Who are the most famous and greatest mathematicians to have ever lived? Well, answering this question is not easy, considering that mathematics has been known to humanity since prehistoric times, long before the birth of Christ.
From the timeless brilliance of Euclid and Pythagoras to the revolutionary insights of Alan Turning and Maryam Mirzakhani, mathematicians across the world have left an indelible mark on the pages of history. They transformed our understanding of the world, solved age-old mysteries, and paved the way for numerous scientific and technological breakthroughs.
The role of mathematics in our lives is immense. Math has made it possible to transmit electricity over thousands of kilometers, aided in the exploration of the concept of DNA, given rise to computers, and is essential in our quest to deepen our understanding of the universe.
“Mathematics is the alphabet with which God has written the universe” — Galileo Galilei
Without math, scientists can’t develop better medicines, researchers can’t explore new technologies, architects can’t design innovative structures, economists can’t make accurate predictions, and our world would be missing the solutions to many important challenges.
Similar to many other fields, the mathematics we know today didn’t just randomly come into existence. The development of new, groundbreaking theorems and equations is a process that spans decades. Now, let’s explore the individuals behind these advancements.
Known For: Ramanujan–Petersson conjecture, Ramanujan’s master theorem
Srinivasa Ramanujan was perhaps the most remarkable mathematician in modern India. Although Ramanujan had no formal training, his advanced mathematical knowledge at a very young age left many completely awestruck.
By the age of 16, he had independently developed and studied Bernoulli numbers, as well as calculated the Euler–Mascheroni constant. Before his untimely death at the age of 32, Ramanujan had successfully formulated nearly 4,000 different mathematical identities.
He gained international fame after G. H Hardy, a prominent British mathematician, recognized his work and compared him with the likes of Euler and Jacobi.
Known For: Lagrangian mechanics, Celestial Mechanics, Number Theory
Joseph Lagrange was one of the most notable students of the great Leonhard Euler. Lagrange started his mathematical career with variational calculus (in 1754), which led to the formulation of the Euler–Lagrange equation.
Lagrange later reformulated classical mechanics, introducing Lagrangian Mechanics. His renowned work on analytical mechanics, titled “Mécanique analytique,” played a crucial role in advancing the field of mathematical physics
Accolades: Wolf Prize (1995/6); Abel Prize (2016)
Sir Andrew John Wiles, a prominent British mathematician, gained widespread recognition for resolving Fermat’s Last Theorem, once regarded as the “most challenging mathematical problem.”
In 1975, under the guidance of John H. Coates, Andrew Wiles started working on the Iwasawa theory, which he continued with American mathematician Barry Mazur.
His most groundbreaking contribution occurred in the early 1990s when he successfully proved a significant portion of the modularity theorem, formerly known as the Taniyama–Shimura conjecture. The modularity theorem, in essence, is related to Fermat’s Last Theorem and was enough to prove it.
Known For: Jacobi’s elliptic functions; Jacobi transform
Carl Gustav Jacobi was one of the prominent mathematicians of the 19th century. His formulation of the theory of elliptic functions is perhaps his greatest contribution to the field.
Jacobi played a key role in advancing the study of differential equations and rational mechanics, notably contributing to the development of Hamilton-Jacobi theory.
Beyond this, his influence extended to the realms of mechanical dynamics and number theory, where he made fundamental contributions that enriched our understanding of these intricate mathematical domains.
Known For: Cryptanalysis of the Enigma, Turing’s proof
Accolades: Smith’s Prize (1936)
During the Second World War, the German intelligence network was considered almost impenetrable. Many allied nations feared that if they could not intercept important transmissions by the Nazi high command, they might eventually lose the war.
It was Alan Turing who, with his unprecedented mathematical and cryptanalytic abilities, made significant improvements over the Polish-made bombe and devised a machine that could decode the Enigma faster.
Post-war, Turing joined the National Physical Laboratory (U.K.), where he designed the Automatic Computing Engine, one of the earliest stored-program computers.
In the later stages of his career, Turing shifted his focus to theoretical biology. During this period, he mathematically predicted the Belousov–Zhabotinsky reaction, an occurrence later observed in the 1960s.
Bernhard Riemann
Known For: Riemann integral, Fourier series
Georg Bernhard Riemann was born in a small village near Dannenberg, Germany. Under the tutelage of Carl Friedrich Gauss, Riemann studied differential geometry and developed his theory of higher dimensions. His work is now known as Riemannian geometry.
