Mathematical Certainty Quotes

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

I can calculate the motion of heavenly bodies, but not the madness of people.

Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.

My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? Because I have studied it from all sides for many years; because I have examined all objections which have ever been made against the infinite numbers; and above all because I have followed its roots, so to speak, to the first infallible cause of all created things.

Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.

I don’t believe in statistics. I believe in calculus.

If two people loved, they slept together; it was a mathematical formula, tested and proved by human experience.

But again and again there comes a time in history when the man who dares to say that two and two make four is punished with death. The schoolteacher is well aware of this. And the question is not one of knowing what punishment or reward attends the making of this calculation. The question is one of knowing whether two and two do make four

I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.

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?

Doubt everything at least once, even the sentence "Two times two is four."

To understand God’s thoughts we must study statistics, for these are the measure of his purpose.

I believe that two and two are four and that four and four are eight.

But twice-two-makes-four is for all that a most insupportable thing. Twice-two-makes-four is, in my humble opinion, nothing but a piece of impudence. Twice-two-makes-four is a farcical, dressed-up fellow who stands across your path with arms akimbo and spits at you.

When speculation has done its worst, two and two still make four.

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.'

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.

I entertain no doubts as to the truths of the tranfinites, which I recognized with God's help and which, in their diversity, I have studied for more than twenty years; every year, and almost every day brings me further in this science.

It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.

I knew that he was as reliable as a mathematical formula.

To every problem there is already a solution, whether you know it or not. To every sum in there is already a correct answer, whether the mathematician has found it or not.

My whole life . . . two and two has made four.”... “But now . . . it’s all gone wrong.” She shook her head. “It doesn’t make four anymore. It makes you.