Grunbaum, Branko (1926 - )
long since regarded
it as demeaning to
work on problems
in two or three
dimensions, in spite
of the fact that it
is precisely this
sort of mathematics
which is of
It would be very
somewhere down the
line you could ask a
computer if the
is correct and it
said, `Yes, it is
true, but you won't
be able to
This is not
mathematics; it is
being exposed to
Hilbert's work in
Quoted in P. Davis
and R. Hersh, The
Goodman, Nicholas P.
There are no deep theorems -- only theorems that we have not understood very well.
The Mathematical Intelligencer, vol. 5, no. 3, 1983.
Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 1754.
It has been said that figures rule the world. Maybe. But I am sure that figures show us whether it is being ruled well or badly.
In J. P. Eckermann, Conversations with Goethe.
I don't believe in natural science.
[Said to physicist John Bahcall.]
Ed Regis, Who Got Einstein's Office? Addison Wesley, 1987.
And for mathematical science, he that doubts their certainty hath need of a dose of hellebore.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956, p. 548.
The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
Gibbs, Josiah Willard (1839-1903)
Mathematics is a language.