On the Work of Madhu Sudan

Madhu Sudan is the recipient of the 2002 Nevanlinna Prize. Sudan has made fundamental contributions to two major areas of research, the connections between them, and their applications. The first area is Coding Theory. Established by Shannon and Hamming over 50 years ago, it is the mathematical study of the possibility of and the limits on reliable communication over noisy media. The second area is Probabilistically Checkable Proofs (PCPs). By contrast, it is only 10 years old. It studies the minimal resources required for probabilistic verification of standard mathematical proofs. My plan is to briefly introduce these areas, their motivation and foundational questions, and then to explain Sudan’s main contributions to each. Before we get to the specific works of Madhu Sudan, let us start with a couple of comments that will set up the context of his work.