Raj Chandra Bose
Encyclopedia
Raj Chandra Bose was an India
n mathematician
and statistician
best known for his work in design theory
and the theory of error-correcting codes in which the class of BCH code
s is partly named after him. 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 there do not exist two mutually orthogonal Latin square
s of order 4n + 2 for every n.
, 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. In very difficult circumstances Bose continued to study coming in first in the M.A. examinations in pure mathematics
at the University of Calcutta
. He did research under the supervision of the geometer Professor Shyamadas Mukherjee from Calcutta. Bose found a job as a lecturer at Asutosh College, Calcutta
. He managed to publish some work on the differential geometry of convex curves.
, 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 in 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 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 Fisher's book
. This will suffice for your statistical education for the present." With S. N. Roy
, who joined the ISI a little later, Bose was the chief mathematician at the Institute.
He first worked in 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 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.
The ISI workers had a joke about Mahalanobis and Bose and their different priorities. The professor wanted Bose to visit the paddy fields and advise him on sampling problems for the estimation of yield of paddy. Bose did not very much like the idea, and he used to spend most of the time at home working on combinatorial problems using Galois fields. Whenever Professor Mahalanobis asked about Bose, his secretary would say that Bose is working in fields, which kept the Professor happy.
In 1935 Bose had become full-time at the Institute. In 1940 joined the University of Calcutta
where C. R. Rao
was in the first group of students he taught. In 1945 Bose became Head of the Department of Statistics. The university authorities told him he had 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 Euler's
conjecture that no Graeco-Latin square
of size 4k + 2 exists. In 1971 he retired aged 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
.
This has a chapter in which Bose tells the story of his life.
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
best known for his work in design theory
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
and the theory of error-correcting codes in which the class of BCH code
BCH code
In coding theory the BCH codes form a class of parameterised error-correcting codes which have been the subject of much academic attention in the last fifty years. BCH codes were invented in 1959 by Hocquenghem, and independently in 1960 by Bose and Ray-Chaudhuri...
s is partly named after him. He was notable for his work along with S. S. Shrikhande
S. S. Shrikhande
Sharadchandra Shankar Shrikhande is an Indian mathematician with distinguished and well-recognized achievements in combinatorial mathematics. He is notable for his breakthrough work along with R. C. Bose and E. T...
and E. T. Parker
E. T. Parker
Ernest Tilden Parker is a professor emeritus from Ohio State University. He is notable for his breakthrough work along with R. C. Bose and S. S. Shrikhande in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of...
in their disproof of the famous conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
made by Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
dated 1782 that there do not exist two mutually orthogonal Latin square
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...
s of order 4n + 2 for every n.
Early life
Bose was born in HoshangabadHoshangabad
Hoshangabad is a city and a municipality in Hoshangabad district in the Indian state of Madhya Pradesh. It is a city in the central india region, located on the south bank of the Narmada River, and is the administrative center of Hoshangabad District.-History:mohammed bharmal & abdeali batawalaThe...
, India; he was the first of five children. His father was a physician
Physician
A physician is a health care provider who practices the profession of medicine, which is concerned with promoting, maintaining or restoring human health through the study, diagnosis, and treatment of disease, injury and other physical and mental impairments...
and life was good until 1918 when his mother died in the influenza
Influenza
Influenza, commonly referred to as the flu, is an infectious disease caused by RNA viruses of the family Orthomyxoviridae , that affects birds and mammals...
pandemic
Pandemic
A pandemic is an epidemic of infectious disease that is spreading through human populations across a large region; for instance multiple continents, or even worldwide. A widespread endemic disease that is stable in terms of how many people are getting sick from it is not a pandemic...
. His father died of a stroke the following year. In very difficult circumstances Bose continued to study coming in first in the M.A. examinations in pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
at the University of Calcutta
University of Calcutta
The University of Calcutta is a public university located in the city of Kolkata , India, founded on 24 January 1857...
. He did research under the supervision of the geometer Professor Shyamadas Mukherjee from Calcutta. Bose found a job as a lecturer at Asutosh College, Calcutta
Asutosh College, Calcutta
Asutosh College is an affiliated college of the University of Calcutta, in Kolkata, India. It was established in the year 1916 under the stewardship of eminent educationist Sir Ashutosh Mukherjee, who was the then Vice-Chancellor of the University of Calcutta. The Present Principal is Dr...
. He managed to publish some work on the differential geometry of convex curves.
Academic life
Bose's course changed in December 1932 when P. C. MahalanobisPrasanta Chandra Mahalanobis
Prasanta Chandra Mahalanobis FRS was an Indian scientist and applied statistician. He is best remembered for the Mahalanobis distance, a statistical measure. He made pioneering studies in anthropometry in India...
, director of the new (1931) Indian Statistical Institute
Indian Statistical Institute
Indian Statistical Institute is a public research institute and university in Kolkata's northern outskirt of Baranagar, India founded by Prasanta Chandra Mahalanobis in 1931...
, offered Bose a part-time job. Mahalanobis had seen Bose’s geometrical work and wanted him to work in statistics. The day after Bose moved in, the secretary brought him all the volumes of Biometrika
Biometrika
- External links :* . The Internet Archive. 2011....
with a list of 50 papers to read and also Fisher's
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
Statistical Methods for Research Workers
Statistical Methods for Research Workers
Statistical Methods for Research Workers is a classic 1925 book on statistics 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. According to ,...
