B. S. Madhava Rao

Bangalore Srinivasarao Madhava Rao (29 May 1900 – 11 June 1987) was an Indian mathematician and theoretical physicist who served as Professor of Mathematics and later University Professor and Principal at Central College, Bangalore. He held a sustained dual affiliation with the Indian Institute of Science (IISc) from 1935 to 1938, during which he worked with Max Born on Born's nonlinear electromagnetic field theory, producing eight published papers and a doctoral thesis on the subject. Homi J. Bhabha, writing from Bombay in November 1939 having recently returned from Cambridge, wrote to Madhava Rao asking if he, Bhabha, could come to Bangalore to work together on relativistic wave equations. Madhava Rao agreed, and for the next three to four years the two men — along with Harish-Chandra — worked closely on the subject. The mathematical constructs produced by this collaboration — the Bhabha–Madhavarao theory, the Madhavarao algebra and the Madhavarao ring — are named in the physics and mathematics literature. In 1938 he published two papers in the German journal Physikalische Zeitschrift engaging directly with Johannes Stark — Nobel laureate and leading proponent of Deutsche Physik — in defence of Max Born's field theory and modern quantum mechanics. He also served from 1934 as Secretary and Editor of the *Proceedings* of the Indian Academy of Sciences, and held the Lokmanya Tilak Chair in Applied Mathematics at the University of Poona.

Early life and education

Rao was born on 29 May 1900 in Chamrajnagar, in the Kingdom of Mysore. His father, M. Srinivasa Rao, served as a Head Master for over forty years across several middle schools in Mysore State. and then Central College, Bangalore (1915–1919), where he obtained his B.Sc. from the University of Mysore with first class in Mathematics and Science, winning a medal and coming first in the University — the degree certificate bearing the signature of Krishna Raja Wadiyar IV, Maharaja of Mysore, as Chancellor. C.V. Raman, then Palit Professor of Physics at Calcutta, described him as having "a distinct taste for mathematical research" and recommended him strongly for a foreign scholarship to European universities. He was subsequently awarded a scholarship to the University of Calcutta (1919–1921), obtaining his M.Sc. in Pure Mathematics, standing second in the first class and winning a medal.

The D.Sc. was a degree by submitted published works, examined externally. The University of Calcutta appointed Hermann Weyl, then at the Institute for Advanced Study, Princeton, as external examiner. In his report dated 26 January 1938, Weyl described the eight submitted papers as forming "an impressive whole dealing with all aspects of Born's non-linear, electro-magnetic field theory," showing their author to possess "a versatile and imaginative mind, and the mathematical skill necessary for handling such problems successfully." While offering technical criticisms and expressing broader reservations about Born's field theory programme, Weyl concluded that Madhava Rao "has turned many stones which before had been left unturned" and that his work was "solid enough to impart convincing power" to the impression that Born's theory had fundamental limitations — and approved the thesis, recommending conferment of the D.Sc. The original examination report, signed by Weyl from Princeton, is preserved in the Madhava Rao family archive. A covering letter from Weyl to Dr. B.B. Dutt, Controller of Examinations at the University of Calcutta, reveals that the University had simultaneously approached Jacques Hadamard in Paris and Oswald Veblen at Princeton as co-examiners. Although Weyl noted in January 1938 that he had been unable to reach Hadamard, all three examiners ultimately submitted reports; the University of Calcutta Syndicate recorded on 31 May 1938 that it had read "a joint report from Prof. Jacques Hadamard, Professor Oswald Veblen and Professor Hermann Weyl" and resolved to admit Madhava Rao to the degree.

Career

Central College, Bangalore

Madhava Rao joined the engineering college of the University of Mysore as Assistant Professor in 1922, following a brief period as Research Scholar in 1921. In 1938 he was appointed to a newly created Chair of Professor of Applied Mathematics at Central College, Bangalore, where he had previously been a student (1915–1919). The head of the mathematics department at Central College at that time was Prof. K.S.K. Iyengar, who had initiated a programme of modernising the curriculum to include post-graduate courses in advanced mathematics and mathematical physics; Madhava Rao collaborated fully in teaching this new programme. After Iyengar's death in 1944, Madhava Rao assumed sole charge of the department. He was promoted to Professor Class I in 1948, and to University Professor and Principal in 1953.

