There are three things we all should do every day. We should do this every day of our lives. Number one is laugh. You should laugh every day. Number two is think. You should spend some time in thought. And number three is, you should have your emotions moved to tears, could be happiness or joy. But think about it. If you laugh, you think, and you cry, that's a full day.
Jimmy Valvano,
1782
 
Mathematics is much more than computation with pencil and a paper and getting answers to routine exercises. In fact, it can easily be argued that computation, such as doing long division, is not mathematics at all. Calculators can do the same thing and calculators can only calculate - they cannot do mathematics.
John A. Van de Walle, from Elementary School Mathematics: Teaching Developmentally.
379
 
[Fourier's theorem] is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly recondite questions in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth's crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.
Edward Van Vleck, quoted in A Radical Approach to Real Analysis by David Bressoud
1146
 
M. Poincet [sic] read Henri Poincare in the text. M. Princet has studied at length non-Euclidean geometry and the theorems of Riemann, of which Gleizes and Metzinger speak rather carelessly. Now then, M. Princet one day met M. Max Jacob and confided him one or two of his discoveries relating to the fourth dimension. M. Jacob informed the ingenious M. Picasso of it, and M. Picasso saw there a possibility of new ornamental schemes. M. Picasso explained his intentions to M. Apollinaire, who hastened to write them up in formularies and codify them. The thing spread and propagated... Cubism, the child of M. Princet, was born.
Loius Vauxcelles, quoted in The Fourth Dimension and non-Euclidean Geometry in Modern Art by Linda Dalrymple Henderson.
664
 
Labor wants also pride and joy in doing good work, a sense of making or doing something beautiful or useful - to be treated with dignity and respect as brother and sister.
Thorstein Veblen,
1427
 
The outcome of any serious research can only be to make two questions grow where only one grew before.
Thorstein Veblen,
1426
 
Any mathematical science is a body of theorems deduced from a set of axioms. A geometry is a mathematical science. The question then arises why the name geometry is given to some mathematical sciences but not to others. It is likely that there is no definite answer to this question, but that a branch of mathematics is called geometry because the name seems good on emotional or traditional grounds, to a sufficient number of competent people.
O. Velben and J. H. C. Whitehead, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
380
 
With education symmetrical and true we will take the dead mass buried by slavery's hand and touch them to life. This beauteous angel, which has always done its work for those on earth, will roll away the stone from the tomb where is buried a race, and my people will come forth to their glory and the amazement of the world.
William Tecumseh Vernon, quoted in Quotations in Black, by Anita King.
381
 
Art is never finished, only abandoned.
Leonardo da Vinci,
1052
 
Simplicity is the ultimate sophistication.
Leonardo da Vinci,
1050
 
There is an astonishing imagination even in the science of mathematics... We repeat, there is far more imagination in the head of Archimedes than in that of Homer.
Francios Voltaire,
382
 
We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.
Francios Voltaire,
383
 
The art of being a bore is to tell everything.
Voltaire,
514
 
When we cannot use the compass of mathematics or the torch of experience... it is certain that we cannot take a single step forward.
Voltaire,
890
 
Prejudices are what fools use for reason.
Voltaire,
984
 
He who can't remember his own childhood is a poor educator.
Marie Von Ebner-Eschenbach, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio.
94
 
Few people have the imagination for reality.
Johann Wolfgang von Goethe,
1626
 
It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.
John von Neumann, from "The Mathematician," in The World of Mathematics, by James R. Newman.
386
 
But still a large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.
John von Neumann, quoted in Out of the Mouths of Mathematicians, by R. Schmalz.
385
 
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
John von Neumann, quoted in Single Variable Calculus, by James Stewart.
384
 
Truth is much too complicated to allow anything but approximations.
John von Neumann, quoted in Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, by Manfred Schroder.
570
 
Just because some of us can read and write and do a little math, that doesn't mean we deserve to conquer the universe.
Kurt Vonnegut, from Hocus Pocus.
387
 
I would rather die for virginity than for petroleum, I think. It's more literary, somehow.
Kurt Vonnegut,
1622
 
All these textbooks [on analysis] share an approach, which I regard as mistaken and harmful. Specifically, in all of them the fundamental concepts of analysis are presented in a formal logical manner. No matter how much individual authors try to simplify proofs, to avoid formal rigor, to introduce intuitive imagery and concrete problems, they invariably, and above all, attempt to explain the formal scheme of modern analysis. As a result, the fundamental concepts of analysis appear not in their evolution but in their congealed form. This is the reason behind the depressing fact that the apparatus of analysis remains a dead apparatus in the hands of the students.
M. Ya. Vygodskii, quoted in "Two letters by N.N. Luzin to M.Ya. Vygodskii," translated by Abe Shenitzer, Monthly, January, 2000, pp. 64-5.
1756
 

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