Such was the life and scientific legacy of the Greek mathematician Archimedes of Syracuse.
Classical Antiquity was a turbulent time but, at the same time, full of new advances and a development of science so significant that, if it had not been for the Middle Ages, surely we would have gone much further from where we are now.
Despite the fact that the majority of the population was illiterate and uneducated, there were not a few great men who lived at that time, among them Archimedes, a great mathematician, physicist and inventor of gadgets for civil and, above all, military purposes.
Next, we will see the life and great contributions to science of this researcher through this biography of Archimedes, and we will better understand how the foundations, although primitive, of what would be our modern scientific method with the passage of almost 2000 years.
Archimedes of Syracuse: biography and contributions to science
Archimedes was a mathematician, physicist, inventor, engineer, and astronomer who lived in Ancient Greek times about 2,000 years ago. At that time, few people were those who had the privilege of knowing how to read and write, so there are not many writings about him and all we know about this inventor is from oral tradition and testimonies of several classic writers, most of them later. Archimedes.
His homeland was Syracuse, a city that was located in Magna Grecia, a region settled on the island of Sicily and the south of the Italian peninsula. The ruler of that city, who ruled it as a tyrant, was Hieron II, who is suspected of being related in one way or another to Archimedes. Whatever their relationship, the two had a very interesting relationship, since Herion II trusted the mathematician to be an adviser and inventor for the defense of the city.
We know little about the Archimedes family. Not much is known about his mother, but about his father Phidias, an astronomer who transmitted his interest in the science of the sky. It does not seem that he married or had children, and if he did, that was erased from the annals of history. Nor can we confirm if he said his famous “eureka” walking naked through the streets of his hometown, or if he really said the phrase “give me a foothold and I will move the world.”
Archimedes was born in 287 BC in Syracuse, Sicily. Thanks to a fragment of his book “The Sand Counter” we know that his father was called Phidias and that he was a well-known astronomer of the time. Seeing Phidias that his son showed great abilities from a very young age, he decided to introduce him to the world of mathematics and astronomy.
Thanks to his great abilities and his good relationship with the king of Syracuse, Hieron II Archimedes was sent to Alexandria in 243 BC, the center of science of the time, to be able to expand his knowledge in mathematics under the teaching of the eminences of the time. Among his teachers was Canon de Samos, a great mathematician from whom the young Archimedes learned a great deal. After his stay in the Egyptian city, Archimedes returned to his homeland to begin his research.
Service for the homeland
Upon his return from Alexandria, Archimedes was accepted as an advisor to Hiero II, in charge of designing systems and gadgets that would help defend the city. Under the protection and patronage of the monarch, the young mathematician had full freedom to do all kinds of experiments, as long as they benefited the king and Syracuse. With Hieron II as a patron, Archimedes would initiate a time of extensive research and great advances.
One of the most important episodes of this time for his career was when the king ordered the construction of the largest boat ever made, with such bad luck that, when he put it in the sea, it was stranded. As even with brute force the ship Hieron II could not be removed, he commissioned Archimedes to manage to put the boat afloat. Thus, Archimedes devised a system of compound pulleys that increased the thrust force, moving the ship with little effort, laying the foundations of his law of lever.
Another of the most important moments in the life of Archimedes was when the king asked him to resolve a doubt that made him sleepless. The monarch wanted to know if his crown was really solid gold or if it had been deceived and its interior was made of a less valuable material. This problem turned out to be a real headache for Archimedes, since he did not know how to solve this question without breaking the crown in two and looking inside.
The Greek scientist knew that he had to find the density of the crown and, considering that it weighed the same as a gold ingot, the answer had to be found in its volume. The problem was that there was no way known at the time to calculate the volume of irregular objects. Legend has it that he discovered how to do it while bathing. As he plunged into the tub, he saw the water level rise. The amount of water that rose was directly proportional to the volume of the body that was submerged.
From this he concluded that if he submerged the crown and measured the variation in the water level, he could know precisely what its volume was. This was one of his great discoveries, and for this reason it was known as Archimedes’ principle. It is said that, faced with such a discovery, he came out of the bath euphoric shouting “eureka”, naked through the streets of Syracuse before the surprised gaze of passers-by.
Conflict in Syracuse
During 213 BC, Roman soldiers attacked Syracuse and harassed its inhabitants into surrendering. This action was led by Marco Claudio Marcelo, a distinguished Roman military and politician baptized as the Sword of Rome, a key figure in the Second Punic War. The war lasted two years, in which the inhabitants of Syracuse fought against the Romans with courage, tenacity and ferocity, among them Archimedes, who played a very important role in the defense of the city.
But unfortunately the city ended up falling. Marco Claudio Marcelo, who knew Archimedes’ great intelligentsia, explicitly ordered that they not hurt or kill him, since he wanted him among his advisers. However, either out of ignorance or the ineptitude of his own subordinates, Archimedes died at the hands of one of the Roman soldiers in 212 BC There are four versions of what happened.
The four deaths of Archimedes
One version says that Archimedes was in the middle of solving a mathematical problem when the Roman soldier approached him. The mathematician asked him for a bit of time to solve the problem and that must not have pleased the soldier, who decided to end his life.