Affiliation with the Indian Institute of Science (1935–1938)

In October 1935, Max Born — who had left Germany following the Nazi rise to power and was briefly based in Cambridge — joined IISc at C.V. Raman's invitation as Reader in Theoretical Physics. During Born's residency, Madhava Rao began working at the IISc Department of Physics, an affiliation he sustained for at least two years after Born's departure. All eight of his physics papers published between 1936 and 1938, indexed in the INSPIRE HEP database, carry the dual institutional affiliation of the University of Mysore and the Indian Institute of Science, Bangalore. The NCBS Archives records that "he had worked with Max Born on non-linear field theory."

Max Born and Hedi Born as guests at Madhava Rao's home in Bangalore, c. October 1935. Standing (l–r): B.S. Venkata Rao, Madhava Rao (holding son Arun), B.S. Bheema Rao. Seated (l–r): Ms. Fryer (teacher, Home School), Subhadra Bai, Shakuntala, Max Born, Hedi Born, Leelavathi, Kapila Bai (Mysore), Ms. Muriel Robinson (founder, Home School). B.S. Madhava Rao family archive; identifications confirmed by Leelavathi (BSM's daughter) in 2026. Several photographs of Born and Hedi Born at Madhava Rao's home in Bangalore, preserved in the Madhava Rao family archives, attest to the personal as well as professional nature of their connection.

Collaboration with Raman and Bhabha

Under the influence of Born and in collaboration with C. V. Raman and Homi J. Bhabha, Madhava Rao moved into the mainstream of theoretical physics. A letter from Bhabha dated 10 November 1939, written from his family home in Bombay having recently returned from Cambridge, proposes that the two collaborate on calculating the "Compton effect" of X-rays on charged mesons, and asks whether he, Bhabha, could come to Bangalore to continue this work together on relativistic wave equations. Madhava Rao agreed, and for a period of three to four years, the two — together with Harish-Chandra — worked on the topic, though mostly publishing individual rather than joint papers. The physicist N. Mukunda similarly noted Madhava Rao's influence on Bhabha in a 2011 appreciation published in Current Science.

The Stark Exchange (1938)

In 1938, Madhava Rao engaged in a direct scientific exchange with Johannes Stark — Nobel laureate in physics and the most prominent advocate of Deutsche Physik, the Nazi-aligned movement that sought to marginalise quantum mechanics and theoretical physics in Germany. The exchange was conducted in the pages of the Physikalische Zeitschrift, a major German physics journal of the period, and unfolded across three consecutive papers in the same issue (Vol. 39, Issue 5):

