Quote by Morris Kline

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

Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori,…

— Carl Gustav Jacob Jacobi

“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

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

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the…

— Timothy Gowers

Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.

— Edward Charles Titchmarsh

“Even science is inductive, relying on observations and best explanations, not always deductive conclusions.”

— Nabeel Qureshi

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

— Alfred North Whitehead

Proofs exist only in mathematics and logic, not in science.

— Satoshi Kanazawa

If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the…

— George Polya

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and…

— Hermann Weyl

The peculiarity of the evidence of mathematical truths is that all the argument is on one side.

— John Stuart Mill