If God spoke a language, it would be mathematics. Ever since the Ancient Greeks started to analyze the world around them, humanity has used numbers to describe the world around them. Mathematics has grown in leaps and bounds to the point where today many theories possess such a level of abstraction that they have little to none practical application. One thing that stays constant is the effect of great thinkers and intellectuals on the development of the field. The following mathematical giants have shaped the study of Mathematics over the centuries.

Pythagoras

Pythagoras is best know today for his Pythagorean Theorem, or a-squared plus b-squared equals c squared. None of his writings remain; however, it is known he made advances in music, philosophy, and astronomy, in addition to mathematics. In the later part of his life, he moved to Croton in Southern Italy and founded a religious group known as the Pythagoreans. The sect believed in the sacredness of numbers and forbid the consumption of meat, among other oddities for the time. During Ancient Greece, they were most known for establishing a new way of life.

Euclid

Euclid of Alexandria lived around 300 B.C. during the reign of Ptolemy I. Famous for creating Euclidean geometry, Euclid wrote Elements, the main books that laid the foundation for modern geometry. In the book, he established the concept of using a small set of axioms to reveal many different geometric theories. No complete original copies of his work survived, so most of his writings exist today from scribes who rewrote his original work. He is known as the father of Geometry.

Muhammad ibn Ms al-Khwrizm

The father of Algebra lived around 800 A.D. in the Persian Empire. He worked in astronomy, geography, and mathematics, which led him to invent the modern days forms of algebra (itself an Arabic word) and trigonometry. He also popularized the Indian/Arabic form of numbers know in use today. His book Algoritmi gave the West the word algorithm. Other works also showed how to solve both linear and quadratic equations. His books had a great effect on European mathematics when they were translated into Latin.

Rene Descartes

Descartes, who lived in Sixteenth century Europe, is famous for his “I think, therefore, I am” in philosophy. In math, he invented the Cartesian plane and the way of writing exponents, used today in every commonplace mathematical subject. In his life, he worked all across Europe, never wanting to wake up before midday. He finished his life working for the monarchs of Sweden, where he died from Pneumonia. He also created analytical geometry, laying the way for the discovery of calculus.

Isaac Newton/Gottfried Wilhelm Leibniz

Both Newton and Leibniz are now credited with independently inventing calculus, the math of change. However, this dual creation caused bitter feuds between British mathematicians and the mathematicians on continental Europe. Both sides accused each other of stealing the other’s work. While Newton was probably the first to discover the essential theories of calculus, Leibniz’s notation is used today due to its simplicity. Neither of the two believed in using much mathematical rigor to prove calculus, leaving that task to later generations.

Euler

Leonhard Euler (1707-1783) was one of the greatest mathematicians of all time, writing around 60-80 volumes of work. His contributions touched all areas of mathematics, from number theory to geometry. He worked on proving some of the assumptions of calculus that Newton and Leibniz failed to do. He developed the Gamma function and numerous constants, among them Euler’s constant or e. Very few fields of mathematics can be learned without touching among one of his contributions.

Riemann

Bernhard Riemann (1826-1866) made contributions to differential geometry, setting the stage for many discoveries in physics in the 20th century. Riemann built on the work of his teacher, Gauss, and developed many ideas for non-Euclidean geometry, which involves geometry on curved surfaces. This helped Einstein formulate his theories of relativity and helped form the study of topology. He is also known for Riemann Sums, a way to solve integrals.

Ramanujan

Srinivasa Ramanujan (1887-1920) developed many theories in Number Theory during his times in both India and Britain. He filled notebooks with his theories but left little mathematical proof, forcing others to figure out his methods. He easily passed through math in school, but would usually fail out due to ignoring his other subjects. Once he contacted G.H. Hardy, he left for Britain. The two published many papers together as they combed his notebooks for theorems. Ramanujan had a genius for calculation and was usually right about his theorems, even if he didn’t prove them.

Witten

Edward Witten (1951) is one of the leading Theoretical Physicists of today. He works at the Institute of Advanced Study, where he focuses on Superstring Theory. He was the first physicist to win a Fields medal, an award for young mathematicians. His work in string theory has led to discoveries in topology and geometry. Some consider him to be Einstein’s intellectual successor.

These mathematicians are just a few of the many who have influenced the shape of humanity today. Their work has allowed us to better examine the world we live in and to understand humanity’s place in the universe.