3500 BC to 350 BC
During the Bronze Age, the first civilisations grew up in The Middle East. Later, in the Iron Age, The Persians, Egyptians, Greeks and Romans spread this culture through conquests and trade. Meanwhile, the Chinese were observing the heavens and starting their own culture and science.
The Sumerians lived in Mesopotamia. This region of fertile plains between the Tigris and the Euphrates is now mostly in modern Iraq. Here the Sumerians built the first advanced civilisation in great cities with administrations, legal systems and irrigation. They developed methods of writing and counting – in base 60.
In around 2300 BC, the Sumerians were invaded by the Akkadians. Between them, they invented the abacus and a basic arithmetic with addition, subtraction and versions of multiplication and division. The Sumerians were displaced by the Babylonians in around 2000 BC. But they passed on their systems of counting and arithmetic.
The Babylonians invaded Sumeria and inherited their number system.
Egyptian civilisation grew up around the Nile Delta from around 3000 BC. The Ancient Egyptians wrote using hieroglyphics drawn on papyrus or carved into stone. Many examples survive, including some mathematical ones.
Being hieroglyphic, the Egyptian number system had no zero and was not suited to multiplication or division. However, they found ways around this.
Their mathematics was very practical – usually to do with engineering projects or trade. However, they set and solved what we would recognise as algebraic problems. For example, ‘a quantity added to a quarter of that quantity becomes 15. What is the quantity?’.
The Egyptians used a lot of geometry (due to the limitations of their number system) and probably passed to Pythagoras the theorem that was named after him. They are well known for the engineering triumph of the pyramids.
In about 3000 BC, they produced a very early calendar that had 365 days in the year and in around 1470 BC, Thutmosis III put up the ‘Needle of Cleopatra’ in Hliopolis. The needle’s shadow was used to calculate the time, seasons and solstices.
Trade with the Babylonians meant a sharing of numbers and geometry.
Greek philosophers like Thales were famliar with Egyptian geometry.
The theorem to which Pythagoras gave his name was known to the Egyptians.
Euclid would have been strongly influenced by the long Egyptian tradition in geometry.
The Babylonians invaded Sumeria in about 2100 BC. They set up their capital in Babylon, whose few ruins can be seen in the Iraqui desert south of Baghdad.
Babylonians inherited the Sumerian number system, counting in base 60. They divided the day into the hours, minutes and seconds that we use today. So we still count in base 60 – with 60 seconds in a minute and 60 minutes in an hour.
Although at first there was no representation of zero (so 536 would be the same as 5036), they began to leave a space, then used a symbol for zero in about 300 BC. Much later, this led to all sorts of mathematical possibilities – like multiplication and long division – which could not be done using Roman numerals or Egyptian hieroglyphics.
Even without zero, they devised ingenious methods to help them multiply or divide two numbers. For example, they could multiply two numbers using the formula ab = [(a + b)2 – (a – b)2]/4 and a stone tablets, or table, of squares.
The Babylonians took the Sumerians’ numbers as well as their country.
Greek philosophers like Thales were famliar with Babylonian number systems.
The theorem to which Pythagoras gave his name was well known to the Babylonians.
Played with a feather and some elektron?
Thales is best known for discovering static electricity and, as one of the Seven Wise Men, an early philosopher.
Thales’ aim was to understand the nature of the physical world without relying on mythology or dogma. Instead, he questioned ideas and tried to understand phenomena – including heavenly ones. He became famous for predicting the eclipse of the Sun that occurred on May 28, 585 BC.
The story is that he noticed that he could pick up feathers with a piece of amber – so long as he rubbed it with cat fur. The effect took its name from the Greek for amber – elektron. From this, we get the modern words – electricity and electron.
Thales left no writings; knowledge of him is derived from an account in the Metaphysics of Aristotle.
Pythagoras built on the philosophy of Thales
Thales would have studies the number ideas of the Babylonians
Democritus developed some of Thales ideas
Aristotle was familiar with Thales philosophy
William Gilbert coined the name electron 2000 years after Thales’ experiments.
Numbers, maths and music were all he needed.
Not much is known about the life of Pythagoras, except that he founded a community in Croton, southern Italy. He believed that we can understand the order of the world with the aid of mathematics and astronomy. As he put it: ‘all is number’.
