Originally Posted by

**aleazk**
Even in modern physics, and particularly in modern Quantum Field Theory, there's a lot of very important things in the standard theory that lack a rigorous definition (e.g., the measures in the path integrals, and a big etc.) Nevertheless, physicists make mathematical jugglings with these little ill-defined monsters and manage to obtain meaningful physical predictions from this mess. Astonishingly, these predictions have been proven to be very accurate in the experiments.