Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.
"The challenge of quantum mechanics is not in its complexity, but in its simplicity—it forces us to rethink our most basic assumptions about the universe."
"A key insight in computational learning theory is that the complexity of a learning problem is determined by the complexity of the hypothesis space and the amount of data available."
There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery.
