Some mathematicians are considered the "greatest of their era". For instance, Archimedes is generally considered the greatest mathematician of Antiquity. Is there any mathematician who stood out similarly from the rest in that timeline?
Al-Khwarizmi was a ninth-century mathematician who created many of the most basic techniques for how we perform calculations. His greatest contributions were in the realm of developing formal, systematic ways of doing arithmetic and solving equations.
His works mark the beginning of what we today understand as Algebra. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Indeed, the word "algebra" comes from part of the title of his book on solving equations (Al-jabr), and the word "algorithm," meaning a systematic set of rules used to solve a problem, descends from his name (in Latin, his name became ‘Algoritmi’ and his systematic calculating procedures were called algorisms — later, algorithms).
Al-Khwarizmi's "On the Calculation with Hindu Numerals", written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe.
There are several prominent mathematicians of the medieval era, most notably Leonardo of Pisa, or more commonly called "Fibonacci". He developed the Fibonacci sequence and he also introduced the Hindu - Arabic numeral system to Europe in the 13th century. As a result, the Roman numeral system was discarded in favor of the former.
Another notable mathematician is Aryabhata. Aryabhata was an astronomer and mathematician. He wrote the influential "Aryabhatiya", where he gave rules for square roots, quadratic equations, and predicting eclipses. He also gave an approximation for the irrational constant pi (π).