Top 115 Theorem Quotes & Sayings

Bell's theorem...proves that quantum theory requires connections that appear to resemble telepathic communication.

Indeed, it is a proven mathematical theorem that a doughnut is topologically distinct from a sphere.

A human being without the proper empathy or feeling is the same as an android built so as to lack it, either by design or mistake. We mean, basically, someone who does not care about the fate which his fellow living creatures fall victim to; he stands detached, a spectator, acting out by his indifference John Donne's theorem that "No man is an island," but giving that theorem a twist: that which is a mental and a moral island is not a man.

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

It is not so much whether a theorem is useful that matters, but how elegant it is.

The three discrete invariances - reflection invariance, charge conjugation invariance, and time reversal invariance - are connected by an important theorem called the CPT theorem.

A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions.

Too much knowledge could be a bad thing. I was lead to the Szemerédi theorem by proving a result, about squares, that Euler had already proven, and I relied on an "obvious" fact, about arithmetical progressions, that was unproved at the time. But that lead me to try and prove that formerly unproved statement- about arithmetical progressions-and that ultimately lead to the Szemerédi Theorem.

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance.

I tend to regard the Coase theorem as a stepping stone on the way to an analysis of an economy with positive transaction costs.

We live in a society where we're not taught how to deal with our weaknesses and frailties as human beings. We're not taught how to speak to our difficulties and challenges. We're taught the Pythagorean theorem and chemistry and biology and history. We're not taught anger management. We're not taught dissolution of fear and how to process shame and guilt. I've never in my life ever used the Pythagorean theorem!

[On the Gaussian curve, remarked to Poincaré:] Experimentalists think that it is a mathematical theorem while the mathematicians believe it to be an experimental fact.

The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.

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 then start to reason. What you do is trial and error, experimentation, guesswork.

Our offense is like the pythagorean theorem: There is no answer!

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem.

But my shift to the serious study of economics gradually weakened my belief in Major Douglas's A+B theorem, which was replaced in my thought by the expression MV = PT.

The missing piece in his stomach hurt so much-and eventually he stopped thinking about the Theorem and wondered only how something that isn't there can hurt you.

One cannot really argue with a mathematical theorem.

It gives me the same pleasure when someone else proves a good theorem as when I do it myself.

Science is the one culture that's truly global - protons, proteins and Pythagoras's Theorem are the same from China to Peru. It should transcend all barriers of nationality. It should straddle all faiths, too.

There's only one problem that bothers me. And that's something my theorem [ of Impossibility] really doesn't cover. In my theorem I was assuming people vote sincerely. The trouble with methods where you have three or four classes, I think if people vote sincerely they may well be very satisfactory. The problem is the incentive to misrepresent your vote may be high.

We re-make nature by the act of discovery, in the poem or in the theorem. And the great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself re-creates them. They are the marks of unity in variety; and in the instant when the mind seizes this for itself, in art or in science, the heart misses a beat.

In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.

I think that if your tenure case depends on your proving what you thought was a mathematical theorem and the proposed theorem turns out to be false just before your tenure decision, and you want to get tenure very badly, there is a sense in which it's perfectly understandable and reasonable of you to wish the proposed theorem were true and provable, even if it's logically impossible for it to be.

What philosophy worthy of the name has truly been able to avoid the link between poem and theorem?

There's no answer for my offense, just like the polythagorean theorem.

I'm no enthusiast for the Coase Theorem. I don't like it, but it's widely used.

Those who have more power are liable to sin more; no theorem in geometry is more certain than this.

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.

Any good theorem should have several proofs, the more the better.

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.

Share prices follow the theorem: hope divided by fear minus greed.

Heaven is angered by my arrogance; my proof [of the four-color theorem] is also defective.

There is no answer to the Pythagorean theorem. Well, there is an answer, but by the time you figure it out, I got 40 points, 10 rebounds and then we're planning for the parade.

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

And I believe that the Binomial Theorem and a Bach Fugue are, in the long run, more important than all the battles of history.

All I remember about the examination is that there was a question on Sturm's theorem about equations, which I could not do then and cannot do now.

To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.

Poetry is a theorem of a yellow-silk handkerchief knotted with riddles, sealed in a balloon tied to the tail of a kite flying in a white wind against a blue sky in spring.

When somebody discovers something like the quadratic formula or the Pythagorean theorem, the convention in science is that he can't control that idea. He has to give it away. He publishes it. What's rewarded in science is dissemination of ideas.

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

Bells theorem dealt a shattering blow to Einsteins position by showing that the conception of reality as consisting of separate parts, joined by local connections, is incompatible with quantum theory... Bells theorem demonstrates that the universe is fundamentally interconnected, interdependent, and inseparable.

We decided that 'trivial' means 'proved'. So we joked with the mathematicians: We have a new theorem- that mathematicians can prove only trivial theorems, because every theorem that's proved is trivial.

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

The great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself recreates them.

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.

You wouldn't think there was a need for a Coase Theorem, really.

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.

The axiom of conditioned repetition, like the binomial theorem, is nothing but a piece of insolence.

The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.

Any effect, constant, theorem or equation named after Professor X was first discovered by Professor Y , for some value of Y not equal to X.

Murphy's Law, that brash proletarian restatement of Godel's Theorem.

The Limbaugh Theorem was not about me giving me credit for something. It was simply sharing with you when the light went off.