Top 10 Most Influential Mathematicians

Mathematics, often dubbed the universal language, is essential for understanding the world around us. In our modern society, it plays a crucial role in everything from the faucet in your kitchen to the satellite transmitting television signals into your home. Great mathematicians have left an indelible mark on history, and their contributions continue to shape our world today. This list highlights some of those exceptional figures, ranked based on their mathematical contributions, their impact at the time, and the lasting influence they left behind. I encourage you to explore the lives of these remarkable individuals, as their discoveries are truly fascinating and too vast to cover here. Of course, such lists are inherently subjective, so feel free to share your own thoughts and additions in the comments!

10. Pythagoras of Samos

Pythagoras, the renowned Greek mathematician, is often regarded as one of the earliest pioneers in the field. Living from around 570 to 495 BC, he is credited with founding the Pythagorean school, which Aristotle recognized as one of the first groups dedicated to advancing mathematical knowledge. He is famously associated with the Pythagorean Theorem (a + b = c) in trigonometry, though some historians question whether he himself proved it (others suggest it may have been his students or even Baudhayana, an Indian mathematician from 300 years earlier). Regardless of the origins of the theorem, its profound impact on modern measurements, technology, and the development of geometry cannot be overstated. Pythagoras's contributions laid the groundwork for the study of mathematics as a legitimate field of inquiry, establishing him as the father of modern mathematics.

9. Pierre de Fermat

Pierre de Fermat, born in 1601, was a French lawyer and an amateur mathematician. He worked in the Parlement of Toulouse and studied at the University of Orleans, where he earned his degree in civil law in 1626. Afterward, he moved to Bordeaux, where he shifted his focus to mathematics. It was in Bordeaux that he shared his restoration of Apollonius’s De Locis Planis with a prominent mathematician and began his work on Maxima and Minima. Fermat is regarded as one of the most influential French mathematicians of the 17th century, having made significant contributions across a variety of mathematical fields, including analytical geometry, infinite descent, and the early development of calculus. Although he saw mathematics as a hobby and never published his work, his most notable contributions lie in number theory, the study of whole numbers and their relationships. He is particularly famous for his Fermat's Last Theorem. Fermat's other accomplishments include laying the groundwork for calculus with his exploration of curve properties, and he is often credited as one of the inventors of differential calculus. He also co-founded probability theory with Blaise Pascal.

8. Isaac Newton and Wilhelm Leibniz

These two remarkable figures are often both credited as the “inventors” of modern infinitesimal calculus. Both made monumental contributions to the field. Leibniz is particularly recognized for introducing the modern notation we use today, including the iconic integral symbol, and for his significant work in the development of Topology. Meanwhile, the brilliant Isaac Newton, due to his groundbreaking work in the Principia, is often considered by many as the true originator of calculus. Nevertheless, what is clear is that both men made profound and unique contributions to the field in their own ways.

7. Leonardo Bigollo Pisano

Leonardo Bigollo Pisano, better known as Fibonacci, is regarded as one of the greatest mathematicians of the Middle Ages. Born around 1170 and passing in 1250, he is most famous for introducing the renowned Fibonacci Sequence to the Western world. Though Indian mathematicians had known of it since around 200 BC, Fibonacci’s work brought the sequence into the spotlight, and it is now seen frequently in biological patterns. Additionally, Fibonacci played a crucial role in the popularization of the Arabic numeral system, an often overlooked yet immensely significant contribution.

Having spent much of his early years in North Africa, he became familiar with the Arabic numbering system. Recognizing its simplicity and efficiency compared to the cumbersome Roman numerals, he traveled through the Arab world to learn from the leading mathematicians of his time. Upon his return to Italy in 1202, he published his famous Liber Abaci, in which he introduced the Arabic numeral system and demonstrated its usefulness in a variety of real-world situations. This work led to the gradual adoption of the system, and he is now considered a pivotal figure in the development of modern mathematics.

6. Alan Turing

Alan Turing, a brilliant computer scientist and cryptanalyst, is widely regarded as one of the greatest minds of the 20th century. During World War II, he worked at the Government Code and Cypher School in Britain, where he made pivotal discoveries and developed groundbreaking methods for breaking codes, ultimately helping to decipher the German Enigma encryption. His work is believed to have played a crucial role in the outcome of the war, or at the very least, in shortening its duration.

After the war, Turing turned his attention to computing. Having conceived the idea of a computing machine before the war, he is considered one of the pioneers of computer science. His insightful papers on computing remain influential today, especially his work on Artificial Intelligence, including the Turing Test, which is still used to measure a computer’s ability to exhibit “intelligence.” In 1948, he began collaborating with D. G. Champernowne, a former undergraduate acquaintance, on a computer chess program for a machine that had not yet been invented. Turing would simulate the machine's actions in testing the program.

