Leibniz

$Mathematicians$

Unlike other great mathematicians, Leibniz came relatively late into mathematical area. He often recalled how little knowledge in mathematics that he acquired. In class, the first book of Euclid's Elements made little impression on him. He looked at mathematics books, but only skimmed them without real attention; he lacked patience to follow the lengthy deduction of reasoning. He prided himself that he could generalize the concepts from several mathematical books which he skimmed.

However, he sometimes found that basic things, such as a typical proof in elementary geometry or a lengthy algebra, were difficult to cope with. Thus, one may find quite a number of errors in his calculations in his writings. To solve this problem, he needed a new approach to overcome the brain limitation by not elaborating the formal side but by finding or inventing new ideas and mechanisms. As a result, for example, in the computation process, he invented the calculating machine.

The slowly retreating Aristotelianism, Euclidean geometry and other major frameworks of thinking motivated him to build an elastic and long-lasting framework not the rigid and easy-to-be-replaced one. To achieve this, the method of reasoning should be simplified. A new method that comprehend or typify the essential features of the thought process must be found. As one result of this motivation, he (and, of course, Isaac Newton) invented the new major framework in mathematics in his time--the calculus.

Lastly, it is particularly interesting to note that most of his growth and achievements in mathematics were largely concentrated in his four year stay in Paris from 1672-1676. With his great effort, he was able to upgrade his numerical sophistication significantly to stay on the same level as other great mathematicians [Hofmann, introduction].