Archimedes: Biography, Scientific Accomplishments, Inventions, & Principle


Archimedes – history and accomplishments | Without a doubt, Archimedes was the greatest scientist in the classical age. His greatest highlight came when he demonstrated the principle of the buoyant force while in his bathtub.

Born in Sicily, Magna Graecia, Archimedes was a critically acclaimed Greek scientist who attained so many feats in a host of scientific disciplines like astronomy, physics, mathematics, mechanics and engineering. He is famed for coming out with the Archimedes principle upon which fluid dynamics as a discipline partly rests on.

Another spectacular accomplishment of him came in his accurate approximation of the mathematical constant pi (π), which he calculated to fall between 3 10/77 and 3 1/7. The fact that many of his inventions – like the Archimedes screw – are still in use to this day makes him an even more remarkable scientist of the classical age.

Here is a complete biography, scientific contributions and major achievements of Archimedes of Syracuse (c. 287 bc – c. 212 bc), one of the most influential scientists in world history and a colossal Greek mathematician of the highest order.

Birth and early life

Archimedes’ place of birth, Syracuse, at the time was a buzzing city filled with many renowned scholars and artists. The city also benefited from its extensive trade ties with merchants from Greece, Phoenicia and Egypt. According to many historians and scholars in antiquity, Syracuse was at the time one of the most famous cities in the known world.

Although not much is known about the early life of this great mathematician, many historians that came after him proposed that he most likely spent his early years in Egypt, particularly in the city of Alexandria. It was during this time that he invented a device known as the Archimedes’ screw (more on that later).

The only thing we know about his family is that he was the son of Phidias, a renowned astronomer. One of his colleagues known as Heracleides is said to have written a biography about him. However, none of those biographies remain to this day.

Although history has come to judge Archimedes as one of the greatest mathematician and inventors of all time, Archimedes never thought highly of some of his inventions. According to Plutarch, it was for the above reason why the mathematicians chose not leave written records of those works.

Archimedes and King Hieron II, the king of Syracuse

What seems to be apparently clear is that he spent a huge chunk of his life in the Greek city-state of Syracuse on the island of Sicily. While in Sicily, he became a close friend of Hieron II (308-215 BC), the tyrant and later king of Syracuse.

A number of accounts have stated that he helped Hieron II in his court. In one particular case he was able to calculate the proportion of silver and gold in a jewelry that had been gifted to King Hieron.


This third century BC Sicilian-born scientist probably received much of his education in Alexandria in Egypt, where he studied geometry and astronomy from/with scholars and successors of Euclid. Alexandria at the time was perhaps the hub of the intellectual world as it housed a wide variety of scholars from different parts of the world.

Archimedes’ Greatest Contributions

Archimedes, a Greek mathematician, inventor, and scholar of critical acclaim, is praised as one of the greatest mathematicians of all time. He is praised due to his remarkable contributions to a host of disciplines such as mechanics, astronomy, geometry, arithmetic, and physics.


To Archimedes, pure mathematics and geometry gave him more satisfaction than his works and inventions in mechanics. | Greek historian and biographer Plutarch describing Archimedes attitude towards pure mathematics and geometry.

Fictional stories about Archimedes

Being an important figure from the classical age, his story and achievements often suffers a lot as the line between myth and factual detail gets blurred.

Heurēka!” (“Eureka! Eureka!”)

Did Archimedes actually jump out of his bath and run out naked into the streets shouting “Heurēka!” (“I have found it!”)? Many claim that the story was anything but an exaggeration. That probably never happened when Archimedes conceived the principle of buoyant force. Like many scientists that make a breakthrough, Archimedes most likely would have been over the moon over his discovery of how to determine the proportion of silver and gold; however, it is unlikely that he stormed out of the bathroom stark naked into the streets.

Similarly, it is highly doubtful that the Syracuse-based mathematician uttered the sentence:  “Give me a lever and a place to stand and I will move the Earth”. To this day, there is no historical evidence to support such claim. Such a statement is demonstrative of the immense power of levers.

