9 quotes
Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
The Development of Mathematics (1940)
Nearly always it is the recondite and complicated which is elaborated first; and it is only when some relatively unsophisticated mind attacks a problem that its deep simplicity is revealed.
The Development of Mathematics (1940)
All computation was greatly simplified early in the seventeenth century by the invention of logarithms.
The Development of Mathematics (1940)
There are no absolutes... in mathematics or in its history.
The Development of Mathematics (1940)
The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future; and should analysis ever appear to be without or blemish, its perfection might only be that of death.
The Development of Mathematics (1940)
In the entire history of Greek mathematics, all but the incomparable Archimedes and a few of the more heterodox sophists appear to have hated or feared the mathematical infinite. Analysis was thwarted when it might have prospered.
The Development of Mathematics (1940)
Whatever its source, mathematics has come down to the present by the two main streams of number and form. The first carried along arithmetic and algebra, the second, geometry. In the seventeenth century these two united, forming the ever-broadening river of mathematical analysis.
The Development of Mathematics (1940)
Each of five men—Lobachewsky, Bolyai, Plücker, Riemann, Lie—invented as part of his lifework as much (or more) new geometry as was created by all the Greek mathematicians in the two or three centuries of their greatest activity.
The Development of Mathematics (1940)
With the intrusion of irrational numbers to disrupt the integral harmonies of the Pythagorean cosmos, a controversy that has raged off and on for well over two thousand years began: is the mathematical infinite a safe concept in mathematical reasoning, safe in the sense that contradictions will not result from the use of this infinite, subject to certain prescribed conditions?
The Development of Mathematics (1940)