He proposed, in The Music of the Spheres that the movement of the planets was mathematically related to musical sounds. The connections that he established between music, astronomy, geometry and arithmetic exist to this day and remained strong until quite recently.
Pythagoras was best known for working out what we know as ‘Pythagoras’ Theorem’. Although, this was already known to the Egyptians and Babylonians, Pythagoras was probably the first to provide a rigorous proof.
The Babylonians knew, but probably never proved, Pythagoras’ triangle theorem.
Pythagoras built on the philosophical ideas of Thales.
Aristotle went to Plato’s academy and Plato was strongly influenced by Pythagoras’ followers.
Ptolemy formalised ideas about planets 400 years later
The geometry of the Greeks – including Pythagoras – was essential to the Arab mathematicians who followed them.
A philosopher with real nous.
Anaxagoras explained his philosophy in Peri Physeos (On Nature), but only fragments of the books have survived.
He thought that all matter started off as infinitesimally small atoms; order was produced out of this infinite chaos through the influence of nous (Greek for ‘mind’ or ‘reason’).
Anaxogoras believed that there were an infinite number of elements at a time when the accepted view was that there were only four: fire, earth, air and water. He was the first person to explain correctly the reason for eclipses.
He set the scene for Democritus to develop his ideas of atoms and his doctrine of nous was adopted by Aristotle, who said that he sounded like the only sober man in a chorus of drunks.
In 450 BC Anaxagoras was imprisoned for suggesting that the Sun was not a god but a hot stone.
Anaxagoras’ ideas on atoms were developed by Democritus
Two thousand years later, Anaxagoras’ ideas on the Sun influenced Copernicus and Galileo who, like him, faced arrest for his work.
A paper ripper (at least in his mind).
Democritus considered what would happen if you kept ripping up a piece of paper. He reasoned that, eventually, you would reach a point where you couldn’t rip any more. The paper (and everything else) must be made of tiny, indivisible blocks of different shapes and sizes. He called these blocks atoms (which means uncuttable).
He developed this idea to say that all changes in matter came from changes in the motion of the atoms, or changes in the way that they are packed together.
Democritus was harshly criticised for his ideas. At a time when beliefs and superstitions dominated the world, his atom theory seemed odd. People found it hard to accept the idea that everything, including human existence, is a product of mere atom collisions. This would leave everything to chance. Of course, although the belief systems are different, there is still a divide between those who are and are not comfortable with their fate being determined by physical rather than divine rules.
Democritus also wrote on ethics, proposing happiness, or ‘cheerfulness’, as the highest good – a condition to be achieved through moderation, tranquillity, and freedom from fear. Later historians sometimes referred to him as the Laughing Philosopher.
Aristotle was the next great Greek philosopher after Democritus.
Democritus’ ideas on atoms were developed by Al-Razi in the 9th century AD.
Teacher to Alexander the Great.
Aristotle believed that all knowledge must proceed directly from observation. He said that everything is made of the four elements (earth, fire air and water) which are only found on Earth. He later added another ‘element’ – ether, which surrounds heavenly bodies.
Aristotle made a distinction between what happened in the heavens (the celestial) and on the Earth (the terrestrial) . The heavens, being the domain of the gods, are ordered and stable; whereas the Earth is chaotic and changing under the influence of people. This distinction is still influential and it was Newton who broke its complete grip on philosophy when he proposed a Universal law of gravitation.
In his books On the Heavens, and Physics, he proposed a finite, spherical universe, with the Earth at its centre surrounded by concentric spheres which carry the planets and fixed stars. This geocentric theory of cosmology was the basis of European thought from the 12th century until it was challenged by Copernicus in the 1500’s.
Aristotle is one of the ‘big three’ philosophers of ancient Greece (with Plato and Socrates). Socrates taught Plato, who in turn instructed Aristotle. After Plato’s death, Aristotle travelled widely, teaching Alexander the Great, before founding his own school, The Lyceum, in Athens.
Archimedes studied in Alexandria which continued Aristotle’s legacy.
Euclid was based in Alexandria, which maintained Aristotle’s legacy
It wasn’t until Copernicus nearly 2000 years later that Aristotle’s ideas on the planets were replaced.