Another made-up story is the one which says that he used a set of mirrors to reflect the sun’s rays to burn a number of Roman ships during the siege of Syracuse in 212 BC. Archimedes did indeed contribute immensely in producing war machines to defend Syracuse during the siege; however, he did not deploy some sort of sun ray-killing machines.

Finally, the story that Archimedes met his end at the hands of a Roman soldier after he refused to abandon a mathematical diagram that he had been working on seems a bit too far-fetched.

Although history has come to judge Archimedes as one of the greatest mathematician and inventors of all time, Archimedes never thought highly of some of his inventions. According to Plutarch, it was for the above reason why the mathematicians chose not leave written records of those works.

However, he took an enormous amount of pride in his work in On the sphere and Cylinder, which shows the mathematical relationship between the volume of a sphere and the cylinder in which it is inscribed. He purposely instructed that his tomb carry image of a sphere inscribed in a cylinder.

Archimedes thus was more pleased by his works in the development of mathematical theorems and proofs than his mechanical inventions. During his time, however, his fame predominantly came as a result of his mechanical inventions.

READ MORE: 12 Greatest Ancient Greek Inventions

Major achievements of Archimedes

Archimedes (287-212 BC). Image

For someone to be described by ancient historians and modern historians alike as the greatest mathematician of all time means that Archimedes was truly indeed a gifted-mathematician.

Below is a quick presentation of the major achievements of Archimedes:

Archimedes’ Law of the Lever


This point of his was captured in his Law of the Lever, which states that “Magnitudes are in equilibrium at distances reciprocally proportional to their weights.”

To demonstrate just how powerful levers can be, there have been some historians that claimed that the statement “Give me a lever and a place to stand, and I will move the world” was uttered by Archimedes. Regardless of whether he uttered it or not, the fact is that Archimedes made tremendous contributions to lever technology. He discovered that the same or even more work could be done when trade-offs are made between force and distance.

Area, surface area and volume of sphere

He used a method of integration to calculate the areas, surface areas and volumes of spheres and other shapes. His works are credited with laying the pillar for calculus, which would later be improved upon by modern mathematicians like Leibniz, Newton and Kepler.

Nine of Archimedes’ treatise survived, including On the Sphere and Cylinder which showed that the surface area of any sphere of radius (r) is four times the value of the greatest circle. This theorem, which is contained in the treatise On the Sphere and Cylinder, can be expressed mathematically as S = 4πr2

Also in the work, the mathematician showed that the volume of the circumscribing cylinder is 2πr3

His mathematical theorem showed that the volume of a sphere is two-thirds that of the cylinder in which it is inscribed. This can be expressed as V = 4/3πr3

In calculating the volume of a sphere, Archimedes discovered that the volume of a sphere is two-thirds the volume of a cylinder that surrounds it.

Approximation of the value of pi (π)

Another significant contribution of Archimedes to mathematics was the value of pi (π). The mathematician calculated that pi fell between 3 10/71 and 3 1/7. He is said to have used a very innovative technique to get the value. That technique was used until the 15th century CE.

In addition to calculating pi, he also accurately approximated square roots.

The mathematician also developed his system of showing large numbers mathematically.

The Archimedes’ principle

Archimedes Principle

The buoyant force on an object immersed in a fluid is equal to the weight of the fluid that is displaced by that object. In other words, a body in a fluid is acted on by an upward force equal to the weight of the fluid that the body displaces.

In addition to developing a host of theorems in mechanics, including in works related to the centre of gravity of solids and plane figures (in the treatise On Plane Equilibriums), he developed a law of buoyancy which is commonly known as Archimedes’ principle. The principle covers the weight of a body that is immersed in a liquid.

Archimedes’ Principle, also known as the Law of Buoyancy, states that an object immersed in fluid will have an upward force equal to the weight of the displaced fluid.

