flip burgers

Sounds like you've bought into the factory/robot mentality.

Working in a factory or in telephone support is different from working in a job which requires thinking, creativity, and problem-solving. People can't invent new solutions for things for 8 hours straight, with only a rigidly-timed lunch break. Our brains don't work like that.

Sure, if your job is flipping burgers and refilling soft drinks, it doesn't take much brain power to do that, and there's no reason to be goofing off on the job. Just turn your brain off and follow the routine, day in and day out. But if you're trying to devise creative solutions to complex problems, this simply isn't going to happen according to a rigid plan, timed to the minute.

Math Vs Science

You can prove things in math. Math isn't science. Math is a special construct where you make a few assumptions and then spend eternity figuring out what the consequences of those assumptions are. Thus, when you prove something in math you're really saying that X is always true assuming your axioms.

In science you don't get to make up the axioms. The universe does and we get to try to figure out what they are.