Leibniz, Gottfried Wilhelm (11646-1716).
Leibniz was a German philosopher who belonged to the Rationalist school of philosophers, to which also Descartes belonged. Leibniz was not only a philosopher, he was also a considerable authority on law, a diplomat, an historian, and outstanding mathematician as is proved by his discovery in 1676, independently of Newton, of the Differential Calculus. Leibniz studied law at the University. When he was30 he became official librarian of the Brunswick family at Hanover, where he remained until he died.
His philosophy is set out in a short paper, The Monadology, which he wrote 2 years before his death. He held that everything from a table to man's soul, and even to God himself, is made up of 'monads', or atoms, each of which is a simple, indivisible, imperishable unit, different from every other monad and constantly changing.
Concerning his great contributions in Calculus, Leibniz published his results of developing the use of infinitesimals into the general operation now known as differentiation promptly and took a keen interest in making his techniques comprehensible and useful to a wide audience. Consequently, he exerted a much greater influence on mathematicians of the next 150 years than Newton did. Leibniz used what he called differentials dx and dy to denote corresponding infinitesimal changes in quantities x and y which were related by an equation.
Leibniz, Newton, and the other prominent mathematicians of the late seventeenth and eighteenth centuries relied generally on the use of infinitesimals. Their intuition and insight into the problems they studied enabled them to develop most of what is now known as "elementary calculus" and a great deal of more advanced mathematics, even though their arguments did not meet modern standards of rigor.