Archimedes’ Principle allows for the calculation of the volume or average density of an object immersed in a fluid. The principle is famed for helping measure the volume of irregular objects, such as jewelry, cutlery, and many others. In addition to that, it allows scantiest to understand how objects behave when immersed in any fluid. With Archimedes principle, one can explain how hot air balloons stay in the air, or how ships float.

Applications of the Archimedes principle is vast and wide, including in disciplines like entomology, engineering, geology, medicine, dentistry, and engineering, among others. For example, in the medical field, the principle comes in useful when determining the densities of teeth and bones.

The Archimedes screw

The invention remains in use even to this day, often being deployed together with irrigation ditches to irrigate large farms.

The screw that Archimedes invented came to be known as the Archimedes’ screw. The screw, which is enclosed in a pipe, is used to lift water from one level to another. The Archimedes’ screw came in very handy when seamen removed water from their ship’s hull.

He touched a bit on integral calculus

His contributions to geometry were unparalleled. He even went as far as anticipating the method of exhaustion which is rudimentary form of modern-day calculus.

Archimedes worked on finding the volumes of the segments of solids that emerged from the revolution of shapes such as circles, ellipse, hyperbola or parabola. This work of his, which is contained in the treatise On Conoids and Spheroids, fall under calculus in our modern time.

His use of method of exhaustion (modern calculus) allowed him to come out with more mathematical theorems.

The compound pulley

This invention of Archimedes ended up bringing the scientist immense praise as it revolutionized the way large objects were lifted. According to Plutarch, the mathematician demonstrated this invention of his to King Hieron by effortless pulling a ship in a straight line.

Archimedes’ passion and associations with other mathematicians of his era

Archimedes was said to be completely devoted to the pursuit of scientific knowledge, particularly mathematics and mechanics. He often did this at a huge expense to his health as he neglected food and drink and basic personal hygiene so he could focus solely on his experiments and studies.

Many of the critically acclaimed works of Archimedes came via his correspondence with mathematicians and colleagues of his in Alexandria, including Eratosthenes of Cyrene and Conon of Samos.

Archimedes – history and accomplishments

A defense contractor for the city of Syracuse

His knowledge in engineering and mechanics enabled him to come out with a number of inventions that he used to defend the city of Syracuse against the Romans in 213 BC. According to Plutarch, his close friend King Hieron was the one who encouraged him to build those war machines.

His engines of war gave him more acclaim that his mathematical theorems. That comes as no surprise considering the fact that it was a BC era, an era when warfare was an extremely important. His war machines received enormous praise for being able to keep the Roman forces at bay for almost two years.

Supplied the city of Syracuse with war machines for its defense. Quote: Plutarch explaining how Archimedes war machines proved extremely useful in temporary keeping the Roman forces at bay.


Many of Archimedes works were theoretical in nature. Much of his work in mathematics was perhaps fanned on by his passion for mechanics.

It’s been stated that his works in theoretical mechanics and hydrostatics enabled him to come out a number of mathematical theorems. As it is seen in his treatise Method Concerning Mechanical Theoremis, Archimedes used much of what he knew in mechanics to advance his knowledge in mathematics.

Famous works of Archimedes that survived

Many of his theorems in mechanics, including those on the center of gravity of plane figures, are contained in the treatise On Plane Equilibriums. In the treatise Quadrature of the parabola, Archimedes calculates the area of a segment of a parabola that had been cut off by any chord.

Archimedes is credited with producing many works. Although many of them were lost, nine of his treaties survived. They are as follows:

  • On Floating Bodies
  • On Spirals
  • On Conoids and Spheroids
  • Measurement of a circle
  • The Sandreckoner
  • Quadrature of the Parabola
  • On Plane Equilibriums
  • On the Sphere and cylinder

In the treatise The Sandrekoner, the mathematician shows how a number system could accommodate astonishing numbers of up to 8 x 1063. He goes on to say that with that number system, he could count every grain of sand which the universe could hold.

He was one of the few scientists of his era that actually thrived to put his mathematical theorems into practice. This is one of the reasons why his works had/and continue to have a huge impact in the world of science.

