Cases Quote by Carl Gustav Jacob Jacobi

“All mathematical proofs must be deductive. Each proof is a chain of deductive arguments, each of which has its premises and conclusion.”

— Morris Kline

This method of deduction ... is often called "combinatory". Its usefulness is not exhausted at this stage, but it does even at the outset…

— John Chadwick

“We may put it in this way: Deduction depends on Induction, if general propositions are only known to us through the facts: Induction depends…

— Carveth Read

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…

— Anonymous

Induction for deduction, with a view to construction.

— Auguste Comte

“Apply reason and evidence to the problems around you. Reach conclusions, then test them. See if your deductions stand up to testing. Only then…

— Mitchell Hogan

The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his…

— Thomas Huxley

“Mathematics works only with computationally reducible systems. Axioms and deductive logic are intended to provide shortcuts, to give general results that can compress a…

— Richard Bookstaber

All mathematics is tautology.

— Ludwig Wittgenstein

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards,…

— Herbert S. Gaskill

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established,…

— Bertrand Russell

Mathematics is not a deductive science, that's a cliché ... What you do is trial and error, experimentation, guesswork.

— Paul Halmos