In our everyday life, whatever task we do somehow consists of Mathematics. Mainly Mathematics is the science of structure, elemental counting practices, measuring, arrangements, and shapes of objects. It is the quantitative calculations that contain sets of axioms and theorems. Mathematics is found in everything around us electronic devices, architectural buildings, sports, and even money. As a result of the apprehension of rapid development of science, mathematics has developed since ancient times in primitive cultures. The need for mathematics in a society depends on its plans. The more intricate a society, the denser requirement of mathematics.

A counting system was first invented by The Sumerians, who built the earliest civilization in Mesopotamia in 3000 BC. Mathematics has been evolving ever since however, from the 15^{th} century to the late 20^{th} century new advancements in Mathematics were made. The mathematician is the most ancient science and is the core of all other sciences.

## Pythagoras:

Pythagoras is considered the first genuine mathematician. He was said to be born approximately in 569 BC in Samos Island, Greece. His death is declared to be between 500 BC to 475 BC in Lucania, Italy. He had two or three brothers and his father was a merchant. His mother’s name was Pythias.

Pythagoras left Samos with priests to study in the temples, for Egypt in about 535 BC. He created much impact on priests which could later be seen practiced in the society such as wearing animal’s skin as clothing, the codes of secrecy, or striving for purity. He was well educated and had great interests in Mathematics, Philosophy, music, and astronomy.

He later after writhing settled in Crotona, a Greek colony in Italy. Formed a philosophical and religious school where the believers lived and worked. The Pythagoreans were well behaved in every aspect of their life may it be living or working. His followers were both Men and women, they had no possessions and were called mathematikoi. They worked together on theories and discoveries of Pythagoras.

Some of Pythagoras’s believes were:

- Mathematics is the basis of everything and the highest form of mathematical study in geometry.
- Numbers have personalities, characteristics, weaknesses, and strengths.
- Symbols have a mystical significance.
- Strict loyalty and secrecy should be observed by members.
- The world depends on the interaction of opposites.

As of the strict secrecy policy among the society and that they shared their intellectuals and ideas with one another without giving individual credit, it is difficult to claim if all the theorems were of Pythagoras or by the members of his society. However, the Pythagoreans always give credit to Pythagoras for the following:

- Geometric algebra and constructing figures of given areas.
- Pythagoras taught that the earth was a sphere in shape and in the middle of the universe. He also proposed that the paths of planets were circular.
- The five regular solids; tetrahedron, octahedron, icosahedron, cube, dodecahedron.
- The sum of angles of a triangle equals to two right angles.
- The theorem of Pythagoras.

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## Archimedes:

Archimedes is the ‘father of mathematics’. He was born in 287 BC in Syracuse, the Greek land of Sicily, and died around 212 BC. Archimedes worked for the king and his army by solving mathematical problems and giving birth to new innovations.

An award was named after Archimedes to pay tribute to his contributions towards Science that is “The Fields Medal”.

Memorable inventions of Archimedes consist of:

- The method of exhaustion to measure the areas of shapes.
- Relationship of spheres and cylinders.
- Calculation of the measurement of a circle.
- Infinity.
- Equilibrium of various shapes.
- Uses of prime numbers.
- Archimedes’ principle
- Quadrature of parabola

As Archimedes lived in Sicily, a colony of Greeks that was occupied and condemned every so often by enemies, he was killed by a Roman soldier in 212 BC.

He was quite popular in his time for all his inventions, and he took interest in science and mathematics from his childhood. Archimedes’s family turned out to be supportive in getting proper education and he joined the School of Mathematics, in Egypt. Later he obliged his whole life to discover mathematical concepts, techniques, and knowledge and all his inventions are now being used critically!

## René Descartes:

Renè Descartes, known to be the father of Modern Mathematics, but also known as one of the main figures in the Scientific Revolution of the 17^{th} Century and ‘The Father of Modern Philosophy.’

He was born in 1596 and died in 1650, at the age of 54. Before achieving his dreams, and meeting with the Dutch scientist and philosopher Isaac Beeckman, who ignited his interest in mathematics and physics, he was employed as a soldier in various forces for Protestants and Catholics.

Later he declared that his real ambition in life was to trail science and a sense of knowledge and that the key to philosophy was to build undeniable facts of mathematics.

Descartes spent most of his adulthood in the substantial environment of the Netherlands and worked hard on his vision to submerge algebra and geometry. He published his mathematical dissertation “LA Géométrie” in 1637 which is now popularly known as a milestone in the history of Mathematics.

Some of his declarations include:

- Any equation can be represented on the plane by the plotting solution set of the equation on it.
- Lowercase a, b and c should be used for known quantities.
- Lowercase x, y, and z go be used for unknown quantities.
- Each point in two dimensions can be described by two numbers on a plane.

For all the work he did for Mathematics, he is the best known today. He also made developmental changes in modern physics. He dies in Stockholm, Sweden far away from his home place in 1650. However, years after his death his work was placed on the Catholic Church’s “Index of Prohibited Books”.

## Leonhard Euler:

Leonhard was born on April 15^{th}, 1707 in Basel, Switzerland, and died on September 18^{th},1783 in St. Petersburg, Russia. He is known as one of the founders of pure Mathematics. He introduced new methods of solutions and provided the subjects of calculus, geometry, and number theory with great progressive contributions. He also exhibited the applications of mathematics in public affairs.

Euler moved to Russia in 1727 and served in the navy and later joined St. Petersburg Academy as a physics professor. His first book was published in 1736, Mechanics. Euler lost his ability to see from the right eye later in the decade, due to cartography work. He was appointed as mathematics director in the Berlin Academy of Science and received Patronage from Catherine II in 1766. As in the early 1770s, Euler lost his eyesight completely yet continued his work with assistance.

The major contributions of Euler include:

- The utilizations of pie and f(x).
- The identity theorem of Euler is quite popular.
- He published a science and Philosophy series Letter to a German Princess.
- Threw light on a range of principles.
- Contributed greatly to the fields of trigonometry, calculus, and differential equations.

Many other people have also worked in the field of mathematics too. Every mathematician’s contribution is very noteworthy and of utmost importance.