Sen was born in 1900 to Harendra Nath Sen, a lawyer and Nabanalini Devi.Their hometown was Gotan, near Shyamsundar in the district of Bardhaman, but Sen was educated at the Burdwan Municipal High School,Burdwan. He received a divisional scholarship in the matriculation examination in 1917.He obtained an F.A. in 1919 from Burdwan Raj College,then affiliated with the University of Calcutta,and earned first class honors in Sanskrit from the Government Sanskrit College in 1921.He then studied Comparative Linguistics|Comparative Philology in Kolkatta, scoring the highest recorded marks in 1923.The linguists Suniti Kumar Chatterji and Taraporewala were his teachers.Following this,he received the prestigious Premchand Roychand Scholarship and a PhD degree,exhibiting brilliant academic performance.He received the prestigious Ashutosh Memorial Gold Medal and Griffith Memorial prize twice,for his research. He was also awarded the University Gold medal and Sarojini medal.He joined the University of Calcutta as a lecturer in 1930, where he served as a professor for thirty four years.He became the second Khaira Professor in the Department of Comparative Philology after his mentor, Suniti Kumar Chatterji,in 1954.After assuming this title,the department attracted many scholars from India and abroad to study and conduct research.Professor Sen retired from the University in 1964. Sen was interested in historical syntax from an early age. He was the first scholar to explore the Old Indo-Aryan syntax in his book,Use of Cases in Vedic Prose(1928), and Buddhist Hybrid Sanskrit (1928).He later analyzed the syntax of Middle Indo-Aryan in An Outline of Syntax of Middle Indo-Aryan (1950).He also contributed significantly to the Bengali literature, addressing themes ranging from Mythology,the Puranas]] and Crime to Horror. Sen's crime stories have been compiled in the book Galpa Samgraha (2009). The London Asiatic Society honored him with the Jubilee Gold Medal in the year 1984, making him the first Asian to receive the prize. Other prizes he has received include the Rabindra Puraskar (1963), Ananda Puraskar (1966, 1984), Vidyasagar Puraskar (1981), Desikottam (1982), and the Padma Bhushan (1990). The Asiatic Society, Calcutta, awarded him the Jadunath Sircar Medal. He was elected as an honorary fellow of Sahitya Academi in 1973.
He published numerous significant articles and research papers during his long academic career. These include the Bangla Sahityer Itihas (5 Vol 1939, 1991), Bhashar Itibritta (1939, 1993), A History of Brajabuli Literature (1935), A Comparative Grammar of Middle Indo-Aryan (1960), Ramkathar Prak Itihas (1977), Bangla Sthannaam (1982), Bharat Kathar Granthimochan (1981), Bharatiya Arya Sahityer Itihas (1963, 1992, and Women’s Dialect in Bengali (1923). Bhashar Itibritta is the first book in the Bengali language that traces its historical evolution. In this book, he postulated Jharkhandi as the fifth dialect of the Bengali language. His book Bangala Sahitye Gadya (1934) still remains the best example of a systematic, stylistic description of the literary prose dialect of the language. The Etymological Dictionary of Bengali (in two volumes, 1971) is one of the largest works on historical etymology in any Indian language. Bangala Sahityet Itihas was also a monumental contribution and towers over his other publications. Rabindranath Tagore commended the book and wrote the preface. The English edition of the book was published by the Sahitya Academy in 1960. Pandit Jawaharlal Nehru wrote the foreword for this book. Diner Pore Din Je Gelo (The Days Pass By), published by Ananda Publishers, Calcutta, is the title of his famous autobiography. A college in his native village of Gotan has been named in his honor.