Mathematics as we know it today has evolved considerably over the past centuries. It has evolved from basic counting, measurement, and calculations to applying abstract logic and several complex concepts. In fact, the history of mathematics is as old as human civilization. Today, we’ll take a trip into the past and explore the story of Archimedes, a mathematician and philosopher who would eventually be known as the “Father of Mathematics.”

Who is Archimedes? 

The Father of Mathematics is the great Greek mathematician and philosopher Archimedes. Perhaps you have heard the name before – the Archimedes’ Principle is widely studied in Physics and is named after the great philosopher. This esteemed scholar has several feathers in his cap in mathematics and physics, coining him one of the leading scientists of the classical era.

[Read: Famous Mathematicians in the World]

Archimedes was the master brain behind pi, also known as the measurement encapsulating the area of the circle and the surface area and volume of spheres. Archimedes devoted his entire life to scholarly pursuits and was fueled by a burning desire to know, explore, and uncover the unknown in all walks of life.

In the following sections, we will take a peek into Archimedes’ early life, education, epic work, and immortal contribution to Mathematics.

Archimedes’ Early Life

Archimedes was born in c. 287 BC in Syracuse, which is modern-day Sicily in Italy. 

Unfortunately, not many details are known about Archimedes’s early life as his biography written by friend Heracleides has been lost. As per his writings in his book the ‘Sand Reckoner,’ his father Phidias was an astronomer. To this day, there is no information available regarding his family, marriage status, or children.

His written works suggest that he had scholarly relations with several scholars in Alexandria in Egypt. He published his works in the form of correspondence with principal mathematicians like Eratosthenes of Cyrene and Conon of Samos. Soon enough, renowned scholars and writers, including Cicero and Plutarch, have mentioned him in their books.

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Archimedes’ Notable Discoveries 

Modern mathematics owes a lot to Archimedes. While inventors and scientists generally gain recognition for a single discovery, Archimedes has a long trail of shiny inventions and explorations to his name. 

Let’s go through the list of the famous discoveries and inventions that make him a scientist of exceptional caliber.

Contribution to Mathematics

Derivation of ‘pi.’

‘Pi’ is the ratio of the circumference of a circle to its diameter. It is calculated to be 22/7 and is a fixed constant irrespective of the circle’s size. 

A calculation in decimal figures gives its approximate value as 3.14. In that classical era, when there were no calculators or computers, Archimedes derived this value by hand with perfect accuracy.

Exponent System for Large Numbers

Archimedes’ contribution to discovering the exponent system or large number is mentioned in his book “The Sand Reckoner”. He discovered and proved the law of exponents, where he constructed the necessary rules to manipulate powers of 10. 

The famous law of exponents that we know of today as 10a.10b = 10a+b is still used to solve many problems which involve repeated multiplication processes. 

[Read: Applications of Trigonometry]

Estimation of the size of the Universe

Archimedes worked heavily on the theory of the Universe. He estimated an upper limit to the number of grains of sand one would need to fill the Universe. He began exploring this brilliant idea while working on grains of sand, as mentioned in his book, “The Sand Reckoner.” 

Previously, Aristarchus of Samos was the only person who had suggested that the sun was in the center of the Universe and that the planets revolved around it. The original work by Aristarchus is lost, but Archimedes’ work contains references to his theory. 

Archimedes made assumptions, including that the Universe was a sphere and that the ratio of the Universe’s diameter to the Earth’s orbital diameter around the sun was equal to the ratio of the Earth’s orbital diameter around the sun to Earth’s diameter.

Method of Exhaustion

Archimedes used the method of exhaustion based on proof by contradiction to answer problems with accuracy. He specified the limits of his answers as well. He used this technique to approximate the figures’ areas and derive the value of Pi and showed that it was less than 22/7 and greater than 223/71, which means he was fairly on point with modern calculations. 


Area of circles and other shapes

Another remarkable achievement of Archimedes and his contribution to mathematics was his method of calculating the area of a circle. He explained his concept in his book, “Measurement of a circle,” where he established the relationship between spheres and cylinders. 

He studied the area and surface of a circle as well as a parabola. He gave a relationship between the area of a parabola and a straight line in his book “Quadrature of a Parabola.”

The principal results he gave in his book On the Sphere include:

  • The surface area of any sphere of radius r is four times that of its greatest circle (in modern notation, S = 4πr2)
  • If a sphere is inscribed in a cylinder, the volume of the sphere is two-thirds the volume of that cylinder. This leads to the formula for the volume of a sphere: V = 4/3πr3.

Archimedes’ Written Works 

Being the genius that he was, Archimedes spread his learnings in several books, articles, and propositions. His works include: 

  • Measurement of a Circle
  • On Spirals
  • On the Equilibrium of Planes
  • On the Sphere and Cylinder
  • On Floating Bodies
  • Stomach
  • The Method of Mechanical Theorems

Several authors who came after Archimedes have made references to his other works that may not have survived to the present day. 

These include: 

  • Treatises on catoptrics also discuss the phenomenon of refraction of light on the 13 semi-regular polyhedra. These are bodies or shapes bounded by regular polygons, not of the same type necessarily, that can be inscribed in a sphere.
  • The “Cattle Problem,” which is the study of polynomial equations with integer solutions.

Contribution to Physics

Archimedes’ Principle

Archimedes discovered a method to determine the volume of an irregularly shaped object. In one of the references made by Roman author Vitruvius, King Hiero II of Syracuse once asked a goldsmith to make a gold crown for the temple. The king suspected that the goldsmith added some silver to the crown and that it was not pure gold. He asked Archimedes to uncover the truth without breaking the crown or melting it down to a body of regular shape for finding its density.

Inspiration can come anytime. One day, Archimedes noticed during his bath in a tub that the water level increased as he got in. Archimedes later used this observation to calculate the crown’s volume.

Archimedes calculated the density of the crown by dividing the crown’s mass by the volume of the displaced water. If the goldsmith added silver to the mass, this density would be less than that of gold. The method worked and led Archimedes to announce his discovery with his famous words, “Eureka!”, which is Greek for, “I have found it!”

He would later explain this principle in detail in his work “On Floating Bodies.”

Archimedes Screw

Archimedes’ contributions also spanned the worlds of physics and engineering. As per Greek writer Athenaeus, King Hiero II once asked Archimedes to design a huge ship, the Syracuse, which was to be built luxury for travel and hold about 600 people. It would carry supplies and serve as a naval warship.

Now, a ship of such massive size posed the problem of potential leakage of water through the ship’s body. To overcome this issue, Archimedes designed the Archimedes’ screw. This screw was a machine that consisted of a cylinder with a screw-shaped blade that could revolve. It was hand-worked, and he used it to remove the extra water levels from a body lying at a low level.

Archimedes Claw 

Archimedes also designed a workable device in the shape of a metallic claw to defend the city of Syracuse. This device had a metal arm like a crane fitted with a big hook to lift enemy ships out of water.

Archimedes’ Death

Greek historian Plutarch details in his works that Archimedes died when the Romans besieged the city of Syracuse. Archimedes was trying to solve a mathematical problem when a Roman soldier came to capture him. Legend says that even in the critical time of his death, Archimedes had requested the Roman soldier not to disturb his mathematical work. 

Archimedes’ Legacy of Honour 

Archimedes’ contributions to the fields of mathematics, physics, astronomy, and philosophy have been outstanding. Mathematics and science historians universally agree to the fact that Archimedes was the greatest mathematician from antiquity. With a long trail of inventions and discoveries in his name, Archimedes has rightly been deemed the “Father of Mathematics.”
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