Mathematics is the queen of the sciences and number theory is the queen of mathematics.
Carl Friedrich Gauss
In this article, we will explore the biographies and notable contributions of ten influential mathematicians throughout history. Discover the history of the sciences and maths through these different mathematical giants and gain some inspiration for your exam preparation in the subject. Who would you include?
| Name | Lifespan | Nationality | Era | Key Contributions |
|---|---|---|---|---|
| Thales of Miletus | c. 625 BCE – c. 547 BCE | Greek | Ancient | Thales’ theorem, early geometry, astronomical observations |
| Leonhard Euler | 1707 – 1783 | Swiss | Modern | Euler’s formula, graph theory, f(x), number theory, mathematical notation (π, e) |
| Pythagoras of Samos | c. 570 BCE – c. 495 BCE | Greek | Ancient | Pythagorean theorem, number theory foundations, Pythagorean school |
| Euclid | c. 330 BCE – c. 265 BCE | Greek | Ancient | Elements, Euclidean geometry, greatest common divisor, axioms |
| Andrew Wiles | 1953 – present | British | Contemporary | Proof of Fermat’s Last Theorem, modular forms, number theory |
| Isaac Newton | 1642 – 1727 | English | Early Modern | Calculus, binomial theorem, laws of motion, gravitation |
| René Descartes | 1596 – 1650 | French | Renaissance / Early Modern | Analytic geometry, Cartesian coordinates, algebraic notation |
| Alan Turing | 1912 – 1954 | British | Contemporary | Turing machine, code-breaking, computer science foundations, AI |
| Archimedes | c. 287 BCE – c. 212 BCE | Greek | Ancient | Principle of buoyancy, π, mechanics, Archimedean screw |
| Carl Friedrich Gauss | 1777 – 1855 | German | Modern | Number theory, Gaussian distribution, least squares, prime number theorem |
How Mathematicians Shaped the World of Science and Knowledge
Throughout history, many mathematicians have created numerous theorems and successfully proved them through rigorous mathematical proofs. Prime numbers, differential calculus, analytic geometry, algebra – all of the history of math can be seen to run in parallel with the history of science. Mathematicians have played a role in shaping the trajectory of humanity. Their efforts encompass not the development of theories and formulas but the facilitation of technological advancements and scientific breakthroughs.
The impact of their work extends far and wide, serving as the foundation for innovations and discoveries in fields such as physics, astronomy, and computer science. Without their contributions, our understanding of the world and the universe would be constrained, depriving us of achievements that we now take for granted. Being a professor in mathematics requires, then, describing the history of the discipline's progression, as well as engaging students in this history through the narratives of some of the most famous and successful mathematicians.
The impact of mathematics spans across various domains, including engineering and finance, and has transformed our lives. These remarkable achievements can be attributed to the intellects of mathematicians who have devoted themselves to unravelling the enigmas surrounding numbers and shapes.
A famous mathematician is not only recognised for solving problems or creating theories, but also for influencing generations of learners and shaping entire scientific fields. Their discoveries often extend far beyond mathematics, impacting physics, astronomy, engineering, and modern computing.
Thales
A great philosopher in ancient Greece, Thales is most known for his famous theorem, which we still learn today in high school. However, going beyond his renowned work, do we really know who Thales is?
Born in what is now part of Turkey in 625 BCE, Thales of Miletus is considered one of the seven sages of ancient Greece. The young mathematician studied various sciences in Egypt, subjects that were then reserved for Egyptian and Babylonian priests.
From them, Thales learned geometry, astronomy, and philosophy. In fact, the Egyptian pyramids were often the subject of the young apprentice's scientific experiments.
After this experience, Thales returned home to Miletus with the hope of establishing the school of Milan. There, Thales became a professor and began teaching his disciples the discoveries he had made abroad, all the while continuing his research in various domains.
The discovery of the theorem that we know today has an interesting origin. According to legend, Thales attempted to calculate the height of a pyramid by measuring the shadow of his cane. It was through this inquiry that Thales invented his now-famous theorem:
If A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.
