Definitions of various schools of thought
Mathematics
Science
Definition
Fundamentally defined by the scientific method of observation, hypothesis, experimentation and communication, science seeks to better understand causality.
Lessons
If it is not possible to devise an experiment in an attempt to prove a theory is wrong, then it isn’t a good scientific theory.
Physics
Engineering
Definition
Apply science and mathematics to create things that help solve human problems, retaining knowledge from previous applications that can be applied in future attempts to create more things.
Lessons
Failure is a critical part of the engineering process.
While engineering practice is largely limited to working with physicial things, engineering techniques can be applied in many disciplines where there are repeatable processes that can be improved.