Let Us Calculate – the Last Universal Academic Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (1646 - 1716)

Gottfried Wilhelm Leibniz (1646 – 1716)

On July 1, 1646, one of the last universally interdisciplinary academics, active in the fields of mathematics, physics, history, politics, philosophy, and librarianship was born. Gottfried Wilhelm Leibniz counts as one of the most influential scientists of the late 17th and early 18th century and impersonates a meaningful representative of the Age of Enlightenment. Moreover, he is also the namesake of the association to which the institute I am working for is a member of, the Leibniz Association (Leibniz Gemeinschaft).

Leibniz made up his interests concerning philosophy and law studies in his early years, following his father’s footsteps. He even decided to acquire Latin auto-didactically at the age of eight, which is impossible to imagine for today’s Latin students, who experience this language more as a constant torture. But Leibniz sticked to it and was therefore able to attend the famous Thomasschule in Leipzig. His later years at the University of Leipzig and the University of Jena were filled with studies in philosophy, law, mathematics, physics, and astronomy. Because of his widely spread field of education he is now titled as the ‘last universal academic’. He was able to establish a great reputation, working for archbishop Johann Phillip von Schönborn in the 1670‘s. During his time in Mainz he published his first work of great reception ‘Nova methodus discendae docendaeque jurisprudentiae’, a new method to teach and study jurisprudence. He also became a member of the British Royal Society due to his achievement of creating a calculating machine with a stepped reckoner. Another contribution to the field of mathematics was his (and Newton’s) development of infinitesimal calculus, revolutionary then and a basis of many calculations in mathematical, physical, stochastic and economical problems today. In philosophy, Leibniz got famous with the phrase of the ‘best of all possible worlds’. It pictures the correlation between the good and the evil, meaning that the world has a huge potential of development and that even God cannot realize the good things on earth without a certain amount of the evil.

Leibniz’s achievements are far too many to be mentioned all in one small blog post [1]. Thus we will focus here only on a small episode. Also for computer scientists, Leibniz anticipated the use of formal logic for automated reasoning and decision making. Besides inventing the binary system, which is the basis of nowadays computers, Leibniz argued that if we would be able to find a formal (logic) language to express problems instead of our ambiguous natural language, we should be able to solve arguments simply performing a calculation. Let us calculate! (in Latin: Calculemus!) he requested, to solve every argument or dispute. He believed that much of human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion:

“The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate [calculemus], without further ado, to see who is right”
— Gottfried Wilhelm Leibniz in a letter to Philip Spener, The Art of Discovery 1685, Wiener 51

Leibniz‘s calculus ratiocinator, which resembles symbolic logic, can be viewed as a way of making such calculations feasible. Leibniz wrote memoranda that can now be read as groping attempts to get symbolic logic – and thus his calculus – off the ground. These writings remained unpublished until the appearance of a selection edited by C.I. Gerhardt (1859). L. Couturat published a selection in 1901; by this time the main developments of modern logic had been created by Charles Sanders Peirce and by Gottlob Frege.[7]

Another highlight in Leibniz‘ career probably was becoming the first president of the Prussian Academy of Sciences in Berlin. His achievements and contributions to the world’s development are numerous and therefore he was honored several times during his lifetime and has not been forgotten today. Since a big part of his scientific work is documented in letters, the collection of these papers have been inscribed on UNESCO‘s Memory of the World Register in 2007.

At yovisto academic video search, you may learn about the Highlights of Calculus, a lecture by Professor Strang, who shows how calculus applies to ordinary life situations, such as: driving a car or climbing a mountain.

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