Mathematics - this may surprise or shock some - is never deductive in creation.

It saddens me that educated people don't even know that my subject exists.

... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."

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.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

The heart of mathematics is its problems.

Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?