15 Geniuses who changed the world of mathematics forever

As the 15 greatest mathematical minds in history, from the ancient Greek genius Thales to the modern revolutionary Mandelbrot, their discoveries in algebra, geometry, number theory and other fields have forever changed the face of mathematics and the world.

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Mathematics has been part of human culture for thousands of years. Its origins lie in the ancient civilisations of Greece, Mesopotamia and Egypt. Over the centuries, the greatest minds have developed new theories and methods that have changed our understanding of the world, from Euclid’s geometry to Kepler’s laws of planetary motion. This article will discuss the contributions of the greatest mathematicians to modern science.

1. Thales of Miletus

Thales of Miletus is considered the father of mathematics and one of the greatest pre-Socratic philosophers. He was born in the ancient Greek city of Miletus in the 7th century BC and made significant contributions to mathematics, astronomy and philosophy. One of Thales’ most significant achievements was the discovery of the principles of geometry and the properties of geometric figures, which we still use today.

Thales also made an important contribution to astronomy. He was one of the first to calculate the timing of solar eclipses based on his understanding of the Earth’s rotation and the position of the Sun in the sky. It is also said that he accurately predicted the size of the next harvest using his knowledge of astronomical cycles and weather conditions.

2. Euclid

Euclid was an ancient Greek philosopher and scientist who developed a systematic approach to mathematical proof, laying the foundations of modern geometry in his book Elements. His work focused on points, lines, angles and parallelism, and he formulated many important ideas about circles, triangles, quadrilaterals, proportionality and incommensurable quantities.

Elements is still considered one of the most influential mathematical works ever written. It contains some of the earliest known arithmetic axioms and theorems, which have been studied and appreciated by generations of mathematicians, philosophers and scientists. Euclid is also credited with creating a rigorous approach to logical reasoning, which remains an important part of mathematics today.

3. Archimedes

One of the most famous mathematicians, Archimedes was born in Syracuse (Sicily) in the 3rd century BC and made groundbreaking contributions to mathematics, physics, engineering and astronomy. He created the “method of exhaustion,” which allowed him to calculate the area and volume of irregular shapes by dividing them into smaller, more manageable parts—essentially inventing the method of integral calculus later developed by Newton and Leibniz.

In addition to his work on calculus, Archimedes made significant contributions to geometry, including the development of the Archimedean spiral and various formulas for calculating the areas and volumes of geometric figures. He was also an outstanding physicist and engineer, known for his study of hydrodynamics and mechanics, and for devices such as the Archimedean screw.

4. Muhammad al-Khwarizmi

Muhammad al-Khwarizmi, born in Khwarizm (modern-day Uzbekistan) in the 8th century, is known as the father of algebra. His greatest work, Al-Jabr wa al-Muqābala (“The Book of Calculation by Completion and Balancing”), introduced systematic methods for solving linear and quadratic equations and coined the term “algebra.”

Beyond algebra, al-Khwarizmi wrote extensively on spherical trigonometry, arithmetic, decimal fractions and numerical methods, marking the beginning of the Golden Age of Islamic science. He also introduced the Arabic numeral system to mathematics, a revolutionary achievement that led directly to modern arithmetic.

5. Leonardo Fibonacci

The Italian Fibonacci, born in Pisa around 1170, travelled throughout the Mediterranean and learned mathematical systems from diverse cultures. His most significant contribution was introducing the Arabic numeral system to Western Europe in Liber Abaci (1202), revolutionising calculations by replacing Roman numerals with a more efficient decimal system.

Fibonacci also described the sequence now bearing his name—a series where each number is the sum of the two previous (starting 0, 1)—which appears in nature’s growth patterns, such as plant phyllotaxis and shell spirals. His work laid foundations for number theory and combinatorics.

6. Johannes Kepler

Johannes Kepler was a great German mathematician and astronomer, known for his laws of planetary motion. Kepler’s contributions to physics and astronomy have significantly influenced our understanding of the cosmos and how planets move.

These laws help explain why planets move at different speeds and accelerate or decelerate at certain points in their orbits, and how to mathematically calculate their motion in our solar system. He also made significant advances in optics, which led to the invention of the modern telescope.

7. Gottfried W. Leibniz

Gottfried Wilhelm Leibniz (1646–1716) is best known for inventing differential calculus, which he developed concurrently with Isaac Newton. Despite their priority dispute, Leibniz’s notation for differential equations became the standard for calculus and is still used today.

In addition to calculus, Leibniz made significant contributions to algebra and number theory. He developed methods for solving linear differential equations and introduced binary arithmetic, which underpins modern computing and algebraic systems.

