Ancient & Classical Mathematics:
* Euclid (c. 300 BC): His *Elements* is a foundational text in geometry and number theory, establishing axiomatic systems and influential theorems.
* Archimedes (c. 287 – c. 212 BC): Made significant contributions to geometry, including calculating the area of a circle and the volume of a sphere, and developed methods of integration.
* Pythagoras (c. 570 – c. 495 BC): While the Pythagorean theorem was likely known before him, he and his school are credited with its proof and significant advancements in number theory.
* Apollonius of Perga (c. 262 – c. 190 BC): Made important contributions to conic sections.
* Diophantus (c. 3rd century AD): Known for his work on indeterminate equations (Diophantine equations).
Medieval & Renaissance Mathematics:
* Al-Khwarizmi (c. 780 – c. 850 AD): A key figure in the development of algebra, his work introduced algorithms and systematic methods for solving equations.
* Omar Khayyám (1048 – 1131 AD): Made contributions to algebra and geometry, including work on cubic equations.
* Fibonacci (Leonardo Pisano) (c. 1170 – 1250 AD): Introduced the Hindu-Arabic numeral system to Europe and is known for the Fibonacci sequence.
* Gerolamo Cardano (1501 – 1576): Made significant contributions to algebra, including solving cubic and quartic equations.
17th-19th Century Mathematics:
* René Descartes (1596 – 1650): Developed analytic geometry, connecting algebra and geometry.
* Pierre de Fermat (1601 – 1665): Made significant contributions to number theory and probability theory, famously formulating Fermat's Last Theorem.
* Isaac Newton (1643 – 1727): Developed calculus (independently of Leibniz), making profound contributions to physics and mathematics.
* Gottfried Wilhelm Leibniz (1646 – 1716): Developed calculus independently of Newton and contributed to logic and philosophy.
* Leonhard Euler (1707 – 1783): One of the most prolific mathematicians of all time, with contributions spanning numerous areas including calculus, number theory, graph theory, and topology.
* Joseph-Louis Lagrange (1736 – 1813): Made significant contributions to calculus, number theory, and mechanics.
* Carl Friedrich Gauss (1777 – 1855): Considered one of the greatest mathematicians of all time, with contributions to number theory, algebra, geometry, analysis, and statistics.
* Bernhard Riemann (1826 – 1866): Made significant contributions to analysis, geometry (Riemannian geometry), and number theory.
20th and 21st Century Mathematics:
* David Hilbert (1862 – 1943): Highly influential in many areas of mathematics, particularly in formulating significant unsolved problems.
* Kurt Gödel (1906 – 1978): His incompleteness theorems revolutionized mathematical logic.
* Alan Turing (1912 – 1954): Made foundational contributions to computer science and mathematical logic, particularly with his work on Turing machines.
* Emmy Noether (1882 – 1935): Her work in abstract algebra is foundational to modern physics and mathematics.
This list is far from exhaustive. Many other mathematicians have made invaluable contributions, and the field continues to evolve with new discoveries and insights. To get a more complete picture, you can research specific areas of mathematics (like algebra, topology, analysis, etc.) to find influential figures in those fields.