Amongst other things they independently invented calculus. Newton probably made the first discovery, but delayed publishing for many years. Leibniz also held off publishing for a long time, waiting, apparently for Newton to do it. Eventually Leibniz published anyway. They became bitter rivals.
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Isaac newton and Gottfried Wilhelm Leibniz independently developed the concept of calculus in the late 17th century. They each made significant contributions to the field, with Newton originating the method of fluxions and Leibniz introducing the notation of calculus that is still used today. Their work laid the foundation for modern mathematics and science.
The German scientist who corresponded with Isaac Newton was Gottfried Wilhelm Leibniz. Leibniz was a mathematician and philosopher known for developing calculus independently of Newton.
Newton was outraged because he believed that Leibniz had stolen his ideas on calculus. Newton and Leibniz both independently developed calculus, but Newton felt that Leibniz had plagiarized his work. This led to a bitter dispute between the two mathematicians known as the "calculus priority dispute."
The theory discovered between Isaac Newton and Gottfried Leibniz was the development of calculus. Both Newton and Leibniz independently developed this mathematical system to describe and analyze change and motion, laying the foundation for modern calculus.
Gottfried Wilhelm Leibniz
As a scientist, he is mainly known for the general law of gravitation, and Newton's laws of movement. As a mathematician, he basically invented calculus (so did another mathematician, Leibniz, independently of Newton).