School of Mathematics and Statistics

PARADOX

	Not truth, nor certainty. These I forswore
	In my novitiate, as young men called
	To holy orders must abjure the world.

	"If ..., then," this only I assert;
	And my successes are but pretty chains
	Linking twin doubts, for it is vain to ask
	If what I postulate be justified
	Or what I prove possess the stamp of fact.

	Yet bridges stand, and men no longer crawl
	In two dimensions. And such triumphs stem
	In no small measure from the power this game,
	Played with the thrice attenuated shades
	Of things, has over their originals.

	How frail the wand, but how profound the spell!

                        Clarence R. Wylie, Jr.,  1948

A mathematician's failures:

"Now a mathematician has a matchless advantage over general scientists, historians, politicians, and exponents of other professions: He can be wrong. A fortiori, he can also be right.

A mistake made by a mathematician, even a great one, is not a "difference of a point of view" or "another interpretation of the data" or a "dictate of a conflicting ideology", it is a mistake. The greatest of all mathematicians, those who have discovered the greatest quantities of mathematical truths, are also those who have published the greatest numbers of lacunary proofs, insufficiently qualified assertions, and flat mistakes. By attempting to make natural philosophy into a part of mathematics, Newton relinquished the diplomatic immunity granted to non-mathematical philosophers, chemists, psychologists, etc., and entered into the area where an error is an error even if it is Newton's error; in fact, all the more so because it is Newton's error. The mistakes made by a great mathematician are of two kinds: first, trivial slips that anyone can correct, and, second, titanic failures reflecting the scale of the struggle which the great mathematician waged. Failures of this latter kind are often as important as successes, for they give rise to major discoveries by other mathematicians. One error of a great mathematician has often done more for science than a hundred impeccable little theorems proved by lesser men. Since Newton was as great mathematician as ever lived, but still a mathematician, we may approach his work with the level, tactless criticism which mathematics demands."

C. A. Truesdell

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