A Quote by Paul R. Halmos on errors, justice, mathematics, reason, and science
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.
Source: I Want to be a Mathematician, Washington: MAA Spectrum, 1985.
Contributed by: Zaady