Johann Gustav Dirichlet also played a significant role in shaping Riemann’s mathematical journey. Employing the Dirichlet principle, Riemann successfully formulated the renowned Riemann mapping theorem.
The legacy of Riemann’s mathematical contributions extends beyond his time, as some of his equations found application in Einstein’s General Relativity theory. His work continues to be foundational in diverse areas of mathematics and physics.
Henry Poincaré along with Marie Curie at the 1911 Solvay Conference
Known For: Three-body problem, Chaos theory, Poincaré–Hopf theorem
According to Eric Bell, a notable Scottish Mathematician, Henri Poincare was probably one of the last Universalists, as he thrived in almost all known fields of mathematics at that time.
Poincare, during his lifetime, contributed numerous theories in the fields of mathematical physics, applied mathematics, and astronomy. He was instrumental in the formulation of the theory of Special Relativity.
His exceptional works on Lorentz transformation and the Three-body problem paved the way for mathematicians and astrophysicists to make discoveries about our planet and outer space.
His theoretical works even inspired famous artists, such as Picasso and Braque, to establish an art movement (Cubism) in the 20th century.
David Hilbert in his Göttingen home | Image Courtesy: idw-online.de
Known For: Proof theory, Hilbert’s problems
David Hilbert was perhaps one of the greatest mathematicians of all time. He was instrumental in developing fundamental theories in the field of commutative algebra, calculus of variations, and mathematical physics.
Hilbert’s problems (a set of twenty-three mathematical problems, which he published in 1900) influenced groundbreaking studies in different fields of mathematics. Some of those problems remain unsolved to this date.
In his later years, David Hilbert devoted himself to physics. It was during this time he competed against Albert Einstein on general relativity.
Known For: Fibonacci numbers
Fibonacci, also known as Leonardo of Pisa, was one of the most accomplished mathematicians of the High Middle Ages.
Perhaps his most significant contribution to the subject is Liber Abaci, a personal book through which he popularized the Indo-Arabic numeral system (0,1,2,3,4..) and the Fibonacci sequence in Europe.Today, the sequence is used in computer algorithms and databases.
In the world of mathematics, the Bernoulli family holds the highest place. Originating from Antwerp, Belgium, Jacob and his brother Johann Bernoulli were the pioneering mathematicians in the Bernoulli lineage.
Both Jacob and Johann worked together on infinitesimal calculus and are credited for theorems and justifications such as Bernoulli numbers and the Brachistochrone curve.
Daniel Bernoulli, Jacob’s son, emerged as one of the most distinguished members of this illustrious family. His seminal work, Bernoulli’s Principle, provides a mathematical explanation for the functioning of a carburetor and an airplane wing. Additionally, Daniel made substantial contributions to the fields of probability and statistics.
Pythagoras (writing a book) depicted by Raphael’s fresco The School of Athens
Known For: Pythagorean theorem, Theory of Proportions
Pythagoras of Samos was born around 570 BC, and like most ancient Greeks, not much is known about his early life. As a philosopher, his works influenced the likes of Plato and Aristotle, as well as Johannes Kepler and Isaac Newton.
Although its authenticity remains debatable, many mathematical findings are attributed to Pythagoras. Perhaps the most famous of them is the Pythagoras theorem (named after him). Many historians have, however, stated the theorem was known by the Babylonians well before the time of Pythagoras.
He may have also been responsible for discovering the Theory of Proportions.
Accolades: Lalande Prize (1809), Copley Medal (1838)
Carl Friedrich Gauss was perhaps the most influential mathematician since the Ancient Greeks. His contributions in various fields of mathematics and physics are almost second to none. Gauss started showing signs of brilliance at the early age of seven when he could solve arithmetic progressions much faster than anyone in his class.
Some of his famous works include Gauss’ Law and Theorema Egregium, which concluded that the Earth could not be displayed on a map without some distortion. He was the first to speculate the possibility of non-Euclidean geometry, although his works were never published.
Known For: Newton’s Laws of Motion, Calculus, Newtonian Mechanics
Sir Isaac Newton is one of the founding fathers of classical mechanics and infinitesimal calculus. His views on gravity remained universally accepted until Einstein’s theory of relativity.
Newton’s most remarkable contribution to mathematics is calculus (then called infinitesimals), which he developed independently of his contemporary Gottfried Wilhelm Leibniz.
