R. C. Bose
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Raj Chandra Bose (19 June 1901 – 31 October 1987) was an Indian American 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 interp ...
,
finite geometry Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...
and the theory of error-correcting codes 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 ''Galois field''). BCH codes were invented in 1959 ...
s is partly named after him. He also invented the notions of partial geometry, association scheme, and
strongly regular graph In graph theory, a strongly regular graph (SRG) is defined as follows. Let be a regular graph with vertices and degree . is said to be strongly regular if there are also integers and such that: * Every two adjacent vertices have comm ...
and started a systematic study of difference sets to construct symmetric block designs. He was notable for his work along with S. S. Shrikhande and E. T. Parker in their disproof of the famous conjecture made by
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
dated 1782 that there do not exist two mutually orthogonal
Latin square In combinatorics and in experimental design, a Latin square is an ''n'' × ''n'' array filled with ''n'' different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3×3 Latin sq ...
s of order 4''n'' + 2 for every ''n''.


Early life

Bose was born in
Hoshangabad Hoshangabad, officially known as Narmadapuram is a city and municipality in the Indian state of Madhya Pradesh. It serves as the headquarters of both Hoshangabad district and Narmadapuram division. It is located in central India, on the south ...
, India; 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 pandemic. 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 (commonly or formerly known as Rashbehari Siksha Prangan & Taraknath Palit Siksha Prangan or Rajabazar Science College & Ballygunge Science College) are two of five main campuses of ...
campus of
University of Calcutta The University of Calcutta (informally known as Calcutta University; CU) is a public collegiate state university in India, located in Kolkata, West Bengal, India. Considered one of best state research university all over India every year, ...
. His research was performed under the supervision of the
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
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, ...
from Calcutta. Bose worked as a lecturer at Asutosh College, Calcutta. He published his work on the differential geometry of convex curves.


Academic life

Bose's course changed in December 1932 when
P. C. Mahalanobis Prasanta Chandra Mahalanobis OBE, FNA, FASc, FRS (29 June 1893– 28 June 1972) was an Indian scientist and statistician. He is best remembered for the Mahalanobis distance, a statistical measure, and for being one of the members of the first ...
, director of the new (1931)
Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...
, 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'' 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 ...
's '' Statistical Methods for Research Workers''. 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 1938–9 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
finite geometry Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...
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
University of Calcutta The University of Calcutta (informally known as Calcutta University; CU) is a public collegiate state university in India, located in Kolkata, West Bengal, India. Considered one of best state research university all over India every year, ...
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 (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
and the
University of North Carolina at Chapel Hill A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States ...
. 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 data storage. Codes are studied ...
(with D.K. Ray-Chaudhuri) and constructed (with S. S. Shrikhande and E. T. Parker) a
Graeco-Latin square In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are ...
of size 10, a counterexample to Euler's conjecture that no
Graeco-Latin square In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are ...
of size 4''k'' + 2 exists. In 1971, he retired at the age of 70. He then accepted a chair at Colorado State University of
Fort Collins A fortification is a military construction or building designed for the defense of territories in warfare, and is also used to establish rule in a region during peacetime. The term is derived from Latin ''fortis'' ("strong") and ''facere'' ...
from which he retired in 1980. His final doctoral student finished after this second retirement. Bose died in
Colorado Colorado (, other variants) is a state in the Mountain states, Mountain West subregion of the Western United States. It encompasses most of the Southern Rocky Mountains, as well as the northeastern portion of the Colorado Plateau and the wes ...
, 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 the research library that officially serves the United States Congress and is the ''de facto'' national library of the United States. It is the oldest federal cultural institution in the country. The library ...
and the younger, Sipra Bose Johnson, is retired as a professor of anthropology from the State University of New York at New Paltz.


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 ''Sankya'' (; Sanskrit सांख्य), IAST: ') is a dualistic school of Indian philosophy. It views reality as composed of two independent principles, '' puruṣa'' ('consciousness' or spirit); and ''prakṛti'', (nature ...
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 Wiley for the Royal Statistical Society. History The Statistical Society of London was founded ...
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''


See also

* Association scheme * Block design * Bose–Mesner algebra *
Combinatorial design Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of ''balance'' and/or ''symmetry''. These co ...
*
Design of experiments The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...


External links


R. C. Bose:another photograph
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* * {{DEFAULTSORT:Bose, Raj Chandra 1901 births 1987 deaths Indian emigrants to the United States Indian statisticians Information theorists Bengali mathematicians Bengali Hindus Colorado State University faculty University of North Carolina at Chapel Hill faculty Latin squares University of Calcutta alumni University of Calcutta faculty Presidents of the Institute of Mathematical Statistics People from Hoshangabad Fellows of the American Statistical Association Indian Statistical Institute faculty American academics of Indian descent 20th-century Indian mathematicians Scientists from Kolkata Members of the United States National Academy of Sciences Indian American American people of Indian descent