At its core, mathematics is a field of scientific study that deals with calculations and logical reasoning. It is a fundamental part of our understanding of the universe—without mathematics, advances in other fields of science and technology are impossible. Yet, despite all this, some of history's most important mathematicians—from Leonhard Euler to Brahmagupta and Euclid—remain largely forgotten and unrecognized.
10. Girolamo Cardano
Girolamo—or Hieronimo—Cardano was an Italian polymath born in 1501. He was a physician, mathematician, astrologer, and philosopher who made important contributions to algebra, probability, physics, and medicine. Some of his discoveries were so influential that he is still considered one of the most important mathematicians of the Renaissance.
Cardano was born in Pavia in the Duchy of Milan, now Italy, the illegitimate child of a lawyer and a widow. He studied at the universities of Pavia and Padua, receiving a medical degree in 1526. He became a lecturer in mathematics and also an accomplished physician. He is credited with writing over 200 books on topics ranging from medicine, mathematics, physics, philosophy, religion, and music, including his autobiography. Cardano's most important contribution was to the field of probability, making him one of the early pioneers of probability theory.
9. Carl Friedrich Gauss
Carl Friedrich Gauss was a German mathematician and physicist who lived in the 18th and 19th centuries. He is also considered one of the greatest mathematicians of all time due to his contributions to number theory, geometry, probability theory, astronomy, function theory, and electromagnetism.
Born in Brunswick in 1777, Gauss was a mathematical prodigy, receiving his doctorate from the University of Helmstedt in 1799 with an initial proof of the fundamental theorem of algebra—a topic he worked on and refined throughout his life. During his studies, he made many important discoveries—in 1796, Gauss proved that it is geometrically possible to construct a 17-sided polygon, or heptagon.
He is best known for his book Disquisitiones Arithmeticae — or Arithmetic Investigations — along with such important contributions as the development of various geodetic instruments and an early form of the magnetometer. Gauss's work describing magnetic and electric fluxes later formed the basis of James Clerk Maxwell's famous electromagnetic theory. Many mathematical concepts and equations, such as the Gaussian distribution, the Gaussian elimination method, the Gaussian gravitational constant, the Gauss-Bonnet theorem, and many others, are still named after him.
8. Srinivasa Ramanujan
Srinivasa Ramanujan was born on December 22, 1887, in Erode, a small town in Tamil Nadu, India. He became an important figure in the history of mathematics, particularly in the field of number theory. Unlike other names on this list, Ramanujan studied higher mathematics by reading books and journals and developed his own formulas from an early age. His work attracted the attention of Godfrey H. Hardy, a renowned British mathematician, who invited him to Cambridge University in 1914.
There's Ramanujan (whom you may remember is mentioned in the film) «Good Will Hunting »"He collaborated with Hardy and other mathematicians on a variety of topics, making important contributions to number theory, infinite series, the partition function, and the Riemann zeta function, among others. He published several papers in prestigious journals and was elected a Fellow of the Royal Society of London in 1918. Even today, mathematical constants such as the Landau–Ramanujan constant and the Ramanujan–Soldner constant are named after him.
7. Bernhard Riemann
Bernhard Riemann was a German mathematician and physicist born in the Hanover region in 1817. He studied mathematics at the universities of Göttingen and Berlin, where he was influenced by renowned mathematicians of the time, such as Carl Friedrich Gauss. He received his doctorate in 1851 with a dissertation on complex analysis and became a professor at Göttingen in 1859, delivering his famous lecture on the foundations of geometry. Throughout his life, Reimann collaborated with other mathematicians, such as Bernhard Bolzano, Richard Dedekind, and Gustav Roch, to improve his work.
Riemann's work revolutionized many areas of mathematics and physics. He introduced new concepts such as Riemann surfaces, Riemann integrals, the Riemann zeta function, the Riemann hypothesis, Riemannian geometry, and the Riemann-Roch theorem. His ideas laid the foundation for the development of concepts such as complex and real analysis, number theory, algebraic and differential geometry, and even Einstein's general theory of relativity. Reimann's discoveries remain useful in fields such as quantum mechanics, cryptography, and string theory even today.