. Mahalanobis told him, "You were saying that you do not know much statistics. You master the 50 papers … and Fisher's book
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
. This will suffice for your statistical education for the present." With S. N. Roy
S. N. Roy
Samarendra Nath Roy or S. N. Roy was an Indian-born American mathematician and an applied statistician. He was the first of two children of Kali Nath Roy and Suniti Bala Roy. His father, Kali Nath Roy was a freedom fighter and the Chief Editor of the newspaper TRIBUNE.Prof. Roy had a brilliant...
, who joined the ISI a little later, Bose was the chief mathematician at the Institute.
He first worked in 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 and finite geometry
Finite geometry
A finite geometry is any geometric system that has only a finite number of points.Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points, in fact as many points as there are real numbers...
to solve problems in design. The development of a mathematical theory of design would be Bose's main preoccupation until the mid 1950s.
The ISI workers had a joke about Mahalanobis and Bose and their different priorities. The professor wanted Bose to visit the paddy fields and advise him on sampling problems for the estimation of yield of paddy. Bose did not very much like the idea, and he used to spend most of the time at home working on combinatorial problems using Galois fields. Whenever Professor Mahalanobis asked about Bose, his secretary would say that Bose is working in fields, which kept the Professor happy.
In 1935 Bose had become full-time at the Institute. In 1940 joined the University of Calcutta
University of Calcutta
The University of Calcutta is a public university located in the city of Kolkata , India, founded on 24 January 1857...
where C. R. Rao
C. R. Rao
Calyampudi Radhakrishna Rao FRS known as C R Rao is an Indian statistician. He is currently professor emeritus at Penn State University and Research Professor at the University at Buffalo. Rao has been honored by numerous colloquia, honorary degrees, and festschrifts and was awarded the US...
was in the first group of students he taught. In 1945 Bose became Head of the Department of Statistics. The university authorities told him he had 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
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
and the University of North Carolina at Chapel Hill
University of North Carolina at Chapel Hill
The University of North Carolina at Chapel Hill is a public research university located in Chapel Hill, North Carolina, 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
Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding...
(with D.K. Ray-Chaudhuri) and constructed (with S. S. Shrikhande
S. S. Shrikhande
Sharadchandra Shankar Shrikhande is an Indian mathematician with distinguished and well-recognized achievements in combinatorial mathematics. He is notable for his breakthrough work along with R. C. Bose and E. T...
and E. T. Parker ) a Graeco-Latin square
Graeco-Latin square
In mathematics, a Graeco-Latin square or Euler square or orthogonal Latin squares of order n over two sets S and T, each consisting of n symbols, is an n×n arrangement of cells, each cell containing an ordered pair , where s is in S and t is in T, such that every row and every column contains...
of size 10, a counterexample to Euler's
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
conjecture that no Graeco-Latin square
Graeco-Latin square
In mathematics, a Graeco-Latin square or Euler square or orthogonal Latin squares of order n over two sets S and T, each consisting of n symbols, is an n×n arrangement of cells, each cell containing an ordered pair , where s is in S and t is in T, such that every row and every column contains...
of size 4k + 2 exists. In 1971 he retired aged 70. He then accepted a chair at Colorado State University
Colorado State University
Colorado State University is a public research university located in Fort Collins, Colorado. The university is the state's land grant university, and the flagship university of the Colorado State University System.The enrollment is approximately 29,932 students, including resident and...
of Fort Collins from which he retired in 1980. His final doctoral student finished after this second retirement.
Bose died in Colorado
Colorado
Colorado is a U.S. state that encompasses much of the Rocky Mountains as well as the northeastern portion of the Colorado Plateau and the western edge of the Great Plains...
, aged 86, in 1987. He is survived by two daughters. The elder, Purabi Schur, is retired from the Library of Congress
Library of Congress
The Library of Congress is the research library of the United States Congress, de facto national library of the United States, and the oldest federal cultural institution in the United States. Located in three buildings in Washington, D.C., it is the largest library in the world by shelf space and...
and the younger, Sipra Bose Johnson, is retired as a professor of anthropology from the State University of New York at New Paltz
State University of New York at New Paltz
The State University of New York at New Paltz, known as SUNY New Paltz for short, is a public university in New Paltz, New York. It was founded in 1828 as the School for teaching of classics. In 1885, the New Paltz Normal and Training School was established as a school to prepare teachers for the...
.
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 4 (1939), 337–372.
- R. C. Bose and S. S. ShrikhandeS. S. ShrikhandeSharadchandra Shankar Shrikhande is an Indian mathematician with distinguished and well-recognized achievements in combinatorial mathematics. He is notable for his breakthrough work along with R. C. Bose and E. T...
, On the falsity of Euler’s conjecture about the non-existence of two orthogonal Latin squares of order 4t + 2, Proceedings of the national Academy of Science 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 SocietyJournal of the Royal Statistical SocietyThe Journal of the Royal Statistical Society is a series of three peer-reviewed statistics journals published by Blackwell Publishing for the London-based Royal Statistical Society.- History :...
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 schemeAssociation schemeThe theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. Indeed, in algebraic combinatorics, association schemes provide a unified approach to many topics,...
- Block design
- Bose-Mesner algebra
- Combinatorial designCombinatorial designCombinatorial design theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties....
- Design of experimentsDesign of experimentsIn general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
