Thomas Kailath began his career at the Digital Communications Group at the Jet Propulsion Laboratory in Pasadena, where he also held a visiting appointment at Caltech. In 1963 he joined Stanford University as an associate professor of electrical engineering, was promoted to professor in 1968, and in 1988 he was appointed the first holder of the Hitachi America Professorship in Engineering. As director of the Stanford Information Systems Laboratory (1971–81), he built it into a leading center for communications, control, and signal processing research before becoming associate chair of the Electrical Engineering Department (1981–87). He assumed emeritus status in 2001, but has been recalled to continue his research and writing activities. 

Professor Kailath’s research and teaching have spanned a number of engineering and mathematical disciplines, with the major focus of his research changing roughly every decade. In the 1960s he contributed to information and communication theory. Next he turned his attention to state space estimation and control. In the 1980s he led a large research group in four major areas: smart antenna array processing, adaptive filtering theory, special purpose VLSI architectures for signal processing, and displacement structure theory for fast matrix and linear algebra computations. In the 1990s his group made contributions to two areas of semiconductor manufacturing: rapid thermal processing and optical lithography, where they showed how to break the widely believed 100 nm barrier for the smallest achievable critical dimensions.  

His work with a stellar array of over 100 doctoral and postdoctoral scholars has led to over 300 journal papers, a dozen patents, and several books and monographs, including the textbooks Linear Systems (1980) and Linear Estimation (2000). With his students, Professor Kailath cofounded several companies, two of which went public, while the others were acquired; his former students have formed over 20 companies themselves.

Professor Kailath received a 2012 National Medal of Science “for transformative contributions to the fields of information and system science, for distinctive and sustained mentoring of young scholars, and for translation of scientific ideas into entrepreneurial ventures that have had a significant impact on industry.” In 2017 he was honored with the Marconi Society’s Lifetime Achievement Award. He has also received the IEEE’s Education and Signal Processing Medals and its highest award, the IEEE Medal of Honor, “for exceptional contributions to the development of powerful algorithms for communications, control, computation, and signal processing.” Other major recognitions include election to the NAE, US National Academy of Sciences, and American Academy of Arts and Sciences; foreign membership in, among others, the Royal Society of London, Royal Spanish Academy of Engineering, Indian National Academy of Engineering, and Indian National Science Academy; the Padma Bhushan, India’s third-highest civilian award, presented by the country’s president, and a BBVA Foundation Frontiers of Knowledge Award for Information and Communication Technologies. In addition to being a fellow of the IEEE, Institute of Mathematical Statistics, Society for Industrial and Applied Mathematics, and American Mathematical Society, Professor Kailath has held Guggenheim, Churchill, and Humboldt fellowships.

He received his BE (telecom) degree from the College of Engineering, Pune, India, in 1956 and MS and ScD degrees from the Massachusetts Institute of Technology in 1959 and 1961, as well as several honorary degrees, most recently from the Technion and the National Technical University of Athens.