It was Newton who first explained the reason behind tidal disturbances on Earth and helped validate Kepler’s laws of planetary motion. His works on optics gave us the first-ever refracting telescope.
A portrait of Leonhard Euler by Jakob Emanuel Handmann
Known For: Euler’s conjectures, Euler’s equations, Euler’s numbers
In a tribute to Leonhard Euler’s immense contributions to mathematics, Pierre-Simon Laplace, a notable French astronomer and mathematician, wrote, “Read Euler, read him again and again; he is the master of us all.”
Mathematicians today hold Euler in the highest regard and consider him the most influential and greatest mathematician of the 18th century.
Euler made significant contributions to almost every major field in mathematics, including algebra, trigonometry, and geometry. In the realm of physics, his unparalleled works on fluid dynamics and Fourier series remain unmatched.
Known For: Archimedes’ principle; Hydrostatics
Born around 287 BC in Syracuse, Sicily, Archimedes was well-versed in mathematics, physics, and astronomy of that time. He was a polymath. However, most of his literary works have not survived.
Archimedes was one of the pioneers of geometry, who derived formulas for the area of a circle, volume, and surface area of a sphere. His method of determining the value of pi remained unchallenged and the only known way to calculate the circumference of a circle for decades.
The Fields Medal, the preeminent honor in mathematics, features a right-facing portrait of Archimedes along with a quote attributed to him.
“Transire suum pectus mundoque potiri” — Rise above oneself and grasp the world.
Known For: Euclidean geometry; Euclidean algorithm
Euclid of Alexandria was a Greek mathematician widely regarded as the founder of geometry. Euclid’s Elements, a compilation of 13 books, is considered one of the oldest and most influential books on mathematics.
While Euclid’s Elements is primarily celebrated for its foundational contributions to geometry, now recognized as Euclidean geometry, it also provides a thorough introduction to elementary number theory.
Euclid’s achievements extend beyond geometry, with his works on optics earning widespread acknowledgment for their significance in the field.
Euclid’s systematic approach in his work — starting from axioms and then logically obtaining complex results, has influenced some of the greatest minds of later generations. Newton’s Principia Mathematica is a perfect example of it.
Known For: The theory of optimal transport
Alessio Figalli has established himself as a leading figure in the study of partial differential equations, metric geometry, and their applications.
In 2018, he was awarded the Fields Medal for his contributions to the theory of optimal transport, which addresses the optimal ways to transport one distribution of mass to another while keeping the associated transportation cost as low as possible.
Figalli’s research goes beyond optimal transport, extending into areas like geometric measure theory, functional inequalities, and Monge-Ampère equations. Not only has his work significantly advanced the theoretical aspects of these subjects, but it has also yielded practical applications in diverse fields, including economics and physics.
Known For: Profound contributions to number theory
Manjul Bhargava has enhanced our understanding of representing integers through quadratic forms, a key aspect of number theory.
His work includes groundbreaking results related to the distribution of values of quadratic forms and higher-degree polynomial equations. He developed efficient techniques to study the distribution of integers represented by these equations, deepening our understanding of the arithmetic properties of these forms.
Bhargava introduced the concept of higher composition laws, generalizing the well-known composition laws for quadratic forms. These laws have applications in algebraic number theory. He also explored the rational points on elliptic curves, which have applications in both pure and applied mathematics.
Bhargava has received many awards and honors for his work, including the Fields Medal in 2014.
Known For: Providing insights into Riemann surfaces and their moduli spaces
Maryam Mirzakhani gained international recognition for her groundbreaking work in mathematics, especially in the field of geometry and dynamical systems. She made history in 2014 by becoming the first woman to be awarded the Fields Medal.
Her early work focused on the moduli space of Riemann surfaces. She developed new methods to calculate the Weil-Petersson volumes of these moduli spaces, providing new insights into the geometry of hyperbolic surfaces.
She also studied Teichmüller dynamics, which involves understanding the behavior of geometric structures on surfaces. Her research provided detailed insights into the dynamics of the mapping class group and the geometry of moduli spaces, connecting complex analysis, geometry, and dynamics.
Unfortunately, she passed away in 2017 at the age of 40. However, her legacy continues to inspire young students, particularly women, to pursue careers in math and contribute to the advancement of the discipline.
