a number of areas of geometry including hyperbolic geometry and its application to statistics, multivariate statistical analysis, finite geometries, orthogonal Latin squares, experimental designs, balanced and partially balanced designs and association schemes, difference sets, orthogonal arrays, factorial designs, rotatable designs, coding theory, information theory, graph theory, projective geometry, partial geometries, characterization and embedding problems in designs and geometries, file organization, and additive number theory. In fact, Bose's name is an integral part of the terms BCH codes, Bose-Mesner algebra, and the like, and he was one of "Euler's spoilers".Let us explain two points from this quote. First of we note that a BCH code is a Bose-Chaudhuri-Hocquenghem error correcting code, discovered in 1960. Second, to explain "Euler's Spoilers" we quote from [14]:-

The proof of falsity of a conjecture of Euler about the non-existence of two mutually orthogonal latin squares of order 2 modulo 4 by Bose and his co-workers, Parker and Shrikhande made it to the front page of the Sunday Edition of the 'New York Times' of April 26, 1959! This result earned them the nickname "Euler Spoilers."In [13] S S Shrikhande gives a detailed account of how the three mathematicians disproved Euler's 175 year old conjecture, and in particular emphasises Bose's insights which were so important.

After taking up the position at Chapel Hill in 1949, Bose remained on the staff there until he retired in August 1971. He was the holder of the Kenan Chair over the last five years he spent at Chapel Hill and it was at this stage that his interests returned from statistics to mathematics [1]:-

Up to 1964, my work had been mainly motivated by applications to statistics and coding theory. Though I continued some statistical work, I now became interested in other combinatorial problems in general for their mathematical interest, apart from any application they might have. In particular, I became interested in the interconnections between the structure of "designs" and "graphs". ... In a way things have come full circle. I started out as a mathematician and, after devoting 30 years to statistics, have come back to mathematics.After he retired in 1971, Bose was appointed Professor of Mathematics and Statistics at Colorado State University, Fort Collins. He retired for the second time in 1980, being made Professor Emeritus at Colorado State University.

Many honours were bestowed on Bose both from his native country of India and from the United States. He received honorary degrees from the Indian Statistical Institute in 1974 and from Visva-Bharati University in Bolpur, West Bengal, India in 1979. In 1976 he was elected to the United States National Academy of Sciences. An International Symposium was held at Colorado State University, Fort Collins in 1971 in honour of his 70th birthday; the papers [3] and [9] were presented to this Symposium. Following his death, the Indian Statistical Institute held its 'Conference on Combinatorial Mathematics and Applications' in memory of Bose in Calcutta in December 1988. In 1995 'R C Bose Memorial Conference' was held in Fort Collins; the paper [13] was presented to this conference. In December 2002 the Indian Statistical Institute held the 'R C Bose Centennial Symposium on Discrete Mathematics and Applications' in Calcutta.

As to Bose's character, we quote from [14]:-

He was an inspiring teacher and many of his students went on to make remarkable contributions to mathematics and statistics. He had a flair for languages and could recite verses in Arabic, Bengali, Persian, Sanskrit and Urdu. One of his friends said of Bose "... he was a great conversationalist in spite of the fact that he would hardly allow anybody else to speak!"Norman Draper also gives insights into Bose's character in [6]:-

RC and Mrs Bose were a much travelled pair, both in the USA and worldwide. Mrs Bose always drove the car: RC never learned how! They had two delightful daughters, Purabi (born 1934), now in Washington DC, and Sipra (born 1938), now in Poughkeepsie, NY. Mrs Bose lives between them near Philadelphia. RC was devoted to his family and was much loved in return.Finally let us record that Bose had several hobbies other than travelling which was noted in the quote above. He became an avid gardener while at Chapel Hill and, along with his wife, created a beautiful garden with flowers, shrubs and trees. He was also passionately interested in history, art and culture, visiting the major art galleries of the world during his travels. He had a fine collection of books on art and history.

RC was astonishingly modest about his superb teaching. His response to a question: 'Ah yes, I see I have not explained that point fully' was typical. He loved to joke: 'So, when we heard that Fisher was working on the same ideas, we quickly brought out an issue of Sankhya', or, 'In the Galois field modulo 2, it is equally as good to give as to receive'. He was a man of great gentleness and kindness, and he enriched the lives of all who knew him.

### References (show)

- J Gani (ed),
*The Making of Statisticians*(Springer-Verlag, New York, 1982) - A Barlotti, The work by Ray Chandra Bose on the representation of non-Desarguesian projective planes: further developments and open problems,
*J. Combin. Inform. System Sci.***17**(1-2) (1992), 171-174. - K A Bush, Bose as teacher-the early years, in
*A survey of combinatorial theory, Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971*(North-Holland, Amsterdam, 1973), 79-80. - S K Chatterjee and B Adhikary, Professor R C Bose: 1901-1987,
*Calcutta Statist. Assoc. Bull.***36**(143-144) (1987), 109-124. - D K R Chaudhuri, A R Rao and B Roy, Foreword, R C Bose Centennial Symposium on Discrete Mathematics and Applications, Kolkata, December 20-23, 2002,
*Discrete Math.***306**(14) (2006), 1463. - N R Draper, Obituary: Raj Chandra Bose (1901-1987),
*J. Roy. Statist. Soc. Ser. A***153**(1) (1990), 98-99. - H H Frisinger, Raj Chandra Bose: universal mathematician,
*Ganita Bharati***4**(3-4) (1982), 83-89. - N L Johnson and S Kotz, Bose, Raj Chandra,
*Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present*(Wiley, New York, 1997), 183-184. - List of publications by R C Bose. A survey of combinatorial theory, in
*A survey of combinatorial theory, Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971*(North-Holland, Amsterdam, 1973), xiii-xviii. - P Nandi, Bose memorial session, Combinatorial mathematics and applications, Calcutta, 1988,
*Sankhya Ser. A***54**(1992), i-viii. - Obituary: Raj Chandra Bose (1901-1987),
*Sankhya Ser. B***50**(1) (1988), 4-6. - Professor Raj Chandra Bose,
*J. Geom.***33**(1-2) (1988), 1-2. - S S Shrikhande, R C Bose Memorial Conference, Fort Collins, Colorado: my reminiscences of Professor R C Bose and disproof of Euler's conjecture, R C Bose Memorial Conference, Fort Collins, CO, 1995,
*J. Statist. Plann. Inference***73**(1-2) (1998), 273-276. - C S Yogananda, Raj Chandra Bose (1901-87),
*Resonance*(September 2003), 51.

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Written by J J O'Connor and E F Robertson

Last Update March 2011

Last Update March 2011