8. Isaac Newton

Isaac Newton was a famous English physicist and mathematician whose Philosophiæ Naturalis Principia Mathematica presented his three laws of motion, still used today to explain the behaviour of moving objects. He invented calculus (“fluxions”) to develop the mathematical basis of classical mechanics and to predict the motion of planets and other bodies.

Newton also made significant contributions to optics—demonstrating that white light consists of a spectrum of colours—and invented the first reflecting telescope, overcoming the limitations of refracting designs.

9. Leonhard Euler

Leonhard Euler (1707–1783) demonstrated exceptional ability from an early age, contributing to calculus, graph theory, mechanics and optics. He developed the celebrated formula linking e, i, π, 0 and 1, and introduced the function notation f(x) and dy/dx that remain standard today.

In graph theory, Euler defined vertices, edges and faces and formulated the “Eulerian path” and “Eulerian circuit” solving the Seven Bridges of Königsberg problem. Despite partial blindness and deafness, he worked tirelessly, producing foundational results across mathematics.

10. Carl Friedrich Gauss

Carl Friedrich Gauss, known as the “Prince of Mathematics,” was born in Braunschweig, Germany, in 1777 and displayed prodigious talent from childhood. At the age of eighteen he wrote a groundbreaking work on the construction of regular polygons, a fundamental contribution to algebraic geometry. Gauss later proved the fundamental theorem of algebra, establishing that every non-constant polynomial equation has at least one complex root.

He developed the method of least squares, which remains essential in statistics, economics and modern physics, and discovered the theory of modular arithmetic, a cornerstone of contemporary cryptography. Gauss’s achievements extended into physics and engineering: he is credited with inventing the electric telegraph, making significant advances in magnetism, and devising methods for predicting planetary orbits—work that led directly to the discovery of the asteroid Ceres.

11. Ada Lovelace

Ada Lovelace (1815–1852), daughter of Lord Byron, received advanced training in mathematics and natural science. Collaborating with Charles Babbage on his Analytical Engine, she realised the machine could perform symbolic operations beyond numbers, likening its patterns to a Jacquard loom.

In her famous notes, Lovelace wrote the first algorithm intended for machine processing—calculating Bernoulli numbers—thus laying the conceptual foundation for modern computer programming despite the engine never being built.

12. David Hilbert

David Hilbert was one of the towering mathematicians of the 20th century, renowned for his vast contributions to geometric algebra, applied mathematics and number theory. His work on logic—particularly the development of first-order, or predicate, calculus—made it possible to formalise mathematical proofs and provided a rigorous foundation for the entire discipline.

Hilbert’s formalism extended into number theory with his theory of Hilbert class fields, deepening our understanding of the relationship between fields of algebraic numbers and their Galois groups. In geometry, his axioms formed the basis of modern geometric algebra, and his famous list of 23 unsolved problems guided much of the mathematical research that followed. Although some of his ideas sparked intense debate, his influence on the shape of modern mathematics is undeniable.

13. Emmy Noether

Emmy Noether developed a number of revolutionary mathematical concepts that challenged existing theories about algebraic equations and their structures. Her most significant contribution, Noether’s theorem, established a profound connection between symmetry in physical systems and the fundamental laws of nature, becoming a cornerstone of modern theoretical physics.

Beyond physics, Noether transformed abstract algebra through her work in ring theory and commutative algebra. Despite facing severe gender discrimination and being forced to work as an unpaid lecturer for many years, she persevered and ultimately secured a paid academic position at the University of Göttingen. Her pioneering ideas continue to underpin contemporary research across algebra, topology and mathematical physics.

14. Kurt Gödel

Kurt Gödel is celebrated as one of history’s most brilliant logicians, whose work has had a profound impact on mathematics and beyond. His incompleteness theorems demonstrated the inherent limitations of formal axiomatic systems, showing that any system powerful enough to express basic arithmetic truths will necessarily contain true statements that cannot be proved within the system itself.

Gödel’s results challenged the prevailing hope for a complete and consistent foundation for mathematics, forcing logicians to re-examine the very nature of mathematical truth. His insights also influenced philosophy and computer science, playing a decisive role in the development of artificial intelligence and the study of computational complexity.

15. Benoît Mandelbrot

Benoît Mandelbrot, a French mathematician of Polish origin, first introduced the term “fractal” to describe objects exhibiting self-similarity at different scales. He pioneered a new branch of geometry—fractal geometry—closely linked to chaos theory and with applications ranging from art to finance.

One of Mandelbrot’s most notable discoveries is the Mandelbrot set, generated by a simple iterative formula yet producing infinitely detailed, complex patterns. His work captured the imagination of both mathematicians and creative professionals. He also developed a mathematical model of turbulence used in hydrodynamics and applied fractal concepts to image compression, revolutionising the field of digital imaging.