20 Greatest Mathematicians of All Times

Portrait of Sir Isaac Newton. Photo by Bonhams- Wikimedia

20 Greatest Mathematicians of All Times

As we all know, mathematics is an area of knowledge that consists of the topic of numbers, formulas and related structures, shapes and spaces in which they are held, quantities and their changes. All these topics are represented in modern mathematics with the major subdisciplines on number theory, algebra, geometry, analysis and many others. For mathematics to exist, it was invented by mathematicians from the ancient time of 2000 to 1800 BC. One of the ancient mathematical concepts was the Pythagorean theorem.

From ancient times to medieval and later, many mathematicians worked on finding solutions to mathematical problems. Most mathematicians were concerned with data, numbers, quantity, change, models, space and structure.

Below are 20 greatest mathematicians of all times.

1. Carl Friedrich Gauss

Carl Friedrich Gauss. Photo sourced from Wikimedia

Carl Friedrich proved to be a German mathematical prowess when he graduated from university; he started developing his mathematical ideas. He has had an exceptional influence in many fields of mathematics and is ranked among history’s most influential mathematicians. At the age of 24, he proved Algebra’s fundamental theorem. He also contributed to differential geometry, matrix theory, statistics, analysis and geodesy.

2. Georg Friedrich Bernhard Riemann

Bernhard Riemann was one of the most popular German mathematicians. He is known for his significant mathematical contributions in the field of Geometry, analysis and number theory. 

He formulated several theories with his name, including the Riemann Integral, Riemannian Geometry and Riemannian Surface. He is known for Riemann Hypothesis, which was ignored for its difficulties. Still, many mathematicians were intelligent enough to understand his work, and it became the most significant question in modern science. 

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3. Leonhard Euler

Euler was one of the mathematicians in history and the greatest of the 18th century. He made pioneering and influential discoveries in many branches, such as infinitesimal calculus, complex analysis and analytic number theory. Also, he established much modern mathematical terminology and notation, such as the notion of a mathematical function.

His mathematical notation shorthand trigonometric functions written (f(x)), symbol pi for the ratio of a circle’s circumference to its diameter and the Greek letter Sigma for summation and concept of€ for the base of natural logarithm known as The Euler Constant.

4. Pythagoras of Samos

Pythagoras was a Greek Mathematician and founder of the Pythagorean cult, which Aristotle viewed as among the first groups to study advanced mathematics widely. He is popularly recognized for his Pythagorean theorem in trigonometry, although some claim his students developed it. 

His Pythagorean theorem has had a significant impact on the world of mathematics and has become the base of most theorems, which paved the development of geometry.

5. Euclid

Euclid was an ancient Greek mathematician known for the Elements treatise, which established the foundation of geometry. His system is now referred to as Euclidean geometry, which involved innovations in amalgamation with a combination of theories from earlier Greek mathematicians, including Thales, Hippocrates of Chios, Theaetetus and Eudoxus of Cnidus.

He is also well known for his logical proofs of various conjectures and theorems. Presently, Euclid has five surviving works as his reminder five works were lost as time passed on. Most of his work revolved around number theory and Geometry.

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6. Rene Descartes

Portrait of René Descartes by Frans Hals- Wikimedia

Rene Descartes was a French mathematician, physicist and philosopher. He made a significant contribution to the world of mathematics. Together with Isaac Newton and Leibniz, they formulated the foundation of calculus. He bridged the separate fields of geometry and algebra, creating Cartesian Geometry, which is known as a standard graph with “x” and “y” axis and square grid lines.

He was the one who invented the use of superscripts to express powers in Algebra and made a contribution to the creation of modern mathematical notation.

7. Sir Isaac Newton

Isaac Newton was an English mathematician and alchemist. Author, theologian, physicist and astronomer. He made a significant contribution to the world of mathematics by inventing calculus. He is attributed with the generalized binomial theorem, valid for exponent. Additionally, he discovered Newton’s identities, Newton’s method classified cubic plane curves, which substantially contributed to the theory of finite differences.

He was also the earliest to use fractional indices and coordinate geometry to derive solutions to Diophantine equations.

8. Gottfried Wilhelm Leibniz

Photo by Christoph Bernhard Francke- Wikimedia

Wilhelm Leibniz was a German polymath active as a mathematician, diplomat, philosopher and scientist. He significantly contributed to developing the main ideas of differential and integral calculus, independently of Isaac Newton’s contemporary developments. Mathematicians recognize him for initiating the modern standard notation known as the integral sign.