Archimedes favored the viewing his scientific experiments, including engineering problems, using the lens of mathematical theorems. His passion for mathematics is what led him to deploy mechanical experiments to gain greater understanding of mathematical theorems. 

Heath (1861-1940), a historian of mathematics in ancient Greece.


The mathematician and inventor Archimedes of Syracuse died in 212 or 211 BC in Syracuse on the island of Sicily. He was killed during Roman siege (214-212 BC) on the city of Syracuse (during the Second Punic War). He was most likely in his mid-70s.

Out of the strong respect and admiration General Marcus Claudius Marcellus had for Archimedes, he ordered that the scientist be giving a burial with honor. Marcellus had hoped to capture Archimedes alive so that he could perhaps benefit from the genius of the scientist.

How Archimedes died

One of Plutarch’s accounts on how Archimedes died

According to the Greek historian Plutarch, Archimedes was busy going about with some very important works in mathematics when a Roman soldier struck him down. The historian goes on to say that Archimedes, in spite of the order from the soldier, refused to halt his work.

Another version of how Archimedes died (also from Plutarch) states that Roman soldiers wrongly thought that the mathematician carried on him a bag that contained gold. Unbeknownst to those soldiers, the bag actually contained mathematical instruments, spheres and angles that the mathematician was sending to Marcellus.

An impatient Roman soldier who had been ordered to capture Archimedes alive struck Archimedes down because the scientist did not want to abandon his mathematical work  Image: The Death of Archimedes (1815) by Thomas Degeorge

Read More: 10 Most Famous Ancient Greeks and their Achievements

More Archimedes Facts

Archimedes of Syracuse

Archimedes of Syracuse – Bronze statue of Archimedes in Berlin

The story of Archimedes running naked into the crowded streets of Syracuse shouting “Eureka! Eureka!” was first written down by a Roman scholar and architect named Vitruvius. According to the accounts, the scientist had discovered the principle of buoyancy in order to help him assess whether King Hieron’s golden crown was pure gold or not.

According to Greek historian Plutarch, Archimedes was probably related to Heiron II, the king of Syracuse. This point could be supported by the fact that he dedicated his treatise The Sandreckoner to Gelon, the son of Hieron.

While in Alexandria, Egypt, he studied with a number of followers of the famous mathematician Euclid. He often corresponded with fellow mathematicians Conon of Samos and Eratosthenes of Cyrene, both lived in Alexandria.

After realizing that some of his friends began to take credit for his mathematical proofs, he desisted from including proofs to theorems in his correspondence with mathematicians in Alexandria.

Compared to other scientists and mathematicians of his, Archimedes has quite a lot more anecdotal details about his life.

Much of what we know about the life and works of Archimedes comes from the accounts of Plutarch (c. 46-119 CE), the Greek historian and biography. Other sources came from the likes of Livy and other Greek historians.

The roman general by the name of Marcus Claudius Marcellus – was saddened by his death as he intended to bring Archimedes into his service. The general was impressed by the machines that Archimedes built to defend the city from the Romans

Following Rome’s siege of Syracuse in 212 BC, Roman General Marcellus is believed to have taken two spheres made by Archimedes back to Rome. The spheres were basically about the various planetary objects as well as their motions.

Like many scientists and geniuses that came after Archimedes, the likes of Galileo and Newton were big admirers of the Sicilian scientist and mechanical engineer.

Following his death, his mathematical works and treatise did not gain large acclaim as compared to the ones of the mathematician and geometer Euclid. Regardless, there were still a good number of mathematicians in Alexandria that were devout followers of his works. Those scholars included Theon, Pappus, and Heron.

When the Roman statesman and scholar Cicero travelled to Sicily in 75 BC he searched for the tomb of Archimedes. Cicero found the tomb to be covered on all side by weeds.

Archimedes believed that pure mathematics was the only worthy pursuit in his illustrious career. He discovered that the ratio of the circle’s circumference to its diameter, which is pi (π), lies between 3 1/7 and 3 10/71. Quote: Cicero on the tomb of Archimedes

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