At its most basic, mathematics is the field of scientific study that deals with calculations and logical reasoning. It’s one of the fundamental parts of our understanding of the universe – without math, it’s impossible to advance in other areas of science and technology. Despite all that, though, some of the most important mathematicians in history – from Leonhard Euler to Brahmagupta to Euclid – remain largely forgotten and unacknowledged.

## 10. Girolamo Cardano

Girolamo – or Hieronimo – Cardano was an Italian polymath born in 1501. He was a physician, mathematician, astrologer, and philosopher, with important contributions in the fields of algebra, probability, physics, and medicine. Some of his discoveries were so influential that he’s still referred to as one of the most important mathematicians of the Renaissance era.

Cardano was born in Pavia in the Duchy of Milan, now Italy, as an illegitimate child of a lawyer and a widow. He studied at the universities of Pavia and Padua, earning his medical degree in 1526. He’d go on to become a lecturer in mathematics, as well as an accomplished physician. More than 200 books on various topics – ranging from medicine, mathematics, physics, philosophy, religion, and music – could be credited to him, including his autobiography. Cardano’s most important contribution was in 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 called one of the greatest mathematicians of all time, thanks to his contributions to fields like number theory, geometry, probability theory, astronomy, theory of functions, and electromagnetism.

Gauss was born in Brunswick in 1777 as 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’d work and improve on throughout his life. He made many important discoveries while he was studying – in 1796, Gauss proved that it was geometrically possible to construct a 17-sided polygon, or a heptadecagon.

He is best known for his book *Disquisitiones Arithmeticae* – or Arithmetical Investigations – along with important contributions like the development of various surveying instruments and an early form of a magnetometer. Gauss’s works describing magnetic and electric fluxes later formed the basis for James Clerk Maxwell’s famous electromagnetic theory. Many mathematical concepts and equations are still named after him, like Gaussian distribution, Gaussian elimination method, Gaussian gravitational constant, Gauss-Bonnet theorem, and many others.

## 8. Srinivasa Ramanujan

Born on December 22, 1887 in Erode – a small town in Tamil Nadu, India – Srinivasa Ramanujan would go on to become an important figure in the history of mathematics, especially in the area of number theory. Unlike the other names on this list, Ramanujan taught himself advanced mathematics by reading books and journals, and developed his own formulas from an early age. His work caught the attention of Godfrey H. Hardy – a famous British mathematician – who invited him to Cambridge University in 1914.

There, Ramanujan (who you might recall being name-checked in the film *Good Will Hunting*) collaborated with Hardy and other mathematicians on various topics, making important contributions in number theory, infinite series, partition function, and the Riemann zeta function, among others. He published multiple papers in prestigious journals, getting elected to the Royal Society of London in 1918. Even today, mathematical constants like 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 1917. He studied mathematics at the universities of Göttingen and Berlin, where he was influenced by established mathematicians of the time like Carl Friedrich Gauss. He obtained his doctorate in 1851 with a dissertation on complex analysis, and became a professor at Göttingen in 1859 after delivering his famous lecture on the foundations of geometry. Throughout his life, Reimann collaborated with other mathematicians like Bernhard Bolzano, Richard Dedekind, and Gustav Roch to improve his work.

Riemann’s work revolutionized many fields of mathematics and physics. He introduced new concepts like Riemann surfaces, Riemann integrals, Riemann zeta function, Riemann hypothesis, Riemannian geometry, and Riemann-Roch theorem. His ideas laid the foundation for the development of concepts like complex and real analysis, number theory, algebraic and differential geometry, and even Einstein’s general relativity. Reimann’s discoveries remain useful across fields like quantum mechanics, cryptography, and string theory even today.

## 6. Leonhard Euler

Leonhard Euler was a Swiss mathematician, physicist, astronomer, and engineer, among many other things. He was one of the early founders of the studies of graph theory and topology, along with pioneering discoveries in branches like analytic number theory, complex analysis, and infinitesimal calculus.

Euler was born in 1707, in Basel, Switzerland, with an aptitude for advanced mathematics throughout his early years. After being tutored by Johan Bernoulli – an important figure in early calculus – he’d go on to attend the University of Basel, earning his master’s degree at the age of 20 in 1726.

Euler made important discoveries that would have a huge impact on modern mathematics and science, particularly in graph theory and analytic number theory, including concepts named after him like the Euler’s formula for complex analysis and the Euler characteristic for topology.

## 5. Euclid

Living in Alexandria during the reign of Ptolemy I, Euclid was one of the most influential of all the early Greco-Roman mathematicians. He is best remembered for his magnum opus – *Elements* – which served as the foundation of all geometrical studies until the 19th century.

While we don’t know much about Euclid’s early life, his mathematical legacy has been recorded and shared many times throughout history. *Elements*, consisting of thirteen books – established the foundations of axiomatic geometry – an important area of study even today. Euclid’s logical approach of rigorous proofs revolutionized the field at the time, providing a codified system of geometric concepts for other Greek mathematicians and scientists. Apart from advancing the understanding of geometry, his work laid the groundwork for mathematical reasoning and proof in general.

## 4. Brahmagupta

Born in ancient India during the sixth century AD, Brahmagupta was one of the most influential mathematicians of the time, thanks to important contributions like the concept of zero. He was the first thinker to define rules for negative and positive numbers, allowing complex practical calculations like debt.

Brahmagupta’s treatise *Brahmasphutasiddhanta* was the first work in history to introduce zero as a calculable number, with strict rules around the arithmetic operations it can be used with. This proved to be a revolutionary idea, influencing important mathematicians and astronomers during the later Arabic and Byzantine ages. He also significantly contributed to the study of algebra, developing some of the earliest solutions for quadratic equations.

## 3. David Hilbert

David Hilbert was a renowned German mathematician living during 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’d later become a professor at the University of Göttingen, where he’d spent most of his professional life.

Hilbert is considered one of the most influential mathematicians in history due to his contributions to fields like algebraic geometry, number theory, and physics.

He is famous for his work on axiomatic systems and formal logic that laid the foundation for many modern mathematical concepts – his work on integral equations in 1999, for example, was the basis for all 20th-century research in functional analysis. In addition to mathematics, Hilbert also made important contributions to physics and philosophy.

## 2. Archimedes

Archimedes – also known as Archimedes of Syracuse – was a polymath living in Syracuse, Sicily between 287 and 212 AD. Also known as one of the most important mathematicians in history, Archimedes is still remembered for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. Additionally, he’s known for the formulation of his famous Archimedes’ principle, and for the invention of a device to raise water called the Archimedes screw.

Archimedes was instrumental in advancing our understanding of simple levers, which were then used to construct impressive parts of the infrastructure of Syracuse. Sadly, he was killed during the infamous siege of the city by the Roman general, Marcus Claudius Marcellus, which also destroyed a large part of that infrastructure.

## 1. Al-Khwarizmi

Muhammad ibn Musa al-Khwarizmi – popularly remembered as al-Khw?rizm? – was a Persian polymath during the Islamic Golden Age. He was born in Khw?rizm, now Khiva, Uzbekistan, around 780 AD, working mainly as a mathematician, astronomer, and geographer in the city known for its universities and scholars.

Most importantly, Al-Khwarizmi is known as the ‘Father of algebra’. The word, algebra, in fact, derives from one of his works known as *The Compendious Book on Calculation by Completion and Balancing*, as it was the first book to present workable solutions to known linear and quadratic equations. He was also influential in the propagation and acceptance of Arabic numerals and the decimal system across the Islamic empire, which remains in popular use around the world today.