mathematical evolution Quotes

Calculus is the outcome of a dramatic intellectual struggle which has lasted for twenty-five hundred years.

Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]

On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.

The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.

We have again a strange gap. We have the big scientific discoveries around the second, third century BC. Then we have an invention of the so-called Arab system, the positional system of counting with zero dated to the eighth or ninth century.

When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.