Quotes About Theorem

Mathematics is not a deductive science - that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

Mean-Value Theorem for Integrals, 123 but for Hal's synoptic purposes here it's enough to say that megatonnage is distributed among Combatants according to an integrally regressed ratio of (a)

We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas. Thus a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences.

You know the theorem of Pythagoras?" "The square of the hypotenuse is equal to the sum of the squares of the other two sides." "That's exactly it. And is that true for every example you've tried?" "Yes.

if a theorem is geometrically obvious why prove it? This was exactly the attitude taken in the eighteenth century. The result, in the nineteenth century, was chaos and confusion: for intuition, unsupported by logic, habitually assumes that everything is much nicer behaved than it really is.     Good

When people asked hilbert why he didn't prove Fermat's Last Theorem and win the Wolfskehl Prize, he said, "Why should I kill the goose that lays the golden egg?

Pythagoras." "Pih-who?" "He invented triangles.

This is where Bayes' Theorem comes in and helps us have a clearer picture. By using the theorem, we are forced to look at all data and update our hypothesis with new evidence.

Bayes' Theorem does: it helps us update a hypothesis based on new evidence.

Geometry has two great treasures; one is the Theorem of Pythagoras ; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

To me, coming from applied mathematics, a theorem was a statement about an everlasting mathematical truth—not the dressing up of a trivial observation in a lot of formalism.

In mathematics, in place of characters, you have variables or unknowns. If I'm trying to plot a theorem, I try to imagine these variables interacting with each other. The boundary of their interaction is the theorem.

The result that Noether obtained was stunning. She showed that to every continuous symmetry of the laws of physics there corresponds a conservation law and vice versa.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel. —Johannes Kepler

what you are doing is sort of architectural. You have to have a design in view, in which you design a chapter, or a proof of a theorem, as the case may be. Then you have to put it together out of words or out of symbols as the case may be, but if you don't have a clear architecture in mind then the thing won't end up being any good.

the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence.

the quadrature problem is a measure of the greatest difficulty, since it was shown in 1882 to be impossible.