Information theory continues to be the one thing that sets my brain on fire to this day. Nothing else in science/engineering/math is as self-reinforcing in its concepts to me. Perhaps this is simply because I deal with the consequences of information theory every single day when I have to make decisions like "should this be a 32 or 64 bit integer" or "Should I compress individual items or batches of those items"

You don't even have to be able to remember the equations to get this stuff right many times. There is definitely an intuition that you can develop where you look at a test file's size and instantly realize it could not contain the x264 stream of data you were expecting it to.

As a physicst I associate him primarily with Shannon-Nyquist, but his name has that Gaussian quality of cropping up everywhere.

He's up there, but von neumann still beats him out IMO.