The Renaissance wasn’t just a revolution in the arts, but also the sciences, particularly mathematics. There was a marked proliferation of mathematical societies and institutions across Europe around this time, like the Accademia dei Lincei in Italy and the Royal Society in England, which in turn produced some of the best mathematical minds in history. 

10. Marino Ghetaldi

Marin Getaldic, also known as Marino Ghetaldi or Marinus Ghetaldus, was a notable Renaissance mathematician from Dubrovnik, Croatia. Born in the late 16th century, he excelled at math from an early age, and would work with other known mathematicians, like Christopher Clavius and François Viète, throughout his career. 

Ghetaldi was known for reconstructing the lost works of Apollonius and several other mathematical papers, including ones on physics and parabolas. Ghetaldi’s interest in scientific instruments, particularly optical devices, grew after his encounters with Galileo. His most remarkable contributions, however, were in the emerging field of applying algebraic concepts to geometry, which led to the development of Cartesian geometry. His contributions to mathematics and specifically geometry have since been acknowledged by scholars like Christian Huygens and Edmond Halley. 

9. Gemma Frisius

Born as Regnier Gemma in Friesland, Netherlands, in 1508, Gemma Frisius was a mathematician, astronomer, and cosmographer during the Renaissance period. Despite a difficult childhood marked by poverty, Gemma went on to study medicine and mathematics at the University of Louvain, eventually becoming a leading theoretical mathematician and professor at the same university. 

Gemma made important contributions in the development of maps, globes, and other astronomical instruments. In 1529, he published a corrected version of Apianus’s Cosmographia. He also designed a combined terrestrial and celestial globe, along with his book De Principiis Astronomiae Cosmographicae, which introduced map designs that would remain in use for decades to come. Gemma described a unique method to determine longitude using a clock and later expanded it to finding the longitude at sea, which turned out to be the solution to the long-standing problem of finding the longitude at sea. 

8. John Napier

John Napier was a Scottish mathematician and theological writer known for his invention of logarithms. He was born in 1550 in Merchiston Castle, near Edinburgh, Scotland, though we don’t know much else about his early life.

Napier was always interested in the inventions of war, as he worked on various military devices throughout his career, like burning mirrors, artillery pieces, and a metal chariot. His most notable contribution to mathematics was his invention of logarithms. He started working on them around 1594, though his work on the topic was only published after his death. Logarithms simplified calculations, especially multiplication, by transforming them into simple addition problems.

7. Scipione Del Ferro

Also known as Scipio del Ferro was a Renaissance-era mathematician from Bologna, Italy. Born in 1465, he attended the University of Bologna, where he’d later work as a lecturer in arithmetic and geometry in 1496 – a position he held until his death in 1526. Although none of his original work has survived, Ferro is credited with finding a solution to an unsolved cubic equation at the time. 

This solution hugely contributed to the study of fractions with irrational denominators, though his mathematical achievements largely remained unknown during his lifetime. Most of his findings were written in a personal notebook, which was passed on to his son-in-law, Hannibal Nave, after his death. The notebook contained Ferro’s solution to the cubic equation, which gained popularity when another influential Renaissance-era mathematician, Girolamo Cardano, discovered and published it in one of his own works.

6. Regiomontanus

Regiomontanus, also called Johannes Müller von Königsberg, was a prominent German scholar born in Königsberg, Bavaria in 1436. He received education at home and later attended the Universities of Leipzig and Vienna, where he became a pupil and friend of Georg von Peuerbach – another notable astronomer of the time.

Regiomontanus and Peuerbach would go on to collaborate on many astronomical topics, like the discrepancy between the predicted and observed positions of planets and lunar eclipses. They also worked on translating and critiquing Ptolemy’s Almagest, which Regiomontanus completed after Peuerbach’s death. This translation, known as the Epitome of the Almagest, played a huge role in Copernicus’ refutation of Ptolemy’s geocentric model. 

