The Persian mathematician known to us as al-Khwarizmi -- from whose name we get the word "algorithm" -- is often credited as the "inventor" of algebra. In fact, many ancient civilizations developed some algebraic methods of solving problems, as far back as the Babylonians, but al-Khwarizmi is considered by many to be the "father of algebra" because some of his techniques on solving quadratic equations are still in use today. (Others point to the works of the Greek mathematician Diophantus.)
Isaac Newton was one of the two inventors of what we now call calculus. (And he did start to dabble in alchemy at the end, but saying he spent the rest of his life working on it after inventing calculus might be a stretch. ;-) )
If you're looking for the greatest mathematician of all time, Newton would be a good candidate, although Leonhard Euler is usually given that title. Check the article on him below.