6. Leonhard Euler
Leonhard Euler was a Swiss mathematician, physicist, astronomer, and engineer, among many others. He was one of the early founders of graph theory and topology, as well as pioneering discoveries in fields such as analytic number theory, complex analysis, and infinitesimal calculus.
Euler was born in 1707 in Basel, Switzerland, and showed an aptitude for higher mathematics from an early age. After studying with Johann Bernoulli, an important figure in early calculus, he entered the University of Basel, receiving his master's degree at the age of 20 in 1726.
Euler made important discoveries that have had a profound impact on modern mathematics and science, particularly graph theory and analytic number theory, including concepts named after him, such as Euler's formula for complex analysis and Euler's characteristic for topology.
5. Euclid
Living in Alexandria during the reign of Ptolemy I, Euclid was one of the most influential of all early Greco-Roman mathematicians. He is best remembered for his seminal work, "«Elements»", which served as the basis for all geometric research until the 19th century.
Although we know little about Euclid's early life, his mathematical legacy has been recorded and passed down many times throughout history.Elements , consisting of thirteen books, laid the foundations of axiomatic geometry, an important field of study even today. Euclid's logical approach to rigorous proofs revolutionized the field at the time, providing a codified system of geometric concepts for other Greek mathematicians and scientists. In addition to deepening the understanding of geometry, his work laid the foundation for mathematical reasoning and evidence in general.
4. Brahmagupta
Born in ancient India in the sixth century CE, Brahmagupta was one of the most influential mathematicians of his time thanks to his crucial contributions, such as the concept of zero. He was the first thinker to define rules for negative and positive numbers, which enabled complex practical calculations such as debt.
Brahmagupta's treatise«Brahmasphutasiddhanta"» was the first work in history to present zero as a countable number with strict rules regarding the arithmetic operations with which it could be used. This proved to be a revolutionary idea, influencing prominent mathematicians and astronomers in the later Arab and Byzantine eras. He also made significant contributions to the study of algebra, developing some of the earliest solutions to quadratic equations.
3. David Gilbert
David Hilbert was a renowned German mathematician who lived in the late 19th and early 20th centuries. Born in 1862 in Königsberg, Prussia—now Kaliningrad, Russia—he began his career as a mathematician at the University of Königsberg. He later became a professor at the University of Göttingen, where he spent most of his professional life.
Hilbert is considered one of the most influential mathematicians in history due to his contributions to fields such as algebraic geometry, number theory, and physics.
He is known for his work on axiomatic systems and formal logic, which laid the foundation for many modern mathematical concepts—for example, his 1999 work on integral equations laid the foundation for all 20th-century research in functional analysis. Beyond mathematics, Hilbert also made important contributions to physics and philosophy.
2. Archimedes
Archimedes, also known as Archimedes of Syracuse, was a polymath who lived in Syracuse, Sicily, between 287 and 212 AD. Known as one of the most important mathematicians in history, Archimedes is still remembered for his discovery of the relationship between the surface area and volume of a sphere and its circumscribing cylinder. He is also known for formulating his famous Archimedes' principle and inventing a device for lifting water, called the Archimedes screw.
Archimedes played a vital role in advancing our understanding of simple levers, which were then used to construct the impressive infrastructure of Syracuse. Unfortunately, he was killed during the infamous siege of the city by the Roman general Marcus Claudius Marcellus, which also destroyed much of this infrastructure.
1. Al-Khwarizmi
Muhammad ibn Musa al-Khwarizmi, commonly known as al-Khwarizm, was a Persian polymath during the Islamic Golden Age. He was born in Khwarazm, now Khiva, Uzbekistan, around 780 CE, working primarily as a mathematician, astronomer, and geographer in a city renowned for its universities and scholars.
Most importantly, Al-Khwarizmi is known as the "Father of Algebra." The word "algebra" actually comes from one of his works, known as «"A Brief Book on Completion and Balancing Calculations"» , as it was the first book to present working solutions to known linear and quadratic equations. It also influenced the spread and adoption of Arabic numerals and the decimal system in the Islamic Empire, which remains widely used throughout the world today.