# Mathematical Quotations -- R

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### Raleigh, [Sir} Walter Alexander (1861-1922)

In an examination those who do not wish to know ask questions of those who cannot tell.
Some Thoughts on Examinations.

### Recorde, Robert (1557)

To avoide the tediouse repetition of these woordes: is equalle to: I will settle as I doe often in woorke use, a paire of paralleles, or gemowe [twin] lines of one lengthe: =, bicause noe .2. thynges, can be moare equalle.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.

### Reid, Thomas

It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

### Renan, Ernest

The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life.
Souvenirs d'enfance et de jeunesse.

### Rényi, Alfréd

If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
P. Turán, "The Work of Alfréd Rényi", Matematikai Lapok 21, 1970, pp 199 - 210.

### Richardson, Lewis Fry (1881 - 1953)

Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians' stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
Mathematics of War and Foreign Politics.

(after Edna St. Vincent Millay)
...Euclid alone
Has looked on Beauty bare.
He turned away at once;
Far too polite to stare.
The Mathematical Intelligencer, V. 16, no. 4 (Fall 1994), p. 20.

### Rivest, R., Shamir, A., and Adleman, L.

The magic words are squeamish ossifrage
[This sentence is the result when a coded message in Martin Gardner's column about factoring the famous number RSA-129 is decoded. See the article whose title is the above sentence by Barry Cipra, SIAM News July 1994, 1, 12-13.]

### Rohault, Jacques (17th century)

it was by just such a hazard, as if a man should let fall a handful of sand upon a table and the particles of it should be so ranged that we could read distinctly on it a whole page of Virgil's Aenead.
Traité de Physique, Paris, 1671.

### Rosenblueth, A

[with Norbert Wiener]
The best material model of a cat is another, or preferably the same, cat.
Philosophy of Science 1945.

### Rosenlicht, Max (1949)

You know we all became mathematicians for the same reason: we were lazy.

Hugo Rossi

In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.
Mathematics Is an Edifice, Not a Toolbox, Notices of the AMS, v. 43, no. 10, October 1996.

### Rota, Gian-carlo

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
In preface to P. Davis and R. Hersh The Mathematical Experience, Boston: Birkhäuser, 1981.

### Russell, Bertrand (1872-1970)

How dare we speak of the laws of chance? Is not chance the antithesis of all law?
Calcul des probabilités.

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

Although this may seem a paradox, all exact science is dominated by the idea of approximation.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.
The Autobiography of Bertrand Russell .

A good notation has a subtlety and suggestiveness which at times make it almost seem like a live teacher.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

If I were a medical man, I should prescribe a holiday to any patient who considered his work important.
The Autobiography of Bertrand Russell .

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
The Scientific Outlook, 1931.

With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway about the flux. A little of this, but not much, I have achieved.
The Autobiography of Bertrand Russell .

At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.
Principles of Mathematics. 1903.

A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.

The method of "postulating" what we want has many advantages; they are the same as the advantages of theft over honest toil.
Introduction to Mathematical Philosophy, New York and London, 1919, p 71.

Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.
The Impact of Science on Society, 1952.

[Upon hearing via Littlewood an exposition on the theory of relativity:]
To think I have spent my life on absolute muck.
J.E. Littlewood, A Mathematician's Miscellany, Methuen and Co. ltd., 1953.

"But," you might say, "none of this shakes my belief that 2 and 2 are 4." You are quite right, except in marginal cases -- and it is only in marginal cases that you are doubtful whether a certain animal is a dog or a certain length is less than a meter. Two must be two of something, and the proposition "2 and 2 are 4" is useless unless it can be applied. Two dogs and two dogs are certainly four dogs, but cases arise in which you are doubtful whether two of them are dogs. "Well, at any rate there are four animals," you may say. But there are microorganisms concerning which it is doubtful whether they are animals or plants. "Well, then living organisms," you say. But there are things of which it is doubtful whether they are living organisms or not. You will be driven into saying: "Two entities and two entities are four entities." When you have told me what you mean by "entity," we will resume the argument.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Portraits from Memory.

Men who are unhappy, like men who sleep badly, are always proud of the fact.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.

Work is of two kinds: first, altering the position of matter at or near the earth's surface relatively to other such matter; second, telling other people to do so. The first kind is unpleasant and ill paid; the second is pleasant and highly paid.

A sense of duty is useful in work but offensive in personal relations. Certain characteristics of the subject are clear. To begin with, we do not, in this subject, deal with particular things or particular properties: we deal formally with what can be said about "any" thing or "any" property. We are prepared to say that one and one are two, but not that Socrates and Plato are two, because, in our capacity of logicians or pure mathematicians, we have never heard of Socrates or Plato. A world in which there were no such individuals would still be a world in which one and one are two. It is not open to us, as pure mathematicians or logicians, to mention anything at all, because, if we do so we introduce something irrelevant and not formal.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

The desire to understand the world and the desire to reform it are the two great engines of progress.
Marriage and Morals.

It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.

### Rutherford, Ernest (1871-1937)

If your experiment needs statistics, you ought to have done a better experiment.
In N. T. J. Bailey the Mathematical Approach to Biology and Medicine, New York: Wiley, 1967.

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