The Greeks are well documented for their foundational influence on Western civilisation. It would seem that they had some part to play in many of the technologies that we use to this very day in some way, shape or form. Throughout your classes at school, you’ll likely have heard many of the inventions that they have gifted the world.
However, when it comes to maths, the Greeks seemingly left their inventive caps at the door. That’s largely due to sophisticated mathematical systems already being in place long before their time, thanks to some of the earlier civilisations, such as the Sumerians. However, what the Greeks contributed to the world of mathematics was far from mere piggybacking, as Greek mathematicians managed to transform borrowed concepts into something truly remarkable. In this article, we’ll refine our lens on ancient Greek math and gain some newfound appreciation for their contributions.
The Roots of Ancient Greek Mathematics
It’s true that the strongest trees have the deepest roots, and that’s most certainly the case with the contributions of Greek mathematicians who built upon the mathematical achievements of earlier civilisations, especially the Egyptians' mathematics and the Babylonians' mathematics. These societies had developed advanced mathematical systems that served practical purposes, creating the foundation that Greek thinkers would use to build their theoretical approach.
So, how exactly did these ideas end up in the hands of the Greeks to begin with? Well, previous mathematical traditions had a profound impact on Greek thought. It’s no secret that the ancient Greeks had some of the strongest trade networks around the eastern Mediterranean, which helped bring these mathematical concepts to Greece.
Both your history and maths teacher will likely be able to tell you how this environment encouraged the study of mathematics beyond everyday use and helped promote deductive reasoning to prove mathematical statements. For extra guidance on these abstract concepts, consulting a maths tutor can provide invaluable insight. Fascinating, right? When summarising the role that civilisation played as a whole, there is no forgetting the transition from practical calculation to theoretical mathematics.
Key figures like Thales, Pythagoras, and Euclid, along with later mathematicians like Eratosthenes, Hipparchus, and Archimedes, made significant contributions that continue to influence modern mathematics.
This change started around the 6th century BCE when Greek thinkers began treating mathematics as an intellectual pursuit rather than just a practical tool. They pioneered an early form of rigour in their proofs and tried to demonstrate their algorithms and theorems with sound reasoning based on axioms.
A valid question that you might be asking yourself at this point is ‘how could one civilisation have been so far ahead of the others?’ Well, the prosperity of their society meant that their upper-class elite had nothing but time to devote to philosophy and learning for its own sake, something not too many others had the luxury of. The shift from empirical to theoretical mathematics played a massive role in shaping our understanding of mathematics to this very day.
Ancient Greek Math Symbols
The ancient Greeks had two numerical systems: the Attic system and the more widely adopted Greek alphabet system. The Attic system predated the latter and was quite like Roman numerals, seeing as they adopted an additive approach deriving from the first letters of number names.
The second system we mentioned, the Greek alphabet system, is also referred to as the Ionic system and came along to replace the Attic.
This one worked by assigning values to the 24 standard Greek letters plus three obsolete ones: stigma (ϛ) for 6, koppa (ϟ) for 90, and sampi (ϡ) for 900.
One little pointer that you’ll need to make note of is that when these letters were combined, they were often marked with a prime symbol (ʹ) to distinguish them from text, eg, αʹ = 1 and ρʹ = 100. Of course, hindsight is 20:20, and when we compare it to the modern decimal system, we can poke holes in this system. But it was truly extraordinary for that period in time and was effective when it came to calculations in trade, astronomy, and mathematics, especially when paired with Greek skill in geometry and ratios.
Interestingly, while the Greek numeral system evolved independently, it still shows some echoes of ancient Babylonian mathematics, which heavily influenced early civilisations through their development of place value and base-60 (sexagesimal) calculations.
The Rise of Greek Mathematicians
Greek mathematics evolved from the work of innovative thinkers who transformed mathematical reasoning from basic calculations into a theoretical study. You’ve got the likes of Thales of Miletus, who was the first Greek mathematician to achieve stardom for solving practical problems.
He used mathematics to solve practical problems like measuring pyramid heights and finding distances to ships at sea.
He also became the first person to use deductive reasoning in geometry, which made him the West's first true mathematician.
