On the Work of Madhu Sudan, Volume 50, Number 1

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 fifty 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 ten 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. • Madhu Sudan works in computational complexity theory. This research discipline attempts to rigorously define and study efficient versions of objects and notions arising in computational settings. This focus on efficiency is of course natural when studying computation itself, but it also has proved extremely fruitful in studying other fundamental notions such as proof, randomness, knowledge, and more. Here I will try to explain how the efficiency “eyeglasses” were key in this study of the notions proof (again) and error correction. • Theoretical computer science is an extremely interactive and collaborative community. Sudan’s work was not done in a vacuum, and much of the background to it, conceptual and technical, was developed by other people. The space I have does not allow me to give proper credit to all these people. A much better job has been done by Sudan himself; his homepage (http://theory.lcs.mit.edu/~madhu/) contains several surveys of these areas which give proper historical accounts and references. In particular see [13] for a survey on PCPs and [15] for a survey on the work on error correction.