Mahesh grew up in India and received his Bachelors' in Computer Science & Engineering from the University of Madras (1998). Following a two year stint in the Indian software industry, he returned to academia and earned his MS Electrical Engineering (2002), MS Physics (2004) and PhD Physics (2006), all from the University of Pittsburgh. He then undertook postdoctoral terms at the Center for Nonlinear Studies and the Materials Physics Applications Division, Los Alamos National Laboratory (2006 - 2009) and the Applied Math. Lab, Harvard University (2009 - 2011).
He was appointed Assistant Professor at the OIST Graduate University, Japan in 2012 and was promoted to Associate Professor in summer 2018. He holds visiting appointments as Research Staff Associate with the Abdus Salam International Centre for Theoretical Physics in Trieste, Italy (since 2018) and as a Faculty Associate with the International Centre for Theoretical Sciences, Tata Institute for Fundamental Research, Bangalore, India (since 2022).