5. Luca Pacioli

Luca Pacioli was born in Borgo San Sepolcro, Tuscany around 1445. He’d go on to become an influential mathematician and educator of his era, receiving his early training in Venice and Rome under the guidance of figures like Piero della Francesca and Leon Battista Alberti. Pacioli’s passion for math led him to compile and summarize many works of his contemporaries.

Pacioli’s works not only made the mathematical knowledge of the time accessible to more people, but also introduced the modern system of double-entry bookkeeping, leading many to regard him as the ‘Father of Accounting’. His use of journals, ledgers, and the concept of balancing debits with credits massively contributed to the development of modern accounting practices. Pacioli is also remembered for his collaboration with Leonardo da Vinci in Milan, which further improved his own work. 

4. Niccolò Fontana Tartaglia

Often referred to as just Tartaglia, Niccolò Fontana Tartaglia was an Italian mathematician and physicist who lived from 1499 to 1557. He saw war and destruction at an early age, as he survived the French sack of Brescia in 1512 that left him severely injured. Despite these serious challenges, Tartaglia was good at math and eventually settled in Venice as a mathematics teacher.

Tartaglia made many contributions to the fields of physics and mathematics, particularly ballistics. He refuted Aristotle’s claim that air sustained motion, claiming instead that air resisted motion and that projectile physics should be studied in conditions without any air resistance. His groundbreaking work on ballistics, including his 1537 book, Nova Scientia, published in 1537, laid the foundation for the modern science of projectiles. Tartaglia also made notable contributions to other areas of mathematics, as he was one of the first mathematicians to provide workable solutions for cubic equations.

3. Francois Viète

François Viète was a Renaissance-era French mathematician and astronomer who made many contributions to the field of algebra. Born in Fontenay-le-Comte, France, in 1540, Viète studied law at the University of Poitiers before beginning his career as an attorney. His mathematical journey began when he was hired to educate the daughter of a prominent military leader, where he wrote some of his earliest treatises and works. 

France experienced some of its most turbulent and politically-unstable times during Viète’s lifetime, as there was an ongoing war between the Protestant and Catholic factions of the empire. Despite that, he continued work as a mathematician for Henry IV, where he was tasked with deciphering code against other European powers. 

His most notable contribution to mathematics is his formulation of the first systematic algebraic notations in his book In Artem Analyticam Isagoge, and to a lesser extent in the Canon Mathematicus, which deals with the concepts of trigonometry and astronomy. 

2. Tycho Brahe

While most people have likely never heard of him, Tycho Brahe, born in Sweden in 1546, made many fundamental contributions to the field of astronomy. Raised by his uncle, Jørgen Brahe, Tycho initially studied law at the University of Copenhagen. However, he would soon turn to astronomy after witnessing a total solar eclipse at the age of 14, which sparked his interest in the subject. 

Tycho continued his astronomy studies at the University of Leipzig, where he made his first recorded observations. He largely worked on improving the field through accurate observations and precise data, which led him to build his own observatory near Copenhagen. There, he designed and built advanced instruments, calibrated them, and carried out nightly observations. 

Tycho Brahe’s contributions to astronomy were profound, as they laid the foundation for future discoveries. Even before the advent of the telescope, Tycho was able to accurately map the entire Solar System, along with the positions of more than 777 fixed stars. His work challenged many prevailing theories of the time, like Aristotle’s notion of an immutable universe, and set the stage for other revolutionary insights of the coming years, like the heliocentric model proposed by Copernicus. 

1. Johannes Kepler

Johannes Kepler was a German mathematician and astronomer who massively advanced our understanding of planets. His three fundamental laws of planetary motion revolutionized the field and are in use to this day, as they transformed Copernicus’s heliocentric view into a dynamic universe with non-circular planetary orbits.

Apart from his achievements in astronomy, Kepler made important contributions to optics and geometry, including the first proof of logarithms and an explanation for the behavior of light inside telescopes. Interestingly, Kepler’s scientific work remained intertwined with his theological and astrological beliefs throughout his life, as he believed that the universe’s design was governed by God. Regardless, some of his works were so influential that they paved the way for other phenomenal works of the future, including some of Isaac Newton’s foundational principles of physics.

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.