The theory of modular form originates from the work of C.F. Gauss of 1831 in which he gave a geometrical interpretation of some basic notions of number theory.
Modular Forms are a special type of function that allows mathematicians to find deep and useful links between widely different fields of mathematics--complex analysis, number theory, group theory, topology, algebra, geometry, differential equations, string theory, cryptography, and others. They were invented in the 1830s by mathematician Carl Frederick Gauss, who was working to interpret the difficult and abstract concepts of number theory in a geometric way. Modular Forms have been key to the solution of a number of difficult problems in mathematics--most famously, Fermat's Last Theorem.