View source for Raj Chandra Bose

{{Short description|Indian American mathematician and statistician (1901-1987)}}
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{{Infobox scientist
| name              = Raj Chandra Bose
| image             = Raj Chandra Bose.jpg
| image_size        = 220px
| caption           = Raj Chandra Bose
| birth_date        = {{Birth date|df=yes|1901|6|19}}
| birth_place       = [[Narmadapuram]], [[Madhya Pradesh]], [[India]]
| death_date        = {{death date and age|df=yes|1987|10|31|1901|5|19}}
| death_place       = [[Fort Collins]], [[Colorado]]
| citizenship       = India
| nationality       =
| alma_mater        = [[Rajabazar Science College]]<br>([[University of Calcutta]])
| doctoral_advisor  = 
| doctoral_students = [[Dijen K. Ray-Chaudhuri]]<br>[[Sharadchandra Shankar Shrikhande]]<br>[[J. N. Srivastava]]
| known_for         = [[Association scheme]] <br /> [[Bose–Mesner algebra]] <br /> [[Graeco-Latin square#History|Euler's conjecture]] on [[Latin square]]s <br /> [[Strongly regular graph]]s <br /> [[Partial geometry|Partial Geometries]]<br />[[Morse Code]]
Notable Awards         Elected Fellow of the US Academy of Sciences
| author_abbrev_bot = 
| author_abbrev_zoo = 
| influences        = 
| influenced        = 
| signature         = 
| footnotes         = 
| ethnicity         = 
| field             = Mathematics and Statistics
| work_institutions = [[Indian Statistical Institute]] <br> [[Colorado State University]]  <br> [[University of North Carolina at Chapel Hill]]
| prizes            = 
| awards            = Elected Member of the US [[National Academy of Sciences]] 
}}

'''Raj Chandra Bose (or Basu)''' (19 June 1901 – 31 October 1987) was an [[Indian American]] mathematician and statistician best known for his work in [[design of experiments|design theory]], [[finite geometry]] and the theory of [[error-correcting code]]s in which the class of [[BCH code]]s is partly named after him. He also invented the notions of [[partial geometry]], [[association scheme]], and [[strongly regular graph]] and started a systematic study of [[difference set]]s to construct symmetric [[block design]]s. 
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]] dated 1782 that for no ''n'' do there exist two mutually orthogonal [[Latin square]]s of order 4''n''&nbsp;+&nbsp;2.

==Early life==
Bose was born in [[Hoshangabad]], India into a [[Bengalis|Bengali]] 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]] [[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]] campus of [[University of Calcutta]]. His research was performed under the supervision of the [[geometry]] Professor [[Syamadas Mukhopadhyaya]] 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 [[Prasanta Chandra Mahalanobis|P. C. Mahalanobis]], director of the new (1931) [[Indian Statistical Institute]], 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]]'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 [[Ronald Fisher|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]] and [[finite geometry]] 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]] 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]] and the [[University of North Carolina at Chapel Hill]]. 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]] (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 [[Leonhard Euler|Euler's]] conjecture that no [[Graeco-Latin square]] of size 4''k''&nbsp;+&nbsp;2 exists. In 1971, he retired at the age of 70. He then accepted a chair at [[Colorado State University]] of [[Fort Collins]] from which he retired in 1980. His final doctoral student finished after this second retirement.

Bose died in [[Colorado]], aged 86, in 1987. He is survived by two daughters. The elder, Purabi Schur, is retired from the [[Library of Congress]] 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 (journal)|Sankhya]] 4 (1939), 337–372.
* {{cite journal|authorlink1=Raj Chandra Bose| last1=Bose|first1=Raj Chandra | last2=Mesner|first2=D. M.|year=1959|title=On linear associative algebras corresponding to association schemes of partially balanced designs|journal=[[Annals of Mathematical Statistics]]|volume=30|issue=1|pages=21–38| url=http://projecteuclid.org/euclid.aoms/1177706356 | doi=10.1214/aoms/1177706356 | mr = 102157 | jstor = 2237117|doi-access=free}}
*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''&nbsp;+&nbsp;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.

==Some books by R. C. Bose==
R. C. Bose and B. Manvel.
Introduction to combinatorial theory.
John Wiley & Sons, Inc., New York, 1984. ix+237 pp.

==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]] Series A, Vol. 153, No. 1. pp.&nbsp;98–99.
*"Bose, Raj Chandra", pp.&nbsp;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 published in ''Encyclopedia of Statistical Science.''

==See also==
* [[Association scheme]]
* [[Block design]]
* [[Bose–Mesner algebra]]
* [[Combinatorial design]]
* [[Design of experiments]]

==External links==
* [http://www.york.ac.uk/depts/maths/histstat/people/bose.gif R. C. Bose:another photograph] on the [http://www.york.ac.uk/depts/maths/histstat/people/welcome.htm Portraits of Statisticians] page.
* {{usurped|1=[https://web.archive.org/web/20060709201106/http://www.vigyanprasar.com/comcom/develop83.htm Indian Statistical Institute: useful background information]}}
* {{MathGenealogy|id=11936}}
* [http://www.maths.qmw.ac.uk/~pjc/comb/quotes.html Peter Cameron's Quotes on Mathematics: where the story about fields comes from]
* {{mathworld|urlname=EulersGraeco-RomanSquaresConjecture|title=Euler's Graeco-Roman Squares Conjecture}} 
* {{MacTutor Biography|id=Bose_Raj}}

{{Authority control}}

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