Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985.

A time will however come (as I believe) when physiology will invade and destroy mathematical physics, as the latter has destroyed geometry.

Daedalus, or Science and the Future, London: Kegan Paul, 1923.

Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle.

In H. Eves,
Mathematical Circles
Squared, Boston:
Prindle, Weber and
Schmidt, 1972.

In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world "simplest." It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = K(d^2x/dy^2) much less simple than "it oozes," of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plainman, namely, the rate of change of a rate of change.

Possible Worlds, 1927.

The shortest path between two truths in the real domain passes through the complex domain.

Quoted in The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.

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.

A mathematical theory is not ... complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

Source unknown

For every problem, there is one solution which is simple, neat, and wrong.

H.L. Mencken
(1880-1956)

Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection.

Manfred Schroeder,
*Fractals, Chaos,
Power Laws* 1991