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Dear Isaac Asimov,

Who is the true inventor of calculus?



Dear Andrew,

Good question. It is actually quite complicated, but I’ll do my best.

The ancient Greeks had no calculus. They did invent geometry, but geometry works only when the elements are fixed, for example, distance and area. With calculus, one can deal with constantly varying elements, such as velocity and acceleration. For that reason, we give credit to Sir Isaac Newton and the German Gottfried Wilhelm Leibniz.

Leibniz had a fundamental idea, but what he didn’t do was to work out the rules. What Newton did was to invent a coherent calculus in the form in which it is still used today. (I’m referring here to Newton’s differential calculus. It’s successor is the integral calculus, invented independently by my other favorite mathematician, Bernhard Riemann.) Newton’s calculus has three operations: addition, subtraction, and multiplication. Leibniz’s had only the multiplication.

However, Leibniz was much more than a mathematician. He was also a philosopher and inventor. He is credited with having invented the binary system that is still used in computers today. He also was a pioneer in the field of artificial intelligence.

That answers your question. It’s a shame, isn’t it, that what’s fundamental in mathematics isn’t always as simple as that!

Isaac Asimov