55 Mathematical Proof Quotes
Following is our list of mathematical proof quotations and slogans full of insightful wisdom and perspective about what is a mathematical proof.
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Proof Mathematical Quotes
If only I had the Theorems! Then I should find the proofs easily enough. — Bernhard Riemann
To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it. — Pierre de Fermat
When you can measure what you are speaking about, and express it in numbers, you know something about it. — Lord Kelvin
We were the first to prove that proof-of-stake can have the same security properties as Bitcoin. — Charles Hoskinson
Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. — Eric Temple Bell
Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis? — Paul Halmos
God has the Big Book, the beautiful proofs of mathematical theorems are listed here. — Paul Erdos
Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science. — Mary Somerville
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs. — Felix Klein
I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof-sheets I read (what now stands), "It was Littlewood who said..." — John Edensor Littlewood
More Mathematical Proof Quotes
If only I had the Theorems! Then I should find the proofs easily enough. — Bernhard Riemann
To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it. — Pierre de Fermat
In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life. — Michael Atiyah
When you can measure what you are speaking about, and express it in numbers, you know something about it. — Lord Kelvin
We were the first to prove that proof-of-stake can have the same security properties as Bitcoin. — Charles Hoskinson
Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. — Eric Temple Bell
Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis? — Paul Halmos
God has the Big Book, the beautiful proofs of mathematical theorems are listed here. — Paul Erdos
Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science. — Mary Somerville
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs. — Felix Klein
I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of the positive integers was one of his personal friends." My reaction was, "I wonder who said that; I wish I had." In the next proof-sheets I read (what now stands), "It was Littlewood who said..." — John Edensor Littlewood
Mathematics consists in proving the most obvious thing in the least obvious way. — George Polya
I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions - they are not just repetitions of each other. — Michael Atiyah
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork. — Paul Halmos
Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof. — David Hilbert
What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas, theorems have not changed since the time of Archimedes. — Stanislaw Ulam
It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of one obvious fact in terms of something equally .. obvious. — Oliver Heaviside
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself. — Paul Lockhart
Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations. — Imre Lakatos
I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. — David Hilbert
What good your beautiful proof on the transcendence of Pi: Why investigate such problems, given that irrational numbers do not even exist? — Leopold Kronecker
A mathematician's reputation rests on the number of bad proofs he has given. — Abram Samoilovitch Besicovitch
[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it. — Proclus
A mathematical proof must be perspicuous. — Ludwig Wittgenstein
Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937. — Charles Proteus Steinmetz
Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof. — Gerolamo Cardano
The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. — George Polya
The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument. — IU?. I. Manin
We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context. — Hermann Weyl
A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem. — Atle Selberg
We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?" — Gian-Carlo Rota
Absence of proof isn't proof of absence. — Robert Buettner
Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does. — Lucio Russo
A mathematical proof is beautiful, but when you're finished, it's really only about one thing. A story can be about many things. — Bonnie Jo Campbell
A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details. — Hermann Weyl
It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out. — Emil Artin
Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed. — Edward Charles Titchmarsh
Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning. — John Locke
Without computers we will be stuck only proving theorems that have short proofs. — Kenneth Appel
... mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious. — Bertrand Russell
What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers. — Timothy Gowers
I think some intuition leaks out in every step of an induction proof. — Jim Propp
A witty statesman said, you might prove anything by figures. — Thomas Carlyle
Where mathematics and spirit join, where proof of the existence of mystery-salvific mystery-shimmers just below the surfaces of human perception, experience and the linguistic veil itself, Killarney Clary's new book-her best to date-dwells, plumbs, persuades and thrills. — Jorie Graham
If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way. — George Polya
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