Raj Chandra Bose (or Basu) (19 June 1901 – 31 October 1987) was an

Indian American Indian Americans are Americans whose ancestry originates wholly or partly from India. The terms Asian Indian and East Indian are used to avoid confusion with Native Americans in the United States, Native Americans in the United States, who ar ...

mathematician and statistician best known for his work in

design theory Design theory is a subfield of design research concerned with various theoretical approaches towards understanding and delineating design principles, design knowledge, and design practice. History Design theory has been approached and inte ...

finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...

and the theory of

error-correcting code In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...

s in which the class of

BCH code In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a '' Galois field''). BCH codes were invented in ...

s is partly named after him. He also invented the notions of

partial geometry An incidence structure C=(P,L,I) consists of a set of points, a set of lines, and an incidence relation, or set of flags, I \subseteq P \times L; a point p is said to be ''incident'' with a line l if . It is a ( finite) partial geometry if there a ...

association scheme The theory of association schemes arose in statistics, in the theory of design of experiments, experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatori ...

, and

strongly regular graph In graph theory, a strongly regular graph (SRG) is a regular graph with vertices and degree such that for some given integers \lambda, \mu \ge 0 * every two adjacent vertices have common neighbours, and * every two non-adjacent vertices h ...

and started a systematic study of

difference set In combinatorics, a (v,k,\lambda) difference set is a subset D of cardinality, size k of a group (mathematics), group G of order of a group, order v such that every non-identity element, identity element of G can be expressed as a product d_1d_2^ o ...

s to construct symmetric

block design In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as ''blocks'', chosen such that number of occurrences of each element satisfies certain conditions making the co ...

s. He was notable for his work along with S. S. Shrikhande and E. T. Parker in their disproof of the famous

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), ha ...

made by

Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

dated 1782 that for no ''n'' do there exist two mutually orthogonal

Latin square Latin ( or ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken by the Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion o ...

s of order 4''n'' + 2.

Early life

Bose was born in

Hoshangabad Hoshangabad (Hindi: ), officially Narmadapuram (), is a city in the Indian States and territories of India, state of Madhya Pradesh. It serves as the headquarters of both Hoshangabad district and Narmadapuram division. It is located in central ...

, India into a

Bengali Bengali or Bengalee, or Bengalese may refer to: *something of, from, or related to Bengal, a large region in South Asia * Bengalis, an ethnic and linguistic group of the region * Bengali language, the language they speak ** Bengali alphabet, the w ...

family; he was the first of five children. His father was a physician and life was good until 1918 when his mother died in the

influenza Influenza, commonly known as the flu, is an infectious disease caused by influenza viruses. Symptoms range from mild to severe and often include fever, runny nose, sore throat, muscle pain, headache, coughing, and fatigue. These sympto ...

pandemic A pandemic ( ) is an epidemic of an infectious disease that has a sudden increase in cases and spreads across a large region, for instance multiple continents or worldwide, affecting a substantial number of individuals. Widespread endemic (epi ...

. His father died of a stroke the following year. Despite difficult circumstances, Bose continued to study securing first class in both the Masters examinations in Pure and Applied mathematics in 1925 and 1927 respectively at the

Rajabazar Science College The University College of Science, Technology and Agriculture (formerly known as Rajabazar Science College) are two of five main campuses of the University of Calcutta (CU). The college served as the cradle of Indian sciences, where Raman won t ...

campus of

University of Calcutta The University of Calcutta, informally known as Calcutta University (), is a Public university, public State university (India), state university located in Kolkata, Calcutta (Kolkata), West Bengal, India. It has 151 affiliated undergraduate c ...

. His research was performed under the supervision of the

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

Professor

Syamadas Mukhopadhyaya Syamadas Mukhopadhyaya (22 June 1866 – 8 May 1937) was an Indian mathematician who introduced the four-vertex theorem and Mukhopadhyaya's theorem in plane geometry. Biography Syamadas Mukhopadhyaya was born at Haripal, Hooghly district, i ...

from Calcutta. Bose worked as a lecturer at Asutosh College, Calcutta. He published his work on the

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

of convex curves.

Academic life

Bose's course changed in December 1932 when P. C. Mahalanobis, director of the new (1931)

Indian Statistical Institute The Indian Statistical Institute (ISI) is a public research university headquartered in Kolkata, India with centers in New Delhi, Bengaluru, Chennai and Tezpur. It was declared an Institute of National Importance by the Government of India und ...

, offered Bose a part-time job. Mahalanobis had seen Bose's geometrical work and wanted him to work on statistics. The day after Bose moved in, the secretary brought him all the volumes of ''

Biometrika ''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for the Biometrika Trust. The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was ...

'' with a list of 50 papers to read and also

Ronald Fisher Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who a ...