Thales' knowledge also extends to cover the field of astronomy, where he discovered how to use the Little Dipper, or Ursa Minor, to guide sailors in the open ocean; how to calculate the duration of a year in relation to solstices and equinoxes; and identified the trajectory of the sun between the two tropics, etc. Thales died in approximately 547 BCE in Miletus. Find out about him in this short video.
Leonhard Euler
Leonhard Euler, a mathematician and physicist, is widely regarded as one of the most exceptional mathematical minds in history. His contributions to branches of mathematics, including calculus, graph theory and number theory, are unparalleled.
Euler's immense and foundational contributions to branches of mathematics have had a lasting impact on the field. Not only did his work expand the boundaries of mathematics, it also laid the groundwork for numerous scientific disciplines. In this concise overview, we will explore some of Euler's notable achievements.
Euler made significant advancements in number theory, with a particular focus on prime numbers. He is credited with proving Fermat's Little Theorem—a result in number theory with applications in cryptography and computer science. Euler also studied numbers extensively and introduced the concept of the Euler totient function while contributing to our understanding of quadratic reciprocity.
Euler's contributions to calculus and mathematical analysis are incredibly vast. He played a role in developing the concept of functions and introduced the notation f(x) to represent them. His deep understanding of calculus fundamentals, coupled with his work on power series expansions, significantly solidified these mathematical concepts.
When it comes to analysis, Euler's name is closely associated with numbers. He expanded the field of numbers by introducing what is now known as Euler's formula. The formula establishes a connection between the number of vertices, edges and faces in a polyhedron and finds use in the realms of geometry and topology.
An area where Euler left an enduring legacy is the development of notation. He made contributions by introducing familiar symbols, such as π (pi), which represents the constant ratio of a circle's circumference to its diameter, and the letter 'e', denoting the base of natural logarithms. These symbols have become iconic in mathematics and science.
With a body of work comprising over 850 research papers, Euler has had a lasting impact on the field of mathematics. He has solidified his place as one of the most influential contributors to the field of mathematics of all time.
mathematical theorems have been published in academic journals worldwide.
Pythagoras
As every student can recall, Thales' theorem is covered in the curriculum alongside Pythagoras' theorem. A concept covered early on in the academic career of high schoolers, Pythagoras' theorem marks one of the most critical chapters in the development of geometry.
Pythagoras, which translates to "announced by Pythia", was born on the island of Samos in Greece at the end of the 6th century BCE. The history of the infamous scientist is derived from only some works written before Pythagoras' death.
Pythagoras was a very gifted and athletic student. Most notably, he participated in the Olympic games in the category of combat. Interested in philosophy, history and the sciences, he became a student of Thales.
Following in his professor's footsteps, Pythagoras left home to learn Egyptian and Babylonian sciences. After finishing his studies, he returned to his island to start a school, exactly as Thales had done.
With his disciples, the mathematician managed to demonstrate his now-infamous theorem:
The square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Or a2+b2=c2.
The influence of Pythagoras on the discipline of mathematics doesn't end there. The Pythagorean snail, Pythagoras' table, along with his School for Pythagoreans, changed the field of mathematics forever. Pythagoras died approximately 500 BCE.
Euclid
The life and discoveries of Euclid altered the approach to teaching mathematics. Trigonometry, algebraic reasoning, equations, fractions, logarithms, Euclid's axioms, Euclidean division, Euclidean geometry, Euclidean algorithms – many of today's maths courses are structured concerning Euclid's research.
Born in Athens around 330 BCE, Euclid became a professor at the School of Alexandria. His mathematical discoveries were inspired by his frequent visits to the library and to the Museum of Alexandria. The mathematician is now celebrated throughout the world over for his seminal work, named Elements, written around 300 BCE.
Considered the Mathematics Bible, this book has, like the Bible, continued to be sold since its inception. Divided into thirteen books, Elements develops several theories concerning the geometric plane and general arithmetic (triangles, right angles, circles, etc.).
Through these works, Euclid managed to prove Pythagoras' theorem and to develop the function of the greatest common divisor (GCD) in Euclidean divisions. Euclidean divisions are simply the division taught in elementary school.
