Mathematical Proofs Quotes

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

I accept no principles of physics which are not also accepted in mathematics.

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

At the age of eleven, I began Euclid, with my brother as my tutor. ... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.

I like - I love calculus. I love linear algebra, probability and statistics, that kind of stuff. I just really like that.

Mathematics is as old as Man.

The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.

When I dealt with set theory, I could never make it be the music that I wanted.

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.

In mathematics we have long since drawn the rein, and given over a hopeless race.

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

All analysts spend half their time hunting through the literature for inequalities which they want to use and cannot prove.

Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.

As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics.

It would be better for the true physics if there were no mathematicians on earth.

I have found a very great number of exceedingly beautiful theorems.

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.

Need we add that mathematicians themselves are not infallible?

Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion.

I was a mathematics major and really into math.

I realized that anything to do with Fermat's Last Theorem generates too much interest.

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 work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practiced, is of the same general nature authority and tradition furnish the data, and the mental operations are deductive.