[3] Eliezer was educated at the Wesleyan Mission School, Puloly and Hartley College, Point Pedro (1926–33) where he passed the Cambridge Local Examinations with honours and distinction.

[1][4] He received a Ph.D. degree from Cambridge in 1946 after producing a thesis, supervised by Paul Dirac, on spinning electron and electromagnetic field.

[1][2][4] During his ten years at the university he was dean of the Faculty of Science from 1954 to 1957 and deputy pro-vice chancellor in 1955.

[1][2][4] Eliezer was a scholar at the Institute for Advanced Study from 1955 to 1956, working with J. Robert Oppenheimer.

[1][2][4] During his 15 years at the university he was dean of the School of Physical Sciences (1969–71 and 1982–83) and deputy vice-chancellor for a period.

[2][4][6] He was awarded the Maamanithar (Great Man) honour by the rebel Liberation Tigers of Tamil Eelam on 19 October 1997.

[3][4][6] Eliezer was vice-president of the Colombo branch of the Young Men’s Christian Association and a member of the Jaffna College board.

[1][6] Eliezer helped Tamil refugees fleeing to Australia following the 1983 anti-Tamil Black July riots.