Halmos, Paul R.
Mathematics is not a deductive science — that’s a cliche. 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.
I Want to be a Mathematician, Washington: MAA Spectrum, 1985.
The other extreme would be: doing only experiment in mathematics and claim that it is true in general. This should be written in: I want to be a Non-mathematician.