This division involves the four main elements: a dividend, a divisor, a quotient and a remainder. Euclid also explained how to find the HCF (highest common factor), a procedure that involves finding the most significant number that is common to two numbers and is divisible by both. Finding the HCF allows division to be accomplished much more easily. Euclid died in 265 BCE in Alexandria.
Andrew Wiles
Andrew Wiles, a mathematician from Britain, achieved recognition by successfully solving Fermat's Last Theorem—a problem that had remained unsolved for more than 350 years. Wiles' proof, presented in 1994, incorporated insights from areas of mathematics such as number theory and algebraic geometry.
Wiles presented a proof for this theorem, which states that it is impossible to find three integers a, b and c that satisfy the equation a^n. B^n = c^n for any value of n greater than 2. This groundbreaking achievement not only built on the work of mathematicians but also revolutionised the field of number theory.
His solution not only provided the awaited resolution to one of history's most celebrated mathematical puzzles but also demonstrated the immense strength of mathematical reasoning and the unwavering commitment needed to tackle such intricate challenges.
Wiles's accomplishment stands as a milestone in the history of mathematics, as it finally resolved one of its renowned unresolved problems. His profound understanding of curves, modular forms, and the Taniyama-Shimura-Weil conjecture significantly contributed to this exceptional feat.
His unwavering dedication, coupled with immense perseverance, has garnered him recognition and exemplified the profound impact his contributions have had on the mathematical community. No list of great mathematicians is complete without the mention of Andrew Wiles.
From the geometry of Ancient Greece to the algorithms behind today’s computers, mathematics has developed across centuries and cultures. Each mathematician in this list made contributions that became the building blocks for future discoveries and technologies.
Sir Isaac Newton
Isaac Newton (1642-1727) is not just a simple mathematician. Physician, philosopher and astronomer, Isaac Newton was born in Woolsthorpe in Lincolnshire in the UK. Raised mainly by his father and his grandmother, he was characterised as being at once a distracted student but also very gifted in building machines of all types.
When his mother decided to take Newton out of school so he could help the family farm, one professor convinced her to let him enrol at the University of Cambridge. There, he studied arithmetic, geometry, trigonometry, astronomy and optics – and subsequently graduated in 1665.
Isaac Newton is known first and foremost for discovering the phenomenon of gravitation. Legend has it that Isaac Newton must have discovered gravity by observing apples fall in an orchard. In the field of mathematics, Newton introduced derivatives as well as binomials, helping prove that the formula [(a+b)n] functions no matter what the value of n is.
While Newton became an accomplished professor, he also used his free time to study the behaviour of light and, more broadly, optics. More specifically, he learned the behaviour of white light on a transparent prism and realised that light separates itself into many beams and different colours.
He utilised his experiences with light to invent the first telescope reflector, which ultimately proved successful within his contemporary scientific community worldwide.
Newton's breakthroughs didn't appear in isolation, though. As we'll see, his work came during the wider Scientific Revolution. This period is when scholars across Europe started merging philosophy with rigorous mathematical reasoning. René Descartes sought to apply mathematics as a universal language for understanding the natural world, as we'll explore now.
René Descartes
Studying René Descartes in maths is an unmissable step in the journey of understanding the history of mathematics and, more precisely, the operation of equations. Born in France in 1596 in the town of La Haye, René Descartes was raised by his grandmother in an upper-class family. His father was an advisor to the Parliament of Brittany.
René Descartes wrote many scientific works during his career. He began, most notably, with "The World, or Treatise on Light," which describes many of the physical phenomena of daily life, including the Earth's movement around the Sun. However, his most celebrated work remains 1637's "Discourse on Method."
Written entirely in French, Descartes produced many mathematical developments, the most significant of which was his utilisation of letters to signify the unknowns in an equation. It is because of this work that we started to use the set of letters x, y, z, or a, b, c to achieve the same result. Descartes also wrote powers in a method that went against the traditions of the era – writing x4 instead of xxxx.
Descartes also invented analytic geometry, which involves representing figures through their algebraic calculations derived from a system of coordinates. Refined calculations and Cartesian equations: we owe thanks to Descartes for developing these great chapters of math taught in secondary school.
