The Problem With Multiplying Field Operators in Quantum Theory

Physicists and mathematicians can't calculate using infinities. They have developed work arounds, ways of approximating quantities that dodge the problem. These work arounds yield approximate predictions, which are good enough because experiments aren't infinitely precise either. You can do experiments and measure things to 13 decimal places and do calculations and they agree to all 13 decimal places. And it's just the most astonishing thing in all of science. It's all to do with field theory.