I am sad to say the following comes from a school that I attended. This was from an alumni newsletter regarding the activities of one of the physics faculty.
“Since the time of Archimedes, sciences advanced along two avenues, through new experiments and through theory….”
I have a problem with just that first part, but it goes on:
“For many centuries, theoretical physicists devised clever mathematical methods to describe many physical phenomena, yet some of the most important ones – like the properties of matter, of proteins and living things, or of weather patterns – are far too complicated to predict with pure mathematics. However, the invention of computers presented another way of solving complex equations … As the these contributions increase, computation became the ‘third leg of science; and important path for future progress.”
The best part is “theoretical physicists devised clever mathematical methods…“. Exactly. One clever mathematical method they created was to break an otherwise unsolvable problem into a whole bunch of little solvable pieces. You don’t even need a computer. The Babylonians did something like this to estimate the square root of 2.
It is important to remember the bipedal nature of science. Create models. Compare models with real life. Maybe the model is a conceptual model, maybe it is a model based on vector calculus, maybe it is a calculation in python. They are all models. There is no third leg.