9. Leonardo Bigollo Pisano

He was an Italian mathematician recognized as one of the world’s greatest mathematicians. Leonardo is extensively recognized for introducing the Fibonacci Series, later known as the Fibonacci numbers. There are also mathematical concepts named after Fibonacci because of a connection to Fibonacci, such as the Fibonacci search technique and Brahmagupta-Fibonacci identity.

Leonardo also introduced the Arabic numbering system and its practical application in his work, liber Abaci.

10. Archimedes of Syracuse

Archimedes was a Greek mathematician considered one of the greatest mathematicians of ancient history. He foresaw modern calculus and analysis by administering the concept of the infinitely small and the method of exhaustion to derive and rigidly prove a range of geometrical theorems such as the surface area, area of a circle, the volume of a sphere, the area under a parabola, the area of a spiral and many more.

He also derived an approximation of “pi”, defining and looking into the spiral that now bears his name and devises a system using exponentiation for illustrating very large numbers. He was one of the first to use mathematics to physical phenomena establishing hydrostatics and statics.

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11. Srinivasa Ramanujan

Srinivasa Ramanujan. Photo by Konrad Jacobs- Wikimedia

Srinivasa Ramanujan was an Indian mathematician; he didn’t have much formal training in pure mathematics. However, he made substantial contributions to mathematical analysis, infinite series, number theory and continued fractions.

12. Pierre de Fermat

Pierre was a French mathematician known for discovering an original method of finding ordinates of curved lines related to that of differential calculus. He contributed to analytical geometry, optics and probability.

He also made a major contribution to number theory and is known for his Fermat’s principle for light propagation and his Fermat’s Last Theorem in number theory.

13. Aryabhata

Aryabhata was an Indian mathematician; he determined square and cube roots, geometrical figures, Algebra, trigonometry and indeterminate equations. One of his notable achievements in mathematics was the Aryabhata Algorithm for solving Diophantine equations.

14. John von Neumann

Photo outsourced from Wikimedia

John von Neumann was a Hungarian-American mathematician, considered the broad coverage of any mathematician of his time. He made a significant contribution to many fields of mathematics, including measure theory, numerical analysis, geometry, matrix theory, functional analysis, operator algebras, representation theory, lattice theory, group theory and ergodic theory.

15. Blaise Pascal

  Blaise Pascal was a French mathematician; his earliest mathematical work was on conic sections, and he wrote a notable treatise on the subject of projective geometry. Together with Pierre de Fermat on probability theory, strongly determining the development of modern economics and social science.

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16. David Hilbert

David Hilbert. Photo outsourced from Wikimedia

David Hilbert was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. He contributed to various fundamental ideas in many areas, including the calculus of variations invariant theory, foundations of geometry, commutative algebra, algebraic number theory and spectral theory of operators and application to mathematical physics, foundations of mathematics and integral equations. He is known as one of the founding fathers of proof theory and mathematical logic.

17. Augustin -Louis Cauchy

He was a French mathematician who contributed to several branches of mathematics, including continuum mechanics and mathematical analysis. Augustin-Louis was the first to state and rigorously prove theorems of calculus and singlehandedly established complex analysis and the study of permutation groups in abstract algebra.

Augustin-Louis was a writer and wrote approximately eight hundred research articles and five complete textbooks on various mathematics and mathematical physics topics.

18. Muhammad ibn Musa al-Khwarizmi

Photo by ms- Wikimedia

Al-Khwa0rizmi was a Persian polymath who contributed largely to mathematics. He popularized a treatise on algebra by presenting the first systematic solution of a linear and quadratic equation. His algebra achievement was solving quadratic equations by completing the square, for which he provided geometric justifications. He is regarded as the founder of algebra because he was the first to treat algebra as an independent discipline and initiated the methods of reduction and balancing.

He was also involved in the contributions to trigonometry, producing accurate sine and cosine tables and the first table of tangents.

19. Georg Ferdinand Ludwig Philipp Cantor

 Georg was a German mathematician who contributed to the creation of set theory, a fundamental theory in mathematics. He set the importance of one-to-one correspondence between the members of two sets and defined infinite and well-ordered sets. He also demonstrated that real numbers are more numerous than natural numbers.

His method of proof of this theorem implies the existence of an infinity of infinities and defines the cardinal and ordinal numbers and their arithmetic.

20. Sir Andrew John Wiles

Andrew Wiles is a living mathematician known for developing the proof of Fermat’s Last Theorem. His contribution may not be as grand, but he was able to formulate portions of new mathematics to support his theorem. He spent seven years of his life formulating his proof and was later found out that there was an error. He went to isolation, reformulated the solution, and his proof was accepted.