1.1 Let us calculate!
Gottfried Wilhelm Leibniz (1646–1716) was a polymath and contemporary of the physicist Isaac Newton (1643–1727). About 2000 years after Euclid, Leibniz proposed that the ways of the mathematicians can be applied more widely:
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, without further ado, in order to see who is right.
(Leibniz, 1685, p. 51)
Figure 3 Frontispiece of the 1690 edition of Leibniz’s extended version of his doctoral dissertation. It illustrates Leibniz’s key idea that all concepts can be obtained from the combination of a relatively small number of simple concepts
Building on previous work by the philosophers Ramon Llull (1232–1315) and René Descartes (1596–1650), Leibniz produced an elaborate system (Figure 3) aimed at taking the passion out of any dispute (not just mathematical ones).