All revolutionary advances in science may consist less of sudden and dramatic revelations than a series of transformations, of which the revolutionary significance may not be seen (except afterwards, by historians) until the last great step. In many cases the full potentiality and force of a most radical step in such a sequence of transformations may not even be manifest to its author.

History without the history of science, to alter slightly an apothegm of Lord Bacon, resembles a statue of Polyphemus without his eye-that very feature being left out which most marks the spirit and life of the person. My own thesis is complementary: science taught ... without a sense of history is robbed of those very qualities that make it worth teaching to the student of the humanities and the social sciences.

Historians of a generation ago were often shocked by the violence with which scientists rejected the history of their own subject as irrelevant; they could not understand how the members of any academic profession could fail to be intrigued by the study of their own cultural heritage. What these historians did not grasp was that scientists will welcome the history of science only when it has been demonstrated that this discipline can add to our understanding of science itself and thus help to produce, in some sense, better scientists.

All revolutionary advances in science may consist less of sudden and dramatic revelations than a series of transformations, of which the revolutionary significance may not be seen (except afterwards, by historians) until the last great step. In many cases the full potentiality and force of a most radical step in such a sequence of transformations may not even be manifest to its author.

Taken over the centuries, scientific ideas have exerted a force on our civilization fully as great as the more tangible practical applications of scientific research.

The seventeenth century witnessed the birth of modern science as we know it today. This science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science-a dependence on numbers, on real numbers of actual experience.