From his youth, Datta was deeply religious. He told his parents when he was in his teens that he wanted to become a sannyasi, that is a religious ascetic. A sannyasi does without worldly pleasures and family, following the path set out by the philosopher and religious teacher Sankara. The Advaita Vedanta school founded by Sankara became pre-eminent among learned people in India. When Datta was at school he was already wishing to do away with worldly possessions such as clothes. However, he wore a kopina, a type of loin cloth, which was a concession to the world. Datta learnt much about the mystic way of life through the teachings of Ramakrishna (1836-1886), known to his followers as Paramahamsa. Ramakrishna's chief disciple was Swami Vivekananda (1863-1902) whose teaching was highly influential in India and other countries. He impressed on followers such as Datta the Vedanta philosophy which he summarised as follows:-
Each soul is potentially divine. The goal is to manifest this Divinity within by controlling nature, both external and internal. One should do this by work, by worship, by mental discipline, by philosophy. By one or more, or all of these, one could achieve the goal and be free.Datta studied these religious teachings, reading many books on religion, and lived his life according to this philosophy. In 1907, he passed the entrance examinations for Calcutta University (now known as Kolkata University) and, given his high level of performance, he was awarded a scholarship. He attended Presidency College, which was an English style higher education college originally named Hindu College. It was founded in 1817 and was renamed Presidency College in 1855 coming under the control of Calcutta University two years later. Datta was awarded a Bachelor of Science degree in 1912 and continued to study for a Master's degree. He was due to sit the examinations for a Master's degree in Pure and Applied Mathematics in early 1914 but, in November of the previous year he was reported missing :-
In November of 1913 (a few months before his Master's examination), he left home (very likely he intended to become sannyasi) and was reported missing. His eldest brother Rebati Raman Datta found him in Haridwar (near the Himalayas) and brought him home, taunting him that he had run away for fear of failing the examination. But Datta said he would receive a first class degree, which in fact he did in 1914 when he passed the Master's examination in Pure and Applied Mathematics.That he had gone to Haridwar is not surprising since it is one of the seven holiest places in India to Hindus. There Hindus bathe in the Ganges which washes away sins. It is also not surprising the Datta did exceptionally well in the Master's examinations he took in 1914 for he had already had two papers accepted for publication by the Calcutta Mathematical Society, namely On a physical interpretation of certain formulae in the theory of elasticity (1910-11) and On the figures of equilibrium of a rotating mass of liquid for laws of attraction other than the law of inverse square (1911-12).
For a complete (at least as complete as we can make it) list of Datta's papers see THIS LINK.
On the results of his Master's examinations, Datta was awarded a scholarship to study for his doctorate at Calcutta University. He was also appointed as a lecturer in Pure and Applied Mathematics at the University Science College. This College of Calcutta University (also known as Rajabazar Science College) was founded in 1914 to form a base for the postgraduate sections of the science departments in the university. The topic that Datta studied for his doctorate was hydrodynamics. He published a number of papers while undertaking research. For example On the stability of two coaxial rectilinear vortices of compressible fluid (1918-19), Notes on vortices in a compressible fluid (1920), and On the stability of two rectilinear vortices of compressible fluid moving in an incompressible liquid (1920). In the introduction to his paper On the motion of two spheroids in an infinite liquid along their common axis of revolution (1921), Datta writes:-
Though the problem of the motion of two spheres in an infinite liquid along the line joining their centres has been completely solved by various investigators, the first writer to attempt the corresponding problem for two spheroids or ellipsoids is Professor Karl Pearson. His method does not, however, admit of further development and therefore, does not lead to the complete solution of the problem. In a previous paper, I have shown how the problem can be completely solved in the case of two spheroids of revolution of small ellipticities, the motion of the solids being along their common axis of revolution. The present paper deals with the more general case of the same problem in as much as no limitation has been imposed as regards the ellipticities. It will be seen that the success of the problem depends on certain transformation theorems for spheroidal harmonics which were not known before, though the corresponding theorems for spherical harmonics were given long ago by Bessel. All the results in this paper are believed to be new.Datta was awarded his doctorate in 1920 but his deep religious beliefs meant that he did not seek a traditional academic career. We have already noted that he was a follower of Sankara and, in 1920, he was initiated into his movement taking as his guru Swami Vishnu Tirthji Maharaj (1889-1969) :-
Datta always retained his religious beliefs and saint-like nature. He completed critical studies and reviews of the 'upanisads' and other philosophical works, always remaining aloof from worldly pursuits. So unconcerned was he for personal gain that when the Rashbehari Ghosh Professorship of the Science College fell vacant and was offered to him, he rejected the honour, saying: "After a couple of days I shall become sannyasi [and so] I have no need for the promotion." However, since no other suitably qualified person was available for the post, he took the assignment and carried out the job successfully for three years without accepting any additional allowance.Ganesh Prasad (1876-1935) was an Indian mathematician who had undertaken research in England at the University of Cambridge and in Germany at the University of Göttingen. After five years in Europe learning from Ernest Hobson and Andrew Forsyth at Cambridge, and David Hilbert, Georg Cantor and Arnold Sommerfeld at Göttingen, Pradesh returned to India where he was appointed first to Muir Central College, Allahabad, and then to Queen's College, Benares. In 1914 he became head of mathematics at the University of Calcutta and so was head of department when Datta was a student. Prasad left Calcutta in 1917 and was at Benares until 1923 when he returned to Calcutta as Hardinge Professor of Mathematics. This was to lead to a significant change in Datta's career. Although Prasad was an expert on potential theory and the theory of real variables, he was also very interested in the history of mathematics. His influence on Datta saw him change his research interests away from hydrodynamics and to the history of mathematics.
