Mathematical Proof Quotes

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain.

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

Induction for deduction, with a view to construction.

I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them.

Many people believe that the grains of sand are infinite in multitude ... Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe

About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.

If you have ever studied geometry, you remember that by a course of reasoning Euclid proves that all the angles in a triangle are equal to two right angles. Euclid has shown you how to work it out. Now, if you undertake to disprove that proposition, and to show that it is erroneous, would you prove it to be false by calling Euclid a liar?

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.

The more I read, to me the more incredible everything is. Based on what I've read, there are all these other dimensional planes and spaces, mathematically proven.

… mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

We are on the verge: Today our program proved Fermat's next-to-last theorem.

No human investigation can be called real science if it cannot be demonstrated mathematically.

It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.'

There is no royal road to geometry.

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

Proof, one might say, does not merely shew that it is like this, but: how it is like this. It shows how 13+14 yield 27.

A mathematical theorem can be true whether or not it is realized in the world.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

We cannot ... prove geometrical truths by arithmetic.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.

...from the same principles, I now demonstrate the frame of the System of the World.

I hope no man takes what I said about the living and dieing of men for mathematical demonstration.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.