In his paper "Bemerkungen zur Ringstruktur des Elektrons" (Remarks on the Ring Structure of the Electron, pp. 187–189), Madhava Rao challenged Stark's classical model of the electron as an axial ring structure, arguing that Born's modified electromagnetic field equations were the only mathematically consistent path to resolving the divergence problem in electrodynamics. Stark published a response (pp. 189–193) in the same issue. Madhava Rao replied in "Antwort auf Starks Bemerkungen" (Reply to Stark's Remarks, pp. 193–194), received by the journal on 2 September 1937, explicitly defending Werner Heisenberg's theoretical methods and Arnold Sommerfeld's models against Stark's experimentalist critique, and arguing that the advance of theoretical physics — not experiment alone — was essential to scientific progress. The paper concludes with a quotation from Hermann von Helmholtz in defence of theoretical understanding. Both papers are signed "Bangalore, University of Mysore." The family archive holds the original author offprints (Sonderdruck) of both papers. From 1960 to 1965, he held the Lokmanya Tilak Chair in Applied Mathematics at the University of Poona. Towards the close of his life he became an Associate of the Centre for Theoretical Studies at the Indian Institute of Science, Bangalore. and in Mathematische Annalen, "Complex representation in Born's field theory" (1936), and "Biquaternions in Born's electrodynamics" (1938). Together with his D.Sc. thesis and two papers published in German — one of which prompted the exchange with Stark described above — these form a substantial body of work in this area of theoretical physics. A 1937 paper by P. Weiss in the Mathematical Proceedings of the Cambridge Philosophical Society noted in a proof addendum that Madhava Rao had independently arrived at the same complex representation of Born's field theory as Schrödinger, whose treatment had appeared in 1935. Madhava Rao's work on action functions in Born's field theory was cited by Born himself as "Madhava Rao's action functions" in the Poincaré Institute Memoirs of 1936, and the subject also attracted a letter from Wolfgang Pauli explaining how some of the points Madhava Rao had raised could be resolved. Madhava Rao's subsequent papers developed the algebraic framework for particles of spin 3/2 and spin 2, culminating in the 1946 paper "Algebra related to particles of spin 3/2," co-authored with V.R. Thiruvenkatachar and K. Venkatachaliengar and published in the Proceedings of the Royal Society, Series A. The resulting mathematical formalism is known in physics literature as the Bhabha–Madhavarao theory or Bhabha–Madhavarao formalism, and continues to be cited in theoretical physics research. E.M. Corson's textbook Introduction to Tensors, Spinors, and Relativistic Wave Equations (Princeton University Press, 1953) refers extensively to the Madhavarao algebra and the Madhavarao ring as named constructs derived from this work, Thiruvenkatachar, writing in 1987, noted that Bhabha's 1949 review of the subject published in the Reviews of Modern Physics omitted any reference to Madhava Rao's work, despite the collaboration and Madhava Rao's independent continued contributions in this area. His final known published paper — "On a conjecture of Ramanujan and some simple deductions" — appeared in the Indian Journal of Mathematics in July 1967, contributed to the Prof. B.N. Prasad Memorial Volume, when he was 67 years old.

Magic squares and recreational mathematics

Madhava Rao maintained a lifelong interest in recreational mathematics. In his later years he devoted himself to a book on magic squares, developing the mathematical concepts found in the final chapter of Narayana Pandita (mathematician)'s fourteenth-century Sanskrit mathematical treatise, the Ganita Kaumudi (1356). He also presided over the Section of Mathematics of the Indian Science Congress in 1958, delivering a presidential address titled "Modern Algebra and Theory of Elementary Particles". In early 1955, shortly before his retirement from Central College, Madhava Rao received visits at his Basavanagudi home from Laurent Schwartz, the French mathematician awarded the Fields Medal in 1950, and Hans Maass, the German mathematician known for his work on Maass wave forms; Schwartz photographed the occasion and later wrote to Madhava Rao that he had shown the photographs to his uncle Jacques Hadamard in Paris.

Personal life

Madhava Rao was married to Subhadra Bai; they had five daughters and two sons. He was a dedicated sportsman: he captained the University of Mysore hockey team and represented the state, playing in Calcutta, Bombay and Madras; he won the B.K.S. Memorial Shield as College Champion in Tennis in 1932; and he served as President, Vice President, Secretary or member of associations including the Mysore State Hockey Association, Mysore Lawn Tennis Association, Basketball Federation and Table Tennis Association.

Awards and honours

Srinivasa Ramanujan Prize, University of Madras (1945) — for contributions to a generalised algebra related to elementary particles of nature Fellow of the Indian National Science Academy (FNA), elected as an Ordinary Fellow of the National Institute of Sciences of India on 1 January 1953

Archives

The B.S. Madhava Rao Papers (MS-013) are held at the Archives of the National Centre for Biological Sciences, Bangalore, spanning approximately 1918 to 1980 across 17 archive boxes. The collection includes correspondence with scientific collaborators, published papers and offprints, lecture notes, question papers, photographs, biographical material and a detailed bio data document in Madhava Rao's own hand. and is being considered for posthumous publication.