Another version tells that Archimedes was solving a mathematical problem when Syracuse was taken. A Roman soldier entered his enclosure and ordered him to meet with Marcelo, to which the mathematician replied that he wanted to solve the problem he was working on. The soldier, upset by the answer, assassinated Archimedes disobeying Marcelo.
There is a third version that tells that Archimedes had in his hands a lot of mathematical instruments. The soldier saw him, thinking that he must be carrying valuable objects or some kind of weapon to win the Roman invaders, so without thinking twice he ended the life of the mathematician.
Finally, the fourth and most realistic version tells that Archimedes was crouched on the ground, contemplating one of his plans. While he was studying him, a Roman soldier approached him from behind and, not knowing that it was the Greek genius, decided to shoot him in the back.
After his death
Having spent more than 130 years after his death, in 137 BC the Roman writer, politician and philosopher Marcus Tullius Cicero occupied a position in the administration of Rome and wanted to find the tomb of Archimedes. It was not easy for him, for Cicero found no one to indicate the precise place where the mathematician had been buried.
Despite the unknowns and total ignorance about where the remains of Archimedes were, Cicero managed to locate the tomb, very close to the door of Agrigento. His resting place was in poor condition, so Cicero decided to clean his tomb and, to his surprise, found that it was inscribed on a sphere inside a cylinder, alluding to one of his discoveries.
Contributions to science
Although the passage of time and the darkness of the Middle Ages caused many knowledge of Antiquity to be lost forever, there are many knowledge attributed to Archimedes that have managed to reach our days. Among the most prominent we have the following:
1. Archimedes’ principle
Archimedes’ principle is surely the most famous and important legacy of the Greek. In a totally accidental way, Archimedes discovered how to calculate the volume of any object, whether or not it had a regular shape.
This principle states that every body partially or totally submerged in a fluid (liquid or gas) receives an upward thrust equal to the weight of the fluid dislodged by the object. That is, depending on the volume of the object, the fluid will rise more or less, regardless of the weight of the object itself.
This principle not only allowed us to know the volume of any object, but it was also key to perfecting the flotation of ships, life jackets, submarines and hot air balloons, inventions that, although much later than Archimedes, would not exist without his findings. .
2. Lever principle
Before modern cranes were invented to move heavy objects it was necessary to use brute force. Building buildings was a labor intensive task, and sometimes it was impossible to build them for lack of men.
Fortunately, Archimedes found the solution using one of the most basic and fundamental principles of physics and mechanics. He observed that by placing an object on one end of a board properly balanced with a fulcrum, anything could be moved with relative effort.
3. Advances in mathematics
There are many mathematical advances that are attributed to the figure of Archimedes. Among them are calculating precisely the number Pi, making the first approximations to the infinitesimal calculation system and discovering that the relationship between the volume of a sphere and the cylinder in which it is found is 2: 3, something that was represented in this way his grave in his honor.
4. Mechanical method
Another of the most interesting contributions of Archimedes was the inclusion of a purely mechanical method in the reasoning and argumentation of geometric problems, something unheard of in his time. Until then, geometry was considered a purely theoretical science and it was common to think that pure mathematics would descend to other more practical sciences that could be more useful for military and civil purposes.
Archimedes, in a letter addressed to his friend Eratosthenes, indicates that with his mechanical method he can approach mathematical questions through mechanics. It also indicates that it is easier to construct the proof of a geometric theorem if you have prior practical knowledge rather than hypothesizing theoretically. This new research method would become the precursor to the informal stage of discovery and hypothesis formulation typical of the current scientific method.
5. The odometer
As surprising as it may sound, Archimedes invented the first odometer. Known as an odometer, it was a device built based on the principle of a wheel that, when it rotates, activates gears that allow the distance traveled to be calculated.
6. The first planetarium
Based on what was said by many classical writers, including Cicero, Ovid, Claudian, Marciano Capela, Cassiodorus, Sextus Empiricus and Lactantius, Archimedes is considered to have invented the first planetarium.
He surely built two, according to Cicero. One of them represented the Earth and several constellations close to it, while another, which only had one rotation, represented the Sun, the Moon, the planets that carried out their own and independent movements in relation to the fixed stars.
7. The Archimedean screw
Archimedes invented a screw that allowed water to be transported from bottom to top across a slope. According to Diodorus, this invention facilitated irrigation in the fertile lands of the Nile River in ancient Egypt, since traditional tools involved mobilizing a lot of human effort.
This cylinder had inside a screw of the same length that interconnected a system of propellers that carried out a rotary movement driven manually by a rotating lever. Thus, the propellers managed to push any substance from the bottom up, forming a kind of endless circuit.
8. The Claw of Archimedes
Archimedes’ claw, also called the iron hand, was one of the most fearsome weapons of war created by the mathematician, crucial in the defense of Sicily against Roman invasions.
It was a large lever that had a grappling hook attached to the lever by means of a chain that hung from it. Through this lever the hook was manipulated in such a way that it would rush over the enemy ship, hooking it up and causing it to either overturn or crash into the rocks on the shore.
- Torres-Asis, AK (2010) Archimedes, the Center of Gravity, and the First Law of Mechanics: The Law of the Lever. Apeiron Montreal.
- Kires, M. (2007) Archimedes’ principle in action. Physics Education.
- Parra, E. (2009) Arquímedes: his life, works and contributions to modern mathematics. Mathematical, Education and Internet digital magazine.