- He started out by talking about a problem ("Common signal processor transformations such as the DFT seem to have arbitrary decompositions"),
- then he developed an algebraic theory to pose the transformations,
- he built the machinery apply his theories (it generates the code that will do the transformation),
- finally he has made the code generation highly portable (that is he can generate for most environments)
So the talk went from some pretty deep math (I read the paper before hand so I knew most of the stuff he skimmed over) to some highly applied/systems areas (he talked a lot about optimization on compiler levels such as hyperthreading). As Dr. Niyogi, my AI professor, said about Turing, "He had a problem and he learn the mechanisms to solve it." He also had excellent presentation skills, as Dr. Dupont pointed out last year, "You not only need to have the great idea, you need to sell it."
Now it seems a lot of people debate over systems and theory, but this is the kind of science I want to do. Find a problem and go with it, doing what it takes to solve it. So that goes against the grain of many mathematicians who really just want to further math, but hey they are developing the theories that guys like Markus, Turing, and (hopefully) me use. With that thought, in answer to Peter's question ("Shouldn't you at some level consider yourself in theory?"): Yes I am at some level in a theoretical part of the world, but I am also at some level in a systems part of the world. I would rather just be called a problem solver, well a problem solver in training.