Dr. Mathur was born in Moradabad, Uttar Pradesh (UP),India, on 30th August 1958, into a family steeped in into a family stepped in civil service. He is the youngest of six siblings, he had four older sisters and an older brother.
His parents were Jagdish Narain Mathur (an eminent irrigation engineer) and Bindeshwari Bali Mathur. His paternal grandfather, Dr Sarup Narain Mathur, was the first Indian civilian to become a Civil Surgeon in the erstwhile United Provinces of Agra and Oudh, and his maternal grandfather, Raja Rajeshwar Bali, the 13th Taluqdar of Daryabad, was Minister of Education, Medical Relief & Public Health and Local Self Government, in the first elected provincial government in the United Provinces from 1924 to 1928.
Dr. Mathur was educated in several schools in UP, as he followed in his father to dam-building sites and to university towns where his father taught dam construction. He finished his school education in Colvin Taluqdars College in Lucknow and at the University of Roorkee (currently Indian Institute of Technology, Roorkee, and also his father’s alma mater) from where he obtained a Bechelors degree in Chemical Engineering in 1979.
After completing his engineering, he was very clear that he wanted to work on energy and received a M.S. in Energy Engineering from University of Illinois at Chicago (UIC). However, UIC, which was one of the few Universities offering sectoral degree programs (in Materials Engineering, Information Engineering, etc., apart from Energy Engineering) changed over to the more traditional engineering disciplines (because of problems in accreditation), and so Mathur received a Ph.D. degree in Chemical Engineering in 1986, even though his doctoral thesis, titled “Hydrodynamics and Heat Transfer in Gas-Solid Fluidized Beds”, was in a mainstream energy engineering topic.
He started his career as Technical Assistant in the Department of Energy Engineering at UIC, and as Research Assistant in the Department of Chemical Engineering during 1979 to 1984.
He married his Roorkee classmate, Geetam Tiwari, in 1984. Geetam received a Ph.D. in Transportation Planning, also from UIC, in 1987, and joined the Indian Institute of Technology, Delhi, in 1990. She is a Professor of Civil Engineering at IIT-D, and currently holds the TRIPP Chair in the Institute. She was awarded a Ph.D. honoris causa by Chalmers University in 2009 for her work on the design of urban roads with mixed traffic.
Ajay and Geetam have two daughters.