He is Professor Emeritus of Applied Mathematics and served as interim Vice Chancellor[1] (President) at the University of Cape Town between March 2023 and July 2024.

He served as dean of faculty of science at UCT for seven years from 1999,[3] and thereafter was appointed to the South African Research Chair in Computational and Applied Mechanics.

[5] Reddy's teaching and research activities reflect his multidisciplinary perspectives, which he has pursued largely through the Centre for Research in Computational and Applied Mechanics (CERECAM) at the University of Cape Town, a centre comprising academic staff and their students in five different departments, straddling the engineering disciplines, mathematics, and biomedical sciences.

[13] The first edition of his research monograph, with Weimin Han, comprised a systematic treatment of mathematical aspects of classical plasticity from a modern perspective.

[17] The InterAcademy Partnership (IAP) is a global network of 140 member academies which work together to provide independent expert advice on scientific, technological and health issues.

Reddy served, over the period 2013 - 2019 as co-chair of IAP-Policy, the arm of the IAP that mobilizes the best scientists and engineers worldwide to provide high-quality, in-depth advice to international organizations and national governments on critical scientific issues.