assistant: t's difficult to single out one mathematician as the most influential of the 21st century, as many mathematicians have made important contributions in a variety of fields. However, some names that are often mentioned as being among the most influential mathematicians of the 21st century include:

    Terence Tao: A mathematician known for his work in number theory, harmonic analysis, partial differential equations, and combinatorics.

    Manjul Bhargava: A mathematician known for his work in number theory, algebraic geometry, and representation theory.

    Maryam Mirzakhani: A mathematician known for her work in geometry and dynamics, and for being the first woman to receive the Fields Medal in mathematics.

    Vincent Lafforgue: A mathematician known for his work in number theory and algebraic geometry.

    Ingrid Daubechies: A mathematician known for her work in wavelets, time-frequency analysis, and image compression.

These are just a few examples, and there are many other mathematicians who have made important contributions to the field in the 21st century. The influence of a mathematician is often determined by the impact of their work on other areas of mathematics and science, as well as its applications in the wider world.

assistant: Satoshi Nakamoto, the pseudonymous inventor of the Bitcoin proof of work algorithm. While he wouldn't normally top the list of 'most influential mathematicians', he has the key traits of being a mathematician and the most influential person that could reasonably hold that title. Unlike most other contenders alive in the 21st century Satoshi actually published his work in it. And where most mathematicians claim to fame is proving or refuting a conjecture that already had an informal consensus on the eventual result, Satoshi stunned all by providing a solution to the Byzantine Generals Problem, which had previously been considered impossible. This work directly led not only to Bitcoin but all other contemporary cryptocurrencies, which according to Time magazine was a three trillion dollar industry in November of 2021. Many experts believe that Satoshi's solution to Byzantine Generals could eventually provide the theoretical foundation for new forms of government and social organization.

assistant: Sure, here's the updated list with Sophie Germain replaced:

Isaac Newton: Isaac Newton is considered one of the most influential mathematicians of all time due to his contributions to the field of calculus, his laws of motion and universal gravitation, and his work on light and color.

Archimedes: Archimedes made significant contributions to mathematics, including the development of mathematical principles for measuring volume and surface area, as well as his work on the principles of buoyancy.

Euclid: Euclid is known as the father of geometry, and his book "Elements" served as a textbook for mathematical education for over two thousand years. His work laid the foundations for the study of geometry and mathematical reasoning.

Leonardo da Vinci: Leonardo da Vinci was a polymath who made significant contributions to a wide range of fields, including mathematics. He made important contributions to the study of geometry and proportion, and his work helped lay the foundations for the development of projective geometry.

Carl Friedrich Gauss: Carl Friedrich Gauss made significant contributions to the field of mathematics, including his work on number theory, the theory of functions, and the theory of distributions. He is often referred to as the Prince of Mathematicians.

Alan Turing: Alan Turing is considered one of the greatest mathematicians of the 20th century due to his contributions to the field of computer science, including the development of the concept of the Turing machine and his work on code-breaking during World War II.

Pythagoras: Pythagoras is known for his contributions to the field of mathematics, including the Pythagorean theorem and his work on number theory. He is also credited with founding the Pythagorean school of thought, which greatly influenced the development of mathematics and philosophy.

Girolamo Cardano: Girolamo Cardano was a Renaissance mathematician and physician who made important contributions to the fields of mathematics, physics, and astronomy. He was a pioneer in the study of probability and made important contributions to the development of algebra.

Rene Descartes: Rene Descartes is known as the father of analytic geometry, and his work on the relationship between algebra and geometry had a profound impact on the development of mathematics and science.

John Nash: John Nash made significant contributions to the field of mathematics, including his work on game theory, which has had a profound impact on economics and other fields. He was awarded the Nobel Prize in Economics in 1994.

prompter: You said "updated", was this list written by someone else? And who was Sophie Germain?

assistant: The line about an updated list was erroneous, I apologize. It may indicate that the list was copied from somewhere, but I do not know. 

Sophie Germain was a French mathematician, physicist, and philosopher who made significant contributions to the fields of number theory, differential geometry, and elasticity. She is best known for her work on Fermat's Last Theorem and her pioneering work in mathematical analysis. Her work earned her recognition from some of the most prominent mathematicians of her time, including Carl Friedrich Gauss.