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.