5. René Descartes

René Descartes, the French philosopher, physicist, and mathematician, is most famously known for his philosophical assertion, ‘Cogito Ergo Sum.’ However, Descartes, who lived from 1596 to 1650, also made groundbreaking contributions to mathematics. Along with Isaac Newton and Gottfried Wilhelm Leibniz, Descartes helped lay the foundations for modern calculus—an area that would later be developed further by Newton and Leibniz. Descartes is also widely recognized for developing Cartesian Geometry, which introduced the standard graphing method (complete with x and y axes) used in algebra to represent different points. Before this, mathematicians had to measure distances physically or rely on materials to draw figures. The advent of Cartesian Geometry allowed points to be expressed on a graph, and graphs could be drawn to any scale. Furthermore, Descartes introduced superscripts in algebra to represent powers, making a significant contribution to the development of modern mathematical notation.

4. Euclid

Living around 300 BC, Euclid is widely regarded as the Father of Geometry, and his seminal work, Elements, is one of the most influential mathematical texts in history, used in education until the 20th century. Unfortunately, little is known about his life, and most of the information we have comes from sources written long after his presumed death. Despite this, Euclid is credited with establishing the method of rigorous, logical proof for theorems and conjectures, a framework that is still fundamental in mathematics today. His influence is arguably unmatched among mathematicians. In addition to Elements, he is believed to have written five other works, mostly focused on Geometry and Number Theory, though another five of his works have been lost over time.

3. Leonhard Euler

If Carl Friedrich Gauss is known as the Prince of mathematics, then Leonhard Euler is undoubtedly the King. Living from 1707 to 1783, Euler is considered one of the greatest mathematicians to ever exist. It is said that for every mathematical formula discovered, the person who followed Euler in making a similar discovery is credited with its name. In his time, Euler was groundbreaking, on par with Einstein in terms of intellectual brilliance. His most significant contribution is perhaps the development of mathematical notation, including introducing the concept of a function (expressed as f(x)), shorthand for trigonometric functions, the use of 'e' for the base of the natural logarithm (Euler's Constant), the Greek letter Sigma (Σ) for summation, the letter 'i' for imaginary units, and the symbol pi (п) for the ratio of a circle’s circumference to its diameter. These notations are foundational to modern mathematics, ranging from the simplest to the most complex.

In addition to his contributions to notation, Euler solved the famous Seven Bridges of Königsberg problem in graph theory, developed the Euler Characteristic to link the number of vertices, edges, and faces of an object, and disproved many well-established theories, far too numerous to mention. His work expanded fields such as calculus, topology, number theory, analysis, and graph theory, and he made countless other contributions. Ultimately, his efforts laid the foundation for modern mathematics and its incredible advancements, which coincidentally led to rapid growth in both industry and technological innovation during his time.

2. Carl Friedrich Gauss

A child prodigy, Carl Friedrich Gauss, often referred to as the “Prince of Mathematics,” made his first significant mathematical discovery while still a teenager. By the age of 21, he had already written his magnum opus, Disquisitiones Arithmeticae. Gauss is widely known for his exceptional mental prowess, famously adding the numbers from 1 to 100 in mere seconds during primary school using a clever shortcut. Recognizing his brilliance, the local Duke sent him to Collegium Carolinum, and later he studied at Göttingen, which at the time was considered the premier mathematical university in the world. After graduating in 1798 at just 22 years old, Gauss contributed major advancements to many mathematical fields, most notably in number theory, particularly around prime numbers. He also proved the fundamental theorem of algebra and introduced the Gaussian gravitational constant in physics—all by the age of 24! Gauss continued to revolutionize mathematics throughout his life, making lasting contributions that have impacted the field to this day.

1. G. F. Bernhard Riemann

Born into a poor family in 1826, Bernhard Riemann would go on to become one of the most influential mathematicians of the 19th century. His contributions to geometry are vast, and he is the namesake of numerous theorems, including Riemannian Geometry, Riemannian Surfaces, and the Riemann Integral. However, Riemann is perhaps most famously known—or rather infamous—for his highly complex Riemann Hypothesis, which addresses the distribution of prime numbers. Initially overlooked for the first 50 years due to the difficulty of his work, it has since emerged as one of the most profound unsolved problems in modern mathematics, perplexing even the most brilliant minds in the field. Despite some progress, the solution remains elusive. A reward of $1 million has been offered by the Clay Mathematics Institute for a proof, and the discovery would almost certainly earn the mathematician a Fields Medal (widely considered the Nobel Prize of mathematics). The ramifications of such a proof are speculated to be vast, with major encryption systems potentially being shattered, causing widespread collapse. Additionally, the solution is expected to involve 'new mathematics,' further solidifying Riemann's legacy. Even after his death, Riemann's work continues to open doors for new advancements in mathematics, just as it did during his lifetime.