To top things off, he’s also to thank for many of the theorems about circles, triangles, and intersecting lines that we see in our log tables.
Additionally, much of the mathematics from ancient civilisations emphasised practical, algorithmic approaches to real-world problems, while Greek mathematics prioritised abstract reasoning and formal proofs. We also have Pythagoras of Samos to discuss, who also had his own unique outlook on the subject. We’ve all associated his name with the theorem that’s named after him, but his impact actually reaches way beyond trigonometry. He famously used numbers to explain cosmic harmony and developed the idea that numerical relationships governed the universe.
Moving on to one of his students, Hippasus of Metapontum went a step above making his teacher proud by discovering irrational numbers while he was studying geometric relationships. These are essentially values that cannot be expressed as fractions of whole numbers. So, when we’re looking at the origin of mathematics, one can’t help but be impressed that an entire kind of number came from the contributions of one man.
Mathematics and Greek Philosophy
While you mightn’t have had the chance to dive into it too much over the course of your education, there is plenty to explore when it comes to the intersection of mathematics and philosophy, something ancient Greece is famous for uncovering. This shift of thinking transformed how scholars approached questions about reality, truth, and knowledge.
Plato's belief in geometry as truth
Without needing to be a maths graduate or aspiring historian, Plato is a name that we’ve all heard come up in conversation, both inside and outside of the classroom. The fact that he remains a household name to this day is a testament to the importance of his work. It’s evident that geometry meant much more than a practical discipline to him, as he believed it to embody the highest form of truth and beauty.
Let no one ignorant of geometry enter.
Plato, at his Academy.
He saw geometry as "knowledge of what always exists" that "draws the soul toward truth and produces philosophical thought". Not exactly what any of our first thoughts were when looking at our GCSE or University maths textbooks, right? So, the next time you’re working through one of your geometry exam questions, remember that according to Plato, you’re not just learning how to calculate, you’re touching eternal truths. We think you’ll agree that it has a nice ring to it!
Plato's view on mathematics was that it deals with abstract, timeless entities that exist independently of human perception and thought.
He believed that numbers, shapes, and sets have an objective reality and that mathematical truths are discovered rather than invented. This perspective is known as mathematical Platonism. Plato also associated mathematical shapes with the elements of the universe, suggesting a connection between mathematics and the physical world.
Aristotle's practical approach to mathematical thinking
The next mathematical giant that should immediately spring to mind when you hear Greek maths is Aristotle. If you haven’t always seen eye to eye with your maths teacher, then let this legend serve as some inspiration to you. He often developed a distinctly different mathematical philosophy from his teacher.
While he is, of course, more renowned as a philosopher, Aristotle actually played a rather substantial role in shaping Greek mathematics and subsequently, the subject as we know it today. In contrast to some of the other mathematicians that we’ve mentioned in this article, he didn’t contribute his own theorems or anything of the sort. Instead, it was how he framed mathematics as a distinct and formal science, separate from physics or metaphysics. By learning bout Chinese numerals, you'll see the extent to which their mathematical approaches differ.
He was the first to pioneer deductive reasoning and the importance of logical structure, laying the groundwork for what would later become formal mathematical proof. Once you get past the fact that he’s the reason why you’ve got all those proofs to learn off for your maths exams, you’ll begin to appreciate how monumental this shift was for mathematics. His impact was more philosophical than computational, but it helped define mathematics as an intellectually rigorous and foundational discipline.
The Impact of Greek Maths
As you can see, it’s easy to see the extent of the impact that ancient Greece had on mathematics when you look back and connect the dots. The same goes for ancient Chinese numeral systems.The civilisation’s legacy stands as one of humanity's greatest intellectual achievements. This piece shows how Greek thinkers reshaped practical mathematical foundations from earlier civilisations into something extraordinary.
Greek mathematicians' precise approach to proof, abstraction, and logical reasoning created a tradition that drives contemporary science. They are largely to thank for the transformation that occurred in the field of mathematics, taking it from practical calculations into a theoretical science. Hopefully, after your reading, you find yourself with a newfound appreciation for Greek maths and perhaps even have been inspired to learn a little more about some of the mathematicians that we’ve discussed throughout the article.
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