importance of the method of mathematical proof for subjects such as logic and philosophy, so he attended summer courses to study mathematics. On the other hand, in 1667, Leibniz worked to reconcile Catholic and Protestant parties and encouraged Christian European countries to work together to conquer non-Christian lands for the civilization of the west. After that, he went to Paris and studied mathematics and physics under Christiaan Huygens and met some important names like Hooke, Boyle, and Pell. During this period in Paris, Leibniz developed the basic features of his version of calculus. In 1673, he was still struggling to develop a good notation for his calculus and his first calculations were clumsy. In 1675, he wrote a manuscript using the                notation for the first time. In the same manuscript the product rule for differentiation was given. In 1676, Leibniz discovered the familiar                     , dx for both integral and fractional n. After that, he faced Newton's accusations of stealing his methods in Newton’s letters. After these accusations, he focused more on his studies. As he worked on his studies, he was in contact with Guillaume de l'Hôpital, a French mathematician. In one of his letters Leibniz raised the following question: "Can the meaning of derivatives with integer order be generalized to derivatives with non-integer orders?" L`Hôpital was somewhat curious about that question and replied by another question to Leibniz: "What if the order will be     ?" Leibniz in a letter dated September 30, 1695 replied and wrote "It will lead to a paradox, from which one day useful consequences will be drawn." This was the first appearance of fractional calculus in history. After that, Leibniz developed his studies on this topic and found the term “fractional calculus.” Till the end of his life, he published his findings in journals and enlightened a broad range of people. He died in 1716 after suffering from gout. Today, he is known as an indefatigable worker, a universal letter writer, a patriot and cosmopolitan, a great mathematician, and one of the most powerful spirits of Western civilization.
 

References: 

“The Hanoverian Period.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., www.britannica.com/biography/Gottfried-Wilhelm-Leibniz/The-Hanoverian-period.

“Gottfried Leibniz - Biography.” Maths History, mathshistory.st-andrews.ac.uk/Biographies/Leibniz/. 

“The Hanoverian Period.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., www.britannica.com/biography/Gottfried-Wilhelm-Leibniz/The-Hanoverian-period.