German Gottfried Leibniz invented infinitesimal calculus independent of Englishman Sir Issac Newton. His notation is still widely used today.
He was an avid inventor of mechanical calculators and added multiplication and division functions to Pascal's calculator. He refined the binary number system in the late 1600s, enabling the development of digital computers centuries later. A notorious optimist, Leibniz coined the phrase "the best of all possible worlds."
Few mathematicians have made as great a contribution to the field as Lagrange. His legacy is so immense, his is one of 72 names inscribed on the Eiffel Tower and he is buried in the Pantheon, the national tomb for great Frenchmen.
Lagrange essentially created the science of partial differential equations from 1772 to 1785. Today that science is used to model heat, sound, electrodynamics and additional difficult-to-model information. Besides that, he entirely re-formulated and simplified Newton's equations of classical mechanics. Lastly, he also advanced the solution to the three-body problem, one of the trickiest problems in physics.
Reference:
http://www.businessinsider.com/important-mathematicians-modern-world-2012-7?IR=T#joseph-lagrange-simplified-newtons-work-12
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