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Mathematics in Ancient Greece and Its Influence on Modern Science

Digital art of a classical Greek temple interior with statues and mathematical symbols.
The Elegance of Greek Mathematics. AI Depiction. Credit: DALLE for the Greek Reporter

Advances in mathematics that can be attributed to ancient Greeks are many and have profoundly shaped the scientific world as we know it today.

Let’s take a look at ancient Greece, a place where the idea of zero was yet to be discovered, and the Earth’s circumference remained a mystery.

In the cradle of Western civilization, a band of intellectual pioneers and great thinkers started to sketch the outlines of what we now recognize as modern mathematics. They did more than that, however. These ancient Greeks influenced science and engineering in a unique and fundamental way. Their journey wasn’t merely about pushing human knowledge further ahead. It was about redrawing the entire map of the human understanding of our world through mathematics.

Evolution from practical mathematics to abstract thinking

Long before the Greeks, civilizations like the Egyptians and Babylonians were using math for building, farming, stargazing, and in general in their everyday lives. What they lacked, however, was the Greek flair for abstraction and logical reasoning.

This is when the journey of the Greeks into the world of mathematics began. Starting around the 6th century BCE, Greek thinkers began treating math as a playground for the mind. For them, it was not just a toolbox to keep their hands busy when they had nothing better to do. This fundamental shift from the empirical aspect to the theoretical one laid the foundations for everything that followed in the mathematical world. It defines our understanding of mathematics to this day.

Key Figures in Greek Mathematics

The history of Greek influence in mathematics is full of famous personalities and lesser-known ones, each contributing their unique brilliance to the mix of what we now call “Greek mathematics.”

Thales of Miletus, the pioneer

Engraving of Thales of Miletus
Thales of Miletus, pre-Socratic Greek philosopher and mathematician. Credit: Wilhelm Meyer, Wikimedia Commons, Public Domain

Imagine Thales as the original innovator of Greek mathematics. He was not just a figure of historical importance but also a visionary who saw the world through geometric lenses.

His ability to use geometry to solve practical problems was legendary—whether it was measuring the pyramids of Egypt or estimating the distance of ships at sea. However, Thales’ contributions went beyond these. He is credited with predicting solar eclipses and laying down the basic principles of geometry, effectively initiating a real mathematical revolution in Greece. Additionally, his work on deductive reasoning laid a foundational stone for the scientific method, marking him as a thinker far ahead of his time.

According to the Encyclopedia Britannica, Thales has been credited with the discovery of five geometric theorems. The first was that a circle is bisected by its diameter. The second, that angles in a triangle opposite two sides of equal length are equal. The third was that opposite angles formed by intersecting straight lines are equal while the fourth posited that the angle inscribed inside a semicircle is a right angle. Finally, he also concluded that a triangle is determined if its base and the two angles at the base are given.

Pythagoras, the number mystic

Engraving of Pythagoras
Pythagoras, the ancient Greek philosopher and mathematician, illustrated in traditional attire with a book in hand. Wikimedia Commons, Public Domain

Unlike what many of us might think, Pythagoras wasn’t just obsessed with triangles. He was a person with fundamental mathematical understanding who went deep into the core of numbers. His work was pioneering and helped the field of number theory advance tremendously. His belief in numbers as fundamental elements of the universe led him to come up with the famous Pythagorean theorem. According to his theorem, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

However, his influence in mathematics was much wider than a single theorem, touching on concepts of harmony and the cosmos.

The teachings of this man from the Greek island of Samos on the relationship between numbers and musical notes laid the groundwork for mathematical harmony, too. This mixed the fields of music, mathematics, and astronomy into a unified theory. His school not only dealt with mathematical problems but also explored fields like philosophy, setting the stage for a more holistic and integrated approach to knowledge.

Euclid, the architect of geometry

Dark-toned painting of Euclid holding open pages of a book with geometric diagrams.
Euclid presenting his geometric findings, as depicted in a Classical painting. Credit: Jusepe de Ribera, J. Paul Getty Museum, Wikimedia Commons Public Domain

Euclid is known as the “Father of Geometry.” His magnum opus, Elements, is a timeless masterpiece that systematized the chaotic world of geometric knowledge. His work placed everything into an organized, logical framework.

Nonetheless, Euclid didn’t just study geometry. He also refined it, introducing axiomatic proofs and a systematic approach. This tactic later became the gold standard for mathematical exposition. His groundbreaking work established the idea that mathematical truths should be derived from a small set of axioms. It was a concept that has come to underpin the development of mathematics ever since.

The influence of Euclid extends beyond mathematics, of course. His work reached the fields of philosophy, logic, and even physical sciences, and his Elements is one of the most influential pieces in the history of human thought.

Archimedes, the genius of Syracuse

Painting of Archimedes deep in thought, examining a globe, with mathematical papers on a table.
Archimedes, engrossed in thought amidst his mathematical inquiries. By Domenico Fetti. Credit: Wikimedia Commons, Public Domain

Archimedes is often hailed as the greatest mathematician of antiquity. He was a true polymath who went beyond the boundaries of mathematics, physics, and engineering.

His vital contributions to the way we understand pi, as well as his methods for calculating areas and volumes were truly revolutionary. Archimedes’ work on topics like levers, buoyancy (think of the famous “Eureka” moment), and his war machines showed an unparalleled ability to apply mathematical principles to practical problems of everyday life.

Additionally, among other things, his invention of the Archimedes screw, a device for literally raising water, is also proof of his genius in engineering. The methodology that Archimedes used, which included the method of exhaustion, laid foundational mathematical methodologies for future generations of scientists and mathematicians across the world.

As we can see, these great figures of ancient Greek mathematics did more than merely solve equations and think about geometric shapes. They did the all-important work that would define scientific thought for centuries to come.

Breakthrough discoveries in Greek mathematics

As one can undoubtedly see, Greek mathematics is a true treasure of discoveries and innovative insights. The Pythagorean Theorem, for example, is a timeless gem that billions of students study around the world. Its simple and yet fundamental idea revealed the deep geometric insights of these ancient thinkers, including those of Pythagoras.

Additionally, in number theory, the Greeks explored topics such as the prime and perfect numbers, using their unique method of exhaustion. This helped future generations develop calculus, which is the mathematical study of continuous change.

These weren’t merely abstract ideas but steps towards a better understanding of the world using mathematics.

Greek inventions: bridging math and technology

Based on this mathematical knowledge, the Greeks also managed to become master inventors. They created devices such as the gnomon and the astrolabe, which helped sailors navigate the stars and stormy seas. The Antikythera mechanism, an ancient analogue computer, is also perhaps the most stunning example of their ingenuity. This tiny machine that was discovered more than a century ago purely unintentionally, predicted astronomical positions with astonishing accuracy that still amazes scientists and experts around the globe.

Fast forward to today, and the Greek mathematical spirit is clearly still alive and kicking. The dedication of the numerous Greek thinkers of the past to proof and structure their theories logically laid the foundations for modern mathematical thought.

It was during the Renaissance that the rediscovery of Greek texts helped fuel the scientific revolution of the modern world, influencing giants like Copernicus and Newton.

The everlasting influence of Greek mathematics

The world of Greek mathematics reminds us of the timeless legacy of these individuals for human knowledge. The ancient Greeks challenged their status quo and strived to see beyond that which could immediately be seen.

They liked to question and explore. This helped them advance our common understanding of the world. Their legacy continues to inspire, reminding us of the enduring strength of human curiosity.

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