Known For: Solving the sphere-packing problem in dimension 8
Maryna Viazovska is famous for her involvement in a collaborative effort related to the “sphere-packing problem.” It’s a classical problem in math that involves determining the most efficient way to arrange identical spheres in a given space in such a way that they do not overlap or leave voids.
In 2016, Maryna Viazovska was part of a group of mathematicians who provided a groundbreaking solution to this problem. The solution involves finding the optimal way to pack spheres in eight-dimensional space, which has applications in coding theory and other areas.
Her contributions were recognized with the prestigious Fields Medal, which she was awarded in 2022. She became the first person with a degree from a Ukrainian university to ever receive this distinguished award.
Beyond the academic realm, her achievements have been acknowledged on a broader scale. For example, in December 2022, she was honored as one of the BBC 100 Women.
Known for: Solving Poincaré conjecture
Grigori Perelman has made notable contributions to the fields of geometric analysis, geometric topology, and Riemannian geometry. He gained international fame for his work on the Poincaré conjecture, a longstanding problem in topology.
This problem remained unsolved for almost a century until Perelman claimed to have proved it in a series of papers posted online between 2002 and 2003.
He won numerous awards and prizes for his contributions, including the Fields Medal and a one-million-dollar prize from the Clay Mathematics Institute. However, he declined most of them and withdrew from active participation in the mathematical community.
His refusal of prestigious awards and his decision to step away from the academic world have made him a somewhat mysterious figure in the mathematical community.
The Fields Medal is one of the highest honors a mathematician can receive. It is often described as the “Nobel Prize of Mathematics.” It is named after Canadian mathematician John Charles Fields, who came up with the idea of establishing this award.
First awarded in 1936, the Fields Medal is given every four years during the International Congress of Mathematicians. It is awarded to mathematicians under the age of 40.
Recipients receive a gold medal, global recognition, and a monetary prize, which, as of 2006, amounts to CA$15,000.
Of course, there have been many accomplished female mathematicians who have made major contributions in this field throughout history. The most popular names are
1. Hypatia was a prominent ancient Greek mathematician and astronomer who lived in Egypt during the late 4th and early 5th centuries AD. She is known for her detailed commentaries on Euclid’s famous mathematical work “Elements.” She also worked on Diophantus’s “Arithmetica,” which ultimately contributed to the development of algebraic concepts.
2. Sofya Kovalevskaya was the first woman to earn a doctorate in mathematics and become a full professor in Europe. She is best known for her Cauchy-Kovalevskaya theorem, which deals with the uniqueness of solutions to specific types of partial differential equations, specifically those related to the theory wave.
3. Emmy Noether is best known for her work in abstract algebra, particularly in the development of Noether’s theorem. This theorem played a critical role in the development of modern theoretical physics, including the formulation of the theory of relativity and quantum mechanics.
4. Mary Cartwright worked in the fields of dynamical systems, chaos theory, and differential equations. Her contributions to Cartwright–Littlewood Theorem helped us understand the stability of solutions to differential equations.
5. Karen Uhlenbeck is known for her groundbreaking work in geometric analysis and gauge theory. She is the first, and so far only, woman to win the Abel Prize, one of the most prestigious awards in mathematics.
While there are countless unsolved problems in mathematics, some have puzzled mathematicians for decades or even centuries. The most popular ones are:
1) P versus NP problem: It asks whether every problem for which a proposed solution can be quickly verified by a computer (NP, “nondeterministic polynomial time”) can also be solved quickly by a computer (P, “polynomial time”). It is also one of the seven Millennium Problems.
2) The Riemann Hypothesis: It deals with the distribution of prime numbers. The hypothesis has remained unproven since its formulation in the 19th century.
3) The Twin Prime Conjecture: It proposes that there are infinitely many pairs of twin primes (which are prime numbers having a difference of 2, for example, 41 and 43 or 71 and 73). Although there is strong numerical evidence, there is no rigorous proof.
4) 3n+1 problem: it is a simple mathematical sequence that starts with any positive integer and repeatedly applies certain operations. This conjecture asks whether all sequences eventually reach the number 1.
5) The Goldbach Conjecture: It was proposed by the German mathematician Christian Goldbach in a letter to Euler in 1742. It suggests that every even integer greater than 2 can be expressed as the sum of two prime numbers.
Read More
15 Scientists That Were Not Rewarded Fairly For Their Contribution
15 Famous Physicists Alive Today And Their Contribution
10 Fun Math Games That Will Make You Smarter