Kayal graduated with a B.Tech from the Computer Science Department of the Indian Institute of Technology, Kanpur (IITK), India in 2002. In that year, he, Manindra Agrawal and Nitin Saxena proposed the AKS Primality Test, which attracted worldwide attention, including an article in the New York Times.
Neeraj Kayal was given the Distinguished Alumnus Award of the IITK, for his work in computational complexity theory. He is also a recipient of the Gödel prize and the Fulkerson Prize for the same along with his co-authors. In 2012, he was awarded the Young Scientist Award from the Indian National Science Academy (INSA) for contributions to the development of arithmetic complexity theory including the development of a deterministic algorithm for primality testing, the resolution of the constant fan-in conjecture for depth three circuits, and a reconstruction algorithm for arithmetic formulas.
Kayal received his PhD in theoretical computer science from the Department of Computer Science and Engineering at the Indian Institute of Technology, Kanpur. He did postdoctoral research at the Institute for Advanced Study in Princeton and at Rutgers University. Since 2008, he has been working with the Microsoft Research Lab India as a researcher.
- Bornemann, F. Primes is in P: A Breakthrough for "Everyman". Notices of the AMS, May 2003.
- Robinson, S. (8 August 2002). "New Method Said to Solve Key Problem in Math". New York Times.
- IIT Kanpur Alumni Association, Distinguished Alumnus Award Profile: Neeraj Kayal
- European Association for Theoretical Computer Science (EATCS) announcement of 2006 Godel prize 
- Fulkerson Prize Announcements
- Young Scientists 2012 Award Announcement