Parthasarathy was born on 25 June 1936 in Madras,[1] into a modest but deeply religious Hindu Brahmin family.

Parthasarathy then moved to Kolkata to attend the Research and Training school at the Indian Statistical Institute, where he completed his Ph.D., under the supervision of C. R. Rao in 1962.

[8] Parthasarathy started his work on theoretical probability during his time at the Indian Statistical Institute.

[8] He later worked at the Steklov Mathematical Institute, USSR Academy of Sciences (1962–63), as lecturer where he collaborated with Andrey Kolmogorov.

[8] Parthasarathy is the namesake of Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants along with Bertram Kostant, R. Ranga Rao and Veeravalli S. Varadarajan which they introduced in 1967.