Ibn Rushd took Aristotlean ideas into Europe in the Middle Ages, laying the foundations for the Renaissance.
Aristotle’s ideas on the separateness of the celestial and terrestrial survived until Newton in the 17th century.
The father of geometry
Very little is known about Euclid’s life except that he worked in Alexandria and published The Elements, the basic book on geometry.
He was probably educated in Athens by pupils of Plato. On moving to Alexandria, he would have had access to the Egyptians’ strong tradition in geometry. In part, this would probably have been thanks to the Great Library in Alexandria, which was founded by Alexander the Great in 332 BC and housed over 7000 works.
Euclid’s main work, The Elements, is a comprehensive treatise on mathematics. Its 13 volumes were used as a standard school text for the next 2300 years. Although much of it is probably original work, it is likely that he organised and explained more clearly ideas that were already in circulation. Nevertheless, because of The Elements and his work in this field, he is called the father of geometry.
Soon after Euclid, Eratosthenes (276 – 195 B.C.) developed the idea that the world is round and measured his latitude and the circumference of the Earth using the Sun’s shadows.
Archimedes studied in Alexandria and would have been the first of many students of Euclidian geometry.
Ptolemy would have studied Euclid in Alexandria.
Al Biruni would have studied Euclid’s geometry
Although Euclid wouldn’t have overlapped with Aristotle, the Greek’s legacy would be felt in Alexandria.
Eureka, you’ve found him!
We believe that Archimedes studied under followers of Euclid in Alexandria before returning to Italy where he spent the rest of his life.
He is known for his mathematical work and applying science to everyday life. He worked out the principle of levers, calculated the surface areas and volumes of solids and invented a machine, the Archimedes screw, for raising water. This is still used in many parts of the world.
Legend has it that Archimedes discovered his famous principle of displacement while taking a bath, shouting ‘Eureka!’ (‘I have found it!’).
When the Romans laid siege to Syracuse he designed catapults and machines to keep them at bay for years. When the Romans finally got into the city, Archimedes was killed by a soldier.
A model, but not as we know it.
Ptolemy is another ancient about whom we know very little. His name is part Roman (Claudius) and part Egyptian/Greek. So it is thought that his ancestors probably moved from Greece to Alexandria in Egypt. One of them may have been granted Roman citizenship.
However, his work is well known because, by refining the geocentric model of Aristotle, he helped it to last for the next 1350 years. His mathematical model has a stationary earth at the centre with the stars, the Sun, the Moon and the 5 known planets all revolving around it.
His model was far better at predicting planetary positions than anything else produced in antiquity. It was so persuasive that it became the official Christian doctrine and guided all European thinking even after Copernicus suggested the Sun as the centre in around 1500.
His theories are preserved in a 13-volume work known as The Almagest.
Ptolemy’s ideas of a geocentric Universe lasted until Copernicus
Ptolemy’s work on optics were next picked up by Al-Haytham 400 years later.
By putting a bamboo stick in the ground and tracking its shadow, the Chinese developed the first recorded example of a timepiece. With it, they could get a good estimate of the time of day.
However, as with many Chinese inventions, it didn’t have any influence on the rest of the world. Sundials crop up in a number of places (and were probably developed independently) in around 300 BC.
In around 300 BC, Shih Shen compiled the first map of the stars. About 200 years earlier, astronomers had recorded comets (referred to as broom stars) in an atlas called The Book of Silk, which was discovered in a tomb in 1976.
The ancient Chinese philosophy of Yin and Yang is based on opposites being complementary and yet in conflict. An example is day and night. Many of their features are the exact opposite to each other – light versus dark; warm versus cold. Nevertheless, they complement each other and without night, there would be no such idea as day.
In around 300 BC, the Chinese philosopher Son Yan integrated these ideas into the developing ideas of science – mainly astronomy.
From early in the first millennium BC, the Greeks, Romans, some Europeans and the Chinese knew of the magnetic properties of loadstone – i.e. that pieces of loadstone would attract and repel each other.
However, unlike the others, the Chinese realised that loadstone magnets all pointed in the same direction. So they had the basis of a primitive compass for geomancy – to ensure that a house was facing in the correct direction – and for guidance.
However, loadstone compasses were not very transportable and it wasn’t until more like 200 AD that navigational compasses were first used – again in China.