Scans of a first edition copy of La Geometrie by René Descartes.

Who are the minds behind the formulas and procedures you’re learning in math class? Take a break from your practice problems and learn about the people behind the concepts you’re studying with this look at 8 renowned mathematicians throughout history, from the Ancient Greeks through today.

Classical Mathematicians

We don’t know much about many of the first ancient mathematicians in societies like Mesopotamia and Ancient Egypt, but we do have clearer records of renowned mathematicians from the classical era (roughly between 800 BCE and 500 CE). Here are some of the earliest and most impactful problem-solvers who paved the way of mathematics discovery for ages to come.

Archimedes of Syracuse, Ancient Greece (c. 287–212 BCE)

“The Death of Archimedes” (1815) by Thomas Degorge. When attacked by a Roman soldier during the Siege on Syracuse, Archimedes is attributed with saying, “Do not disturb my circles”, referencing the geometric work he was in the middle of.

A mathematician considered by many to be the greatest of all time, there’s not much we know about Archimedes’ life past his birth in Syracuse, Sicily. We do, however, have a strong record of his many mathematical discoveries and inventions.

While you’re probably more familiar with Pythagoras, much of your geometry lessons are actually based on Archimedes’ work from long ago. He rigorously proved geometrical theorems, like the area of a circle, volume of a sphere, and area of a spiral. In The Sand Reckoner, he developed exponentiation by proving the law of exponents (10a · 10b = 10a+b), and in On the Sphere and Cylinder, he gave an approximation of pi (π). 

On top of his work with mathematical theory, he was one of the first scientists to apply math to the real world. Rome began a siege on Syracuse near the end of his life, and he used his expertise in mathematics to construct weapons and instruments such as creating a heat ray from mirrors, designing a claw-like weapon to grapple attacking ships, and improving the catapult.

Aryabhata of Pataliputra, Gupta Empire (476–550 CE)

Illustration of Arybhata.

The first mathematician-astronomer from India’s classical age, Aryabhata was a leader in math discovery, rivaling many of the Ancient Greeks. As described in Aryabhatiya, his magnum opus, he found an approximation of pi (π) and concluded that pi is irrational. He also defined sine, cosine, versine, and inversine, contributing to the origin of trigonometry.

He’s especially renowned for his application of zero (0) as a placeholder for powers of ten without coefficients; so, zero’s use in numbers like 100 and 10,000. Arybhata’s proficiency in mathematics helped his study of the stars and planets, greatly influencing India’s understanding of astronomy. So much so, in fact, that India’s first satellite was named after him.

Famous Mathematicians of the Middle Ages

The Middle Ages (also known as the medieval period) are the period of history between the end of the classical period through the 15th century. In sharp contrast to the European Dark Ages of 500-1000 CE, which are characterized by population decline and the fall of governments, the High Middle Ages (1000-1300 CE) saw a rapidly increasing population, widespread sociopolitical development, and a rediscovery of intellectualism. 

The mathematicians from this era were able to translate their classical predecessors’ work and expand on their discoveries.

Omar Khayyam, Islamic Golden Age (1048–1131 CE)

A statue of Hakim Omar Khayam by sculptor Abolhassan Sadighi, located in Tehran.

The Islamic Golden Age (around 700-1200 CE) was a time of great scientific and cultural development in Islamic history, a precursor to the High Middle Ages of Europe.

Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī, generally known as Omar Khayyam, was a prolific polymath who lived in the Seljuk Empire. This renowned mathematician was famous during his time for his mathematical work in the fields of Algebra & Geometry.

Khayyam’s Commentary on the Difficulties Concerning the Postulates of Euclid’s Elements treatise grapples with the parallel axiom, the theory of proportions, and irrational numbers. In Treatise on the Division of a Quadrant of a Circle, he identified the start of analytic geometry; or, geometry that uses a coordinate plane. Later developed independently by René Descartes, this key concept allows for the manipulation of equations for lines and shapes. 

Khayyam also solved every type of cubic equation (the first to do so) and applied his expertise in mathematics to astronomy, building the Isfahan Observatory and updating the Persian calendar. His many achievements show why he was called the King of the Wise, unmatched in scientific knowledge at his time—the western world barely took notice of his work in the 18-19th century Orientalism movement.

Leonardo Fibonacci, the Republic of Pisa (c. 1170–1250)

Illustration of Leonardo Fibonacci.

Possibly the most talented mathematician of the western Middle Ages, Fibonacci first learned about the Hindu-Arabic number system (a precursor to the number system we use today) as a young boy in an Algerian school. When he traveled around the Mediterranean as a young man, he learned from everyday people about their number-crunching systems. After years of studying number theory and calculation, he wrote the Liber Abaci (the Book of Abacus)—what solidified his legacy today.

The Liber Abaci introduced Europeans to the Hindu–Arabic numeral system as an alternative to other systems like Roman numerals. A guide for tradespeople on how to do everyday, real-world calculations, Liber Abaci demonstrated how to utilize this number system to calculate and convert values, advancing the growth of business and banking across the continent.

Fibonacci also introduced what we know him for today in Liber Abaci—the Fibonacci sequence, in which each number is the sum of the previous two numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so forth. Fibonacci numbers are special because they appear unexpectedly, throughout both mathematics and the natural, physical world (like the swirl in a shell or the way petals/leaves are arranged on a plant stem). 

