He attended the University of London, where he obtained his Bachelor of Science in Mathematics and Physics in 1943, his Master of Science in Mathematics in 1945, and his Doctor of Philosophy in Mathematical Physics in 1948, his thesis being entitled "The flexure problem in elasticity".
He was the Leader of the Democratic Labour Party (DLP) from 1960 to 1969 and Leader of the Opposition in Parliament from 1961 to 1963, succeeding Ashford Sinanan. He was also a faculty member at the University of London, eventually holding the position of Reader of Mathematics. He also has a daughter, Anne Gasteen, born in 1959.
He was awarded the Trinity Cross (the nation"s highest award) in 1969.
Capildeo held lectureships at the University of London, including at both University College London and at Westfield College. He also taught briefly at Queen"s Royal College (1945) and was Principal of the Polytechnic Institute in Portuguese of Spain in 1959.
While Capildeo was a man of undoubted intelligence, his entry into politics in the late 1950s was because the political figures who entered the DLP in 1957 did not trust each other, and could only agree on him. Though he left Trinidad in 1939 to study medicine, Rudranath Capildeo changed his course of study, focusing on applied mathematics and physics.
He was committed to understanding the nature of space and time and this sparked his interest in understanding Einstein"s Theory of Special Relativity.
This work led to several new theories, which had practical implications in aerodynamics and space. They included "The Flexure Problem in Elasticity" (Doctor of Philosophy thesis) and his study on the "Theory of Rotation and Gravity" named Capildeo’s Theory, which had applications in early outer-space expeditions in the 1960s and 1970s. His political career was unusual, since he was active only during election campaigns (in 1961 and 1967) and during the summer months.
His conduct of the last pre-independence electoral campaign, in 1961, was also unusual, beginning with his declaration that because he understood Einstein he could "compress the time" necessary to undo what the sitting government had done.
Not only did Capildeo produce many significant mathematical theories and a book on Vector Algebra and Mechanics in 1967, he also studied law in London in 1956. Two years later he was admitted to practice as a barrister-at-law in Trinidad.
He founded and led the Democratic Labour Party (DLP) in 1960, and became Leader of the Opposition in the Trinidad & Tobago Parliament (1960-1967). With Doctor Eric Williams as Prime Minister, both men laid the foundation for an independent Trinidad and Tobago.
Capildeo was also responsible for having the freedom of worship included in the Constitution of Trinidad and Tobago and Service Commissions (because he felt that service commissions would ensure equality and fairness in the appointment of people to public office).