's ''

Statistical Methods for Research Workers ''Statistical Methods for Research Workers'' is a classic book on statistics, written by the statistician R. A. Fisher. It is considered by some to be one of the 20th century's most influential books on statistical methods, together with his '' T ...

''. Mahalanobis told him, "You were saying that you do not know much statistics. You master the 50 papers ... and Fisher's book. This will suffice for your statistical education for the present." With Samarendra Nath Roy, who joined the ISI a little later, Bose was the chief mathematician at the Institute. He first worked with multivariate analysis where he collaborated with Mahalanobis and Roy. In 1938–39 Fisher visited India and talked about the design of experiments. Roy had the idea of using the theory of

finite fields In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subt ...

and

to solve problems in design. The development of a mathematical theory of design would be Bose's main preoccupation until the mid-1950s. In 1935 Bose had become full-time at the Institute. In 1940 joined the

where C. R. Rao and H. K. Nandi were in the first group of students he taught. In 1945 Bose became Head of the Department of Statistics. University authorities in the United States told him he needed to have a doctorate. So he submitted his published papers on multivariate analysis and the design of experiments and was awarded a D. Litt. in 1947. In 1947 Bose went to the United States as a visiting professor at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

and the

University of North Carolina at Chapel Hill The University of North Carolina at Chapel Hill (UNC, UNC–Chapel Hill, or simply Carolina) is a public university, public research university in Chapel Hill, North Carolina, United States. Chartered in 1789, the university first began enrolli ...

. He received offers from American universities and he was also offered positions in India. The Indian jobs involved very heavy administration, which he saw as the end of his research work and in March 1949 he joined the University of North Carolina at Chapel Hill as Professor of Statistics. In the years at Chapel Hill Bose made important discoveries on

coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...

(with D.K. Ray-Chaudhuri) and constructed (with S. S. Shrikhande and E. T. Parker) a Graeco-Latin square of size 10, a counterexample to Euler's conjecture that no Graeco-Latin square of size 4''k'' + 2 exists. In 1971, he retired at the age of 70. He then accepted a chair at

Colorado State University Colorado State University (Colorado State or CSU) is a Public university, public Land-grant university, land-grant research university in Fort Collins, Colorado, United States. It is the flagship university of the Colorado State University Syst ...

Fort Collins A fortification (also called a fort, fortress, fastness, or stronghold) is a military construction designed for the defense of territories in warfare, and is used to establish rule in a region during peacetime. The term is derived from La ...

from which he retired in 1980. His final doctoral student finished after this second retirement. Bose died in

Colorado Colorado is a U.S. state, state in the Western United States. It is one of the Mountain states, sharing the Four Corners region with Arizona, New Mexico, and Utah. It is also bordered by Wyoming to the north, Nebraska to the northeast, Kansas ...

, aged 86, in 1987. He is survived by two daughters. The elder, Purabi Schur, is retired from the

Library of Congress The Library of Congress (LOC) is a research library in Washington, D.C., serving as the library and research service for the United States Congress and the ''de facto'' national library of the United States. It also administers Copyright law o ...

and the younger, Sipra Bose Johnson, is retired as a professor of anthropology from the

State University of New York at New Paltz The State University of New York at New Paltz (SUNY New Paltz or New Paltz) is a public university in New Paltz, New York. It traces its origins to the New Paltz Classical School, a secondary institution founded in 1828 and reorganized as an ...

Some articles by R. C. Bose

*R. C. Bose, On the construction of balanced incomplete block designs, Annals of Eugenics. 9 (1939), 358–399. *R. C. Bose and K. R. Nair, Partially balanced incomplete block designs,

Sankhya Samkhya or Sankhya (; ) is a dualistic orthodox school of Hindu philosophy. It views reality as composed of two independent principles, '' Puruṣa'' ('consciousness' or spirit) and ''Prakṛti'' (nature or matter, including the human mind an ...

4 (1939), 337–372. * *R. C. Bose and S. S. Shrikhande, On the falsity of Euler's conjecture about the non-existence of two orthogonal Latin squares of order 4''t'' + 2, Proceedings of the National Academy of Sciences USA, 45, (1959), 734–737. *R. C. Bose and D.K. Ray-Chaudhuri On a class of error-correcting binary codes, Information and control, 3, (1960), 68–79.

Autobiography

*J. Gani (ed) (1982) ''The Making of Statisticians,'' New York: Springer-Verlag. This has a chapter in which Bose tells the story of his life.

Discussions

*Norman R. Draper (1990) Obituary: Raj Chandra Bose,

Journal of the Royal Statistical Society The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Oxford University Press for the Royal Statistical Society. History The Statistical Society of ...

Series A, Vol. 153, No. 1. pp. 98–99. *"Bose, Raj Chandra", pp. 183–184 in ''Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present, '' (ed. N. L. Johnson and S. Kotz) 1997. New York: Wiley. Originally p''

External links