Reliable Meaningful Communication

Madhu Sudan (Microsoft Research, New England)

Around 1940, engineers working on communication systems encountered a new challenge: How can one preserve the integrity of digital data, where a minor errors in transmission can have catastrophic effects?  The resulting theories of information (Shannon 1948) and error-correcting codes (Hamming 1950) created a ``marriage made in heaven'' between mathematics and its applications. On the one hand emerged a profound theory that could measure information and preserve it under a variety of adversarial injections of errors; and on the other hand the practical consequences propelled telephony, satellite communication, digital hardware and the internet. Today, as we allow computers and computational devices to interact freely with each other and control complex engineering systems, all with limited human intervention, we encounter a new challenge: How can we ensure that computers interpret the messages they receive from each other correctly so that they do not cause catastrophic actions due to misinterpretation? The resulting class of questions poses new challenges to mathematics: both in modelling, and in analysis. In this talk I will give a brief survey of the history of reliable communication, and outline the challenges of communicating meaningfully.