An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity.
In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
Loci: Convergence
Mathematical Quotations
Our library of quotations is organized alphabetically by surname of the author.
Leibniz, Gottfried Wilhelm (1646-1716)
Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.
Leibniz, Gottfried Wilhelm (1646-1716)
[About him:]
It
is rare to find
learned men who are
clean, do not stink
and have a sense of
humour.
Leybourn, William (1626-1700)
But leaving those of the Body, I shall proceed to such Recreation as adorn the Mind; of which those of the Mathematicks are inferior to none.
Lichtenberg, Georg Christoph (1742 - 1799)
I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.
Lichtenberg, Georg Christoph (1742 - 1799)
In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.
Lichtenberg, Georg Christoph (1742 - 1799)
The great trick of regarding small departures from the truth as the truth itself -- on which is founded the entire integral calculus -- is also the basis of our witty speculations, where the whole thing would often collapse if we considered the departures with philosophical rigour.
Lichtenberg, Georg Christoph (1742-1799)
All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true.
Lippman, Gabriel (1845-1921)
[On the Gaussian
curve, remarked to
Poincare:]
Experimentalists
think that it is a
mathematical theorem
while the
mathematicians
believe it to be an
experimental fact.
Littlewood, J. E. (1885-1977)
The theory of numbers is particularly liable to the accusation that some of its problems are the wrong sort of questions to ask. I do not myself think the danger is serious; either a reasonable amount of concentration leads to new ideas or methods of obvious interest, or else one just leaves the problem alone. "Perfect numbers" certainly never did any good, but then they never did any particular harm.
Littlewood, J. E. (1885-1977)
We come finally, however, to the relation of the ideal theory to real world, or "real" probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: "If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician." In practice he is apt to say: "Try this; if it works that will justify it." But now he is not merely philosophizing; he is committing the characteristic fallacy. Inductive experience that the system works is not evidence.