As well as being highly intelligent when working with science and the physical world, Newton was gifted in the field of mathematics and made one of the most vital contributions to the suject, of all time - calculus. Calculus is the mathematical study of change and Newton was the first to apply it to Physics.

 

Newton developed the theory of finite differences and used fractional exponents and coordinate geometry to solve Diophantine problems (questions about the rational (integral) solutions for a system of equations).

 

Isaac developed the binomial theorem which describes the algebraic expansion of binomial powers and worked out solutions to analytical geometrical problems through drawing tangents to curves and defining areas with curves. He also found that these were inversely related and finalized his solution in his 'method  of fluxion'.