Greek letters are used everywhere in science and mathematics. When did this tradition start? If it is because the Greeks were pioneers of maths? why did the Indian literals, for example, not become popular?
It is not the idea of any individual I suppose.Greeks were one of the most advanced of all in science and all other fields in the ancient times.They had their own list of alphabets which they used.Slowly,it spread to some neighboring groups who followed their alphabets and methods.This then spread all around the globe and there has been perhaps no change or modifications in the language since then and till now widespreadly used.
There was no one person who decided one day to use Greek letters for all of their mathematics. It was a very slow process. The person to popularize the use of $ \pi $ to signify the mathematical value was Euler. He also started the use of $ \Sigma $ for summations. Alternatively, Francois Viete was the first to use letters to represent unknowns. This in all likelihood led to the introduction of Greek letters when Latin characters ran out.