First, it would be better to ask WHETHER he was mad; I don't know whether this is the case, and I suggest you look this up.Both Newton and Leibniz worked on calculus, independently - and it's possible that there have been some conflicts there, with respect to deciding who really discovered it.
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He had also worked on some of the ideas which Leibniz published in the book. However, a crude distinction is that Leibniz developed the theory of calculus whereas Newton worked on their application - mainly in physics. But apart from that Newton did believe in Alchemy and some other aspects of the occult.
Isaac Newton and Gottfried Wilhelm Leibniz
Calculus was independently discovered by Sir Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century. Newton developed his own system of calculus called "fluxions" and "method of fluents," while Leibniz developed his system of calculus based on differentials and integrals. Both their work laid the foundation for modern calculus.
The argument between Newton and Liebniz (and others) revolved around whether or not Newton was the first to invent calculus and/or if Leibniz developed his calculus independently of Newton or if he simply used different notation.The problem was that Newton did not publish his initial work.
Newton and Leibniz
Issac Newton and Leibniz developed it independently. Newton discovered it first, but kept it to himself. Leibniz, on the other hand, published. Newton accused Liebnitz of stealing his ideas, thus starting a long feud between the two. Today, they are both recognized as being the founding fathers of calculus. It is however, Leibniz's notation of the calculus that has flourished.