The Role of History in the Study of Mathematics
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I believe that the following summary describes the view of the history of modern mathematics that is universally believed by mathematicians today and believed by all too many historians of mathematics as well.
Summary History: The invention of differential and integral calculus in the seventeenth century by Newton and Leibniz was an enormous advance, but it remained on a shaky logical basis throughout the eighteenth century. With Cauchy in the early nineteenth century and, more seriously, with Weierstrass later in the nineteenth century, the calculus was finally given a firm and rigorous foundation. What was achieved at that time was a proper understanding of limits and, more generally, of the infinite processes of integration and differentiation.
A related development in the second half of the nineteenth century that was central to modern mathematics was Cantor’s creation of his theory of infinite numbers, both cardinal and ordinal, which made it possible, for the first time, to deal...
This paper is a revised version of a presentation written for the 5th International Conference on the History of Modern Mathematics, held in August 2019 at Northwest University in Xi’an, China. Unfortunately, an injury prevented the author from traveling to China, and the paper was presented in absentia.