Because fame is so subjective, any attempt to name a single most famous mathematician of all time is completely subject to opinion. Many big names in the history of mathematics vie for the title of most famous mathematician:

**Pythagoras (6th century B.C.):** Although his name is most associated with the Pythagorean Theorem, which is used to calculate the length of the sides of a right triangle, Pythagoras was also the first to discover irrational numbers. He was also an acoustician, philosopher, and cult leader.
**Archimedes (3rd century B.C.):** Considered one of the greatest mathematicians of all time, Archimedes estimated *∏* (pi) with great precision and showed that a circle's area is equal to *∏* times the square of the circle's radius. He also figured out how to calculate the area under a parabola, discovered how to measure an item's mass by dropping it in water, and developed an explanation for the principle of the lever.
**Rene Descartes: **Although he's most well-known for his philosophical endeavors (including the oft-quoted phrase, "I think, therefore I am"), Rene Descartes also developed the *Cartesian coordinate system,* the old*x-y axis* graphing system at the heart of any geometry class, and the basis of analytical geometry.
**Isaac Newton and Gottfried Leibniz: **Isaac Newton is most famous for his theories of gravity, his laws of motion, and his experiments with prisms. In the world of mathematics, Newton, working in Great Britain, and Gottfried Leibniz, working in Germany, independently discovered calculus. Leibniz also discovered binary theory, which is the foundation of all computer systems today.
**Alan Turing:** In the early 20th century, British mathematician Alan Turing was important to the development of the concept of the algorithm and of computation in general. During World War II, he was crucial to England's success in cracking Nazi naval transmission codes, and his ideas and discoveries led to the development of the first stored-program computer. Today, he is considered the father of computer science.
**Albert Einstein:** You know you've made a big impact when your name becomes synonymous with *genius.* Although his main focus was theoretical physics, he couldn't have accomplished what he did without a hefty bit of mathematical magic. Einstein is, of course, the author of the world's most famous equation: *E = mc*^{2}.

Mathematicians are recognized for great work with a number of awards. Perhaps the most prestigious is the Fields Medal, which is awarded every four years to two to four mathematicians under the age of 40. But many other awards exist, many of them named after great mathematicians of the past, including the Abel Prize, the Euler Medal, the Fermat Prize, and the Wolf Prize in Mathematics.