Datta came from a poor Bengali family. He was a student of Ganesh Prasad, studied at University of Calcutta and secured the master's degree in mathematics in 1914 and doctorate degree in 1920 in applied mathematics. He taught at Calcutta University where he was Lecturer at University Science College, and during 1924–1929 he was Rhashbehari Ghosh Professor of Applied Mathematics. During the 1920s and 1930s he created a reputation as an authority on the history of Indian mathematics. He was also deeply interested in Indian philosophy and religion. In 1929 he retired from his professorship and left the University in 1933, and became a sannyasin (an ascetic, a person who has renounced worldly pleasures) in 1938 under the name Swami Vidyaranya.
History of Hindu Mathematics: A Source Book, written by him jointly with Avadhesh Narayan Singh (1901–1954) became a standard reference in the history of Indian mathematics. He also wrote a monograph on the shulba sutras. He published more than 70 research papers mostly related to history of Indian mathematics.
In the last years of his life, Swami Vidyaranya lived mainly at Puskara (in Rajasthan).
- R. C. Gupta (May 1980). "Bibhutibhusan datta (1888–1958), historian of Indian mathematics" (PDF). Historia Mathematica. 7 (2): 126–133. doi:10.1016/0315-0860(80)90033-6. Retrieved 9 March 2016.
- Bibhutibhushan datta and Awadhesh Narayan Singh (1962). History of Hindu Mathematics: a Sourcebook. Asia Publishing House.
- Frank J. Swetz (February 2010). "Mathematics in India". Convergence. doi:10.4169/loci003292. Retrieved 9 March 2016.
- L. G. Simons (1936). "L G Simons, Review: History of Hindu Mathematics – A Source Book. Part I. Numeral Notation and Arithmetic". American Mathematical Monthly. 43 (6): 367–368. doi:10.2307/2301803.
- Bibhtibhushan Datta (1932). The Science of the Sulba. A study in early Hindu geometry. University of Calcutta.
- J J O'Connor and E F Robertson. "Publications of Bibhutibhusan Datta". MacTutor History of Mathematics archive. University of St Andrews, Scotland. Retrieved 10 March 2016.