Alan Turing
Alan Turing, a mathematician and computer scientist from Britain, is widely recognised as the founding figure of computing. His groundbreaking achievements during World War II, which involved the creation of code-breaking machines and the formulation of the concept of a Turing machine, form the bedrock upon which modern computers are built.
Turing's significant contributions to the realm of artificial intelligence and his theoretical exploration of computability and the halting problem have profoundly influenced the evolution of computer science.
Among his contributions to the field of mathematics, his research on the Turing Test became an essential aspect of the field of intelligence, used to assess how well machines can demonstrate human-like intelligence. His mathematical insights into computability and the challenge of halting set limits on what computers can accomplish were also significant.
His profound contributions to mathematics, cryptography and computer science still profoundly impact our world today, emphasising the significance of his legacy, in both advancements in knowledge and human rights.
Archimedes
Great mathematician and physician of antiquity, Archimedes, alive between 287-212 BCE, is one scientist who is most known in the field of inventing machines. After having studied astronomy with his father, Archimedes continued his studies at the prestigious School of Alexandria.
There, he rubbed elbows with the greats of the time, which inspired him to develop his numerous mathematical theories. Mathematics as a discipline owes many of its tools to Archimedes, one of which is the number Pi.
He calculated the relationship between the circumference of a circle and its diameter and discovered that the number he found was always the same, regardless of the circle's size. Archimedes also took pleasure in calculating areas, such as the area under a parabola, and other geometric figures.
His various mathematical contributions don't stop there. Science also benefited from his knowledge and experiments, as well as his explanation of what is now known as the "principle of flotation."
This theorem explains the force exerted on a solid body when it is submerged in a fluid, whether liquid or gas. This resulted in the construction of the biggest boat of Antiquity: the Syracusia.
Archimedes concluded his career in the service of the city of Syracuse, focusing on the development of war machines. Catapults, powerful boats - the art of war and its innovations have all been influenced by Archimedes. Among all his machines, he also developed the screw, which was used to move liquid from a lower altitude to a higher one.
Carl Friedrich Gauss
Carl Friedrich is certainly one name that surfaces time and time again for students studying the subject at the university level. If you have ever taken modules in data analytics and statistics, then you will likely have heard your teacher praising the contributions of the field.
Carl Friedrich Gauss, known as the "prince of mathematicians", was a mathematician and physicist. He made contributions to areas of mathematics. Gauss is credited with devising the method of squares, a utilised statistical tool for data analysis.
His groundbreaking research in number theory, including his discovery of the prime number theorem, had a significant impact on various fields, such as cryptography and computer science.
Without even realising it, you are likely already familiar with Friedrich's works from as early on as your secondary school education. The mark that he left on mathematics is a true marvel, and he has undoubtedly earned his place on this list.
Other Influential Mathematicians
We've explored ten of the most famous mathematicians in history, but that is far from everyone. We could go on forever if we were to go through them all, but if you're interested in exploring more mathematicians, here are some we'd recommend. Each has easily influenced mathematics like the others we've seen and would be just as worthy an inclusion in our list.
As you can see, mathematics is a vast field. It doesn't belong to a single location, culture, or even age. Every country and era has produced great mathematicians, and every mathematician builds on the body of work of those who came before them, influencing future generations of great minds.
Mathematics has never belonged to one culture alone. Ancient Greeks laid down early geometry, Indian scholars developed the numeral system later spread by Fibonacci, and modern mathematicians from Oxford to Princeton continue to push the subject forward. This universality shows how discoveries build across nations and centuries.
The impact made by these mathematicians on mathematics is truly profound. Their work has not only expanded our understanding of the subject. It has also resulted in practical applications across various fields. From developing computer algorithms to uncovering the laws, theories, and discoveries put forth by these brilliant minds, their work continues to shape our world.
The legacy they left behind serves as an inspiration for future generations, urging them to explore the depths of knowledge and push the boundaries of human understanding.
Mathematics owes a great deal of its progress to the brilliance and dedication of those who have devoted their lives to unravelling its mysteries. These top 10 influential and famous mathematicians in history have left a lasting mark on the field, revolutionising our understanding of numbers, shapes, and the fundamental laws governing our universe.
All the mathematicians who have earned their place on this list will be forever known and celebrated for their contributions that have shaped the trajectory of history.
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