Renaissance Mathematicians

The start of the Late Middle Ages is marked by years of crisis and collapse—famines, plagues like the Black Death, and unrest across Europe interrupted the previously flourishing economies and societies of the continent. This crisis led to the birth of the next period of western history: the Renaissance (1400-1600 CE), a cultural movement marked by social change and intense cultural and intellectual development.

The core concept of the Renaissance is a revival of classical antiquity; Europeans wanted to revisit the ideas of the Ancient Greeks and Romans and surpass their discoveries and achievements. As such, the Renaissance saw vast development in the fields of math and science. These celebrated, famous math experts from the era are the contemporaries of Leonardo da Vinci and Isaac Newton.

Rafael Bombelli of Bologna, Italy (1526–1572 CE)

Illustration of Rafael Bombelli.

Rafael Bombelli did not receive a college education, but was taught by engineer and architect Pier Francesco Clementi. As an engineer surrounded by the developing study of mathematics, he felt that the Algebra publications available were only written for those with a strong understanding of math. So, he decided to write Algebra (1572), an account of all that was known in the subject at the time, written to be accessible to a wide audience.

Algebra was the first mathematics publication in Europe to show how to calculate with negative numbers:

“Plus times plus makes plus

Minus times minus makes plus

Plus times minus makes minus

Minus times plus makes minus”

With Algebra, Bombelli also became the first to write the rules for operations with complex numbers (except for division), giving him acclaim as the inventor of complex numbers. What especially made him one of the most renowned mathematicians was that he was also the first to use a form of notation in a printed text. Mathematicians before him had always written out equations in words, and bombelli’s notation was the predecessor to the one we know today. For example,  1U3 a. 6U1 p. 40 represented the equation x³ = 6x + 40.

René Descartes, France (1596–1660)

Portrait of René Descartes by Frans Hals.

You may know René Descartes from his famous principle, “I think, therefore I am.” Just as he is a celebrated philosopher, he’s also a renowned mathematician for his contributions to algebra and geometry.

During Descartes’ time, the Scientific Revolution was in full swing. Like Bombwlli, he also improved mathematical notation, inventing the representation of unknowns with the letters x, y, and z, as well as the use of superscript to represent exponents. 

In his philosophical treatise, Discourse on the Method, he discusses topics across morality, religion, and, most notably, the natural sciences. It is in that book’s appendix, La Géométrie, that he produced and popularized the Cartesian coordinate system, the coordinate chart that we use today. 

René Descartes’ impact was strong and lasting. Notably, Isaac Newton was greatly influenced by Descartes, whose work became the basis for calculus.

Modern Renowned Mathematicians

Finally, the famous mathematicians from the modern era; that is, the past few hundred years. Globalization and industrialization expedited humanity’s pace of innovation, leading to great expansion of technology, medicine, and related fields—all of which take advantage of the vast amount of math and science study the individuals in this article have conducted. 

David Blackwell (1919–2010)

David Blackwell

One of the most renowned African American mathematicians, David Blackwell is known for his many contributions to a variety of topics in math. After graduating high school two years early, he studied mathematics for years, earning a bachelor’s, a master’s, and, at 22, a Ph.D.—making him the seventh African American to earn a Ph.D. in mathematics. 

AS aBlackwell made significant contributions to the world of statistics over his lifetime. By his retirement in 1988, he published nearly 100 works on game theory, dynamic programming and statistics. In fact, the Rao-Blackwell theorem, which provides a way of optimizing statistical estimates, is partly named after him. In 1965, he became the first African American to be named a member of the U.S. National Academy of Sciences.

Looking at David Blackwell’s life shows how far passion and determination can take someone. From teaching himself to read as a child to persevering in academia even when he was excluded for his race, he was always able to reach new heights with commitment and hard work. 

Paul Erdős (1913–1996)

Paul Erdős in 1985 with a 10-year-old Terence Tao, who one day became a Fields medalist and solved the $10,000 problem.

The last in this look at famous math experts is Paul Erdős, who was driven by problems and solving them. The son of two math teachers, he was always fascinated with mathematics—he even taught himself to read with the math textbooks around the house. 

Erdős was the most prolific publisher of mathematical papers in history, authoring or co-authoring over 1,500 distinct works—unrivaled to this day. His vast contributions to number theory, probability, and mathematical analysis were a result of his commitment to the subject. For example, he was a strong believer in the practice of mathematics as a social activity, spending much of his career in collaboration with other academics and attending various seminars and conferences.

His eccentric personality made him a force for innovation in the field. He developed a reputation for posing problems, offering cash prizes to those who could solve the complex problems he raised. The prize for the most intensely complex & mathematically significant problem he suggested was $10,000—a check cashed by a group of contemporary mathematicians, years after his death. (The problem was related to prime numbers: how large can the gap between consecutive prime numbers be?)

Math Practice for 5th Grade through High School with Piqosity

As you’ve seen in this article, every one of these renowned mathematicians continued the work of the hundreds of problem-solvers who came before them. While many of the biggest questions have already been answered, there are many still-unsolved problems (like those posed by Paul Erdős) and unique areas of study in need of innovation! 

Whether you’re inspired by these mathematicians or just want to get through your standardized assessments this Spring, Piqosity can help you improve your math skills.

Not only do we offer test prep courses for the ISEE, SAT, and ACT, we also have full-length English and Math courses for grades 5 through 11.

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