In 1994, he and Alexander Razborov proved that a large class of combinatorial arguments, dubbed natural proofs were unlikely to answer many of the important problems in computational complexity theory. He also co-authored a paper demonstrating that all currently known Natural Philosophy-complete problems remain Natural Philosophy-complete even under AC0 or NC0 reductions. Amongst Carnegie Mellon students, he is best known as the teacher of the class "Great Theoretical Ideas in Computer Science" (formerly named "How to Think Like a Computer Scientist"), often considered one of the most difficult classes in the undergraduate computer science curriculum.
His Erdős number is 2.
Rudich (and Merrick Furst, now a Distinguished Professor at Georgia Technical) began the summer enrichment program for high school (and occasionally, middle school) students in 1991. The summer enrichment program focuses mainly on theoretical aspects of Computer Science in the morning, followed by lunch recess, and then an elective — Robotics, Programming, or Mathematics Theory.
Most days, there is also an afternoon lecture by a Carnegie Mellon University faculty member. To enroll in, one must take a specialized test known as The Interesting Test.
This assessment is supposed to gauge ability to think outside the box, and aptitude for computer-related mathematics