Datta's first publications on the history of mathematics were five papers all published in 1926. These are: Al-Birini and the origin of Arabic numerals; A note on Hindu-Arabic numerals; Two Aryabhatas of Al-Birini; Hindu (non-Jaina) values of π ; and Early literary evidence of the use of zero in India.
See THIS LINK for a complete list of Datta's publications on the history of mathematics.
On 20 December 1927 he delivered the lecture 'Contribution of the Ancient Hindus to Mathematics' to the Allahabad University Mathematical Association. This address was published in the Bulletin of the Allahabad University Mathematical Association in two papers totalling 60 pages in length. However, in 1929 he retired from his position at the university intending to give up both teaching and research. In 1931 he was persuaded by Ganesh Prasad to come out of retirement and deliver the Readership Lectures at Calcutta University. He chose as his topic The Science of the Sulba. A study in early Hindu geometry and the lectures were written up as a 240-page book published by the University of Calcutta. In reviewing this book Raymond C Archibald writes :-
Dr Datta's volume is one which should be in the hands of every student of the history of mathematics. It is serious in purpose, presents arguments pro and con fairly and fully and contains many original points of view and scores of exact references to authorities and texts. So much information regarding the sulbas has not been earlier available in any readily accessible English source. Coming from a proved scholar long experienced in dealing with historical questions, it will undoubtedly inspire further research leading to more correct views of early Indian geometry and its relation to intellectual achievements of other nations.The book was published in 1932 and in a Preface, written on 28 July of that year, Datta writes:-
I tender grateful thanks to Mr A C Ghatak, Superintendent, and to the staff of Calcutta University Press for kindly expediting publication of the book in order to help me to go back to my retirement earlier.Indeed, in 1933 Datta retired from the University of Calcutta for the second and final time. He lived a simple itinerant life over the following years, drifting from place to place. However, he continued to undertake research in the history of mathematics and published papers in 1935, 1936 and 1937. In 1938 he became a sannyasi, taking the name Swami Vidyaranya. He had been a vegetarian all his life but now he lived in total poverty, accepting no gifts, and having no material possessions or emotional attachments. He did not give up research, however, for in these years he undertook research on the ancient history of the Bhagavata religion and the ancient story of Advaita philosophy. This work was published in several volumes after his death.
When he retired in 1933, Datta gave the manuscript of his three volume work History of Hindu Mathematics to his young colleague Avadhesh Narayan Singh. The basis for this book had been the lectures Datta gave to the Allahabad University Mathematical Association in December 1927. Singh published the first two of these volumes as a joint publication, the first volume History of Hindu Mathematics. A Source Book (Part 1: Numerical notation and arithmetic) in 1935 and the second volume History of Hindu Mathematics. A Source Book (Part 2: Algebra) in 1938. In a review of the first volume Lao Genevra Simons writes :-
Readers of the 'Monthly' have become familiar with the name of one of the authors of this work since articles by B Datta have been appearing over a period of ten years. Through these articles, he has won a place as a reliable research worker in the field of Hindu mathematics. It is gratifying that a work on the history of Hindu mathematics has now come from the hands of these two Hindu scholars; moreover that a complete history to appear in compact form is here begun with the promise of volumes to come. The work under consideration is the first part and deals with the history of the numeral notation and of arithmetic. The second part, we are told, is devoted to algebra and the third part contains the history of geometry, trigonometry, calculus and various other topics such as magic squares, theory of series and permutations and combinations. ... Datta and Singh's 'History of Hindu Mathematics' should be in every library which reaches standards covered by the word "approved." It should be owned by individuals who have any interest whatever in the history of the progress of science. From the standpoint of authoritative subject matter and from that of book-making, it is a notable history.However, the third volume was never published. Beginning in 1980 Kripa Shankar Shukla revised the material of the third volume and published it as a series of nine papers between 1980 and 1993. See THIS LINK for the titles of these papers.
Article by: J J O'Connor and E F Robertson