Mathematical Quotations -- F

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Focus Newsletter (MAA)

Sample recommendation letter:

Dear Search Committee Chair,

I am writing this letter for Mr. John Smith who has applied for a position in your department. I should start by saying that I cannot recommend him too highly.

In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you.

His dissertation is the sort of work you don't expect to see these days. It definitely demonstrates his complete capabilities.

In closing, let me say that you will be fortunate if you can get him to work for you.

A. D. Visor (Prof.)

de Fermat, Pierre (1601?-1665)

[In the margin of his copy of Diophantus' Arithmetica, Fermat wrote]
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.

And perhaps, posterity will thank me for having shown it that the ancients did not know everything.
In D. M. Burton, Elementary Number Theory, Boston: Allyn and Bacon, Inc., 1976.

Feynman, Richard Philips (1918 - 1988)

We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work.
Nobel Lecture, 1966.

Finkel, Benjamin Franklin

The solution of problems is one of the lowest forms of mathematical research, ... yet its educational value cannot be overestimated. It is the ladder by which the mind ascends into higher fields of original research and investigation. Many dormant minds have been aroused into activity through the mastery of a single problem.
The American Mathematical Monthly, no. 1.

Fisher, Irving

The effort of the economist is to "see," to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.
Transactions of Conn. Academy, 1892.

Fisher, Ronald Aylmer (1890 - 1962)

Natural selection is a mechanism for generating an exceedingly high degree of improbability.

To call in the statistician after the experiment is done may be no more than asking hm to perform a postmortem examination: he may be able to say what the experiment died of.
Indian Statistical Congress, Sankhya, ca 1938.

Flaubert, Gustave (1821-1880)

Poetry is as exact a science as geometry.

Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?

Fontenelle, Bernard Le Bovier (1657-1757)

Mathematicians are like lovers Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another.
Quoted in V. H. Larney Abstract Algebra: A First Course, Boston: Prindle, Weber and Schmidt, 1975.

A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry.
Preface sur l'Utilité des Mathématiques et de la Physique, 1729.

Leibniz never married; he had considered it at the age of fifty; but the person he had in mind asked for time to reflect. This gave Leibniz time to reflect, too, and so he never married.
Eloge de le Leibniz.

Frankland, W.B.

Whereas at the outset geometry is reported to have concerned herself with the measurement of muddy land, she now handles celestial as well as terrestrial problems: she has extended her domain to the furthest bounds of space.
Hodder and Stoughton, The Story of Euclid. 1901.

Frayn, Michael

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.
Constructions. 1974.

Frederick the Great (1712-1786)

To your care and recommendation am I indebted for having replaced a half-blind mathematician with a mathematician with both eyes, which will especially please the anatomical members of my Academy.
[To D'Alembert about Lagrange. Euler had vacated the post.]
In D. M. Burton, Elementary Number Theory, Boston: Allyn and Bacon, Inc., 1976.

Frege, Gottlob (1848 - 1925)

A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.
In Scientific American, May 1984, p 77.

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