user: List 10 of the most influential mathematicians of all time and write an argument for each of them as to why they are the greatest mathematician of all time.

assistant: Here is a list of 10 influential mathematicians and an argument for each one:

Isaac Newton - He made major contributions to calculus, optics, and the laws of motion and universal gravitation. He is considered one of the most influential scientists in history and his work laid the foundations for modern physics and science.

Carl Friedrich Gauss - He is often referred to as the "Prince of Mathematicians" and made important contributions to number theory, statistics, differential geometry, and astronomy. He is also known for his groundbreaking work in magnetism and electricity.

Archimedes - He is considered one of the greatest mathematicians of the ancient world and made important contributions to mathematics, physics, and engineering. He is best known for his work in geometry, specifically his discovery of the principle of buoyancy.

Leonhard Euler - He made important contributions to mathematics, physics, and engineering and is considered one of the most prolific mathematicians of all time. He is best known for his work in number theory, calculus, and topology.

Pythagoras - He is best known for his theorem in geometry, but he also made important contributions to mathematics, philosophy, and religion. He is considered one of the founders of mathematics and his theorem is still widely used today.

Euclid - He is considered the father of geometry and wrote the influential text "Elements", which is still widely studied today. He made important contributions to mathematical rigor and the development of mathematical proof.

René Descartes - He is considered the father of analytic geometry and made important contributions to mathematics, physics, and philosophy. He is best known for his method of representing points in space using coordinates, which is now called the Cartesian coordinate system.

Alan Turing - He is considered the father of computer science and made important contributions to mathematics, computer science, and cryptography. He is best known for his work in code-breaking during World War II and his concept of the Universal Turing Machine, which is considered a foundation of modern computing.

John von Neumann - He made important contributions to mathematics, computer science, and physics and is considered one of the pioneers of modern computing. He is best known for his work in game theory, quantum mechanics, and the development of the Von Neumann architecture for computers.

Srinivasa Ramanujan - He was an Indian mathematician who made important contributions to number theory and mathematical analysis. Despite having limited formal training in mathematics, he made groundbreaking discoveries and his work continues to inspire mathematicians today.

Each of these mathematicians made significant contributions to the field and had a lasting impact on mathematics and other fields. Their work continues to inspire and influence mathematicians today.

user: that's helpful, thanks!

assistant: You're very welcome. Is there anything else you'd like to know about these mathematicians?