Over the course of history, many mathematicians have created numerous theorems and have succeeded in proving them through the process of experimentation. Prime numbers, differential calculus, analytic geometry, algebra – all of the history of math can be seen to run in parallel with the history of sciences. Being a professor in mathematics requires, then, describing the history of the progression of the discipline, as well as engaging students in this history through the narratives of some of the most famous and successful mathematicians. According to many sociological studies investigating mathematics taught in higher education, students in math are today, as was the case centuries ago, are for the majority men. Thales, Pythagoras, Euclid, Descartes, Newton and Archimedes - discover the history of the sciences and math through these different mathematical giants.

## Everything to Know About Thales' Theorem

A great philosopher in ancient Greece, Thales is most known for his infamous theorem that we still learn today in high school. However, going beyond his famous work, do we really know who Thales is? Born in what is now part of Turkey in 625 BCE, Thales of Miletus is considered one of the seven sages of ancient Greece. The young mathematician studied various sciences in Egypt, at the time subjects reserved for Egyptian and Babylonian priests.

From them, Thales learned geometry, astronomy, and philosophy. In fact, the Egyptian pyramids were often the subject of the young apprentice’s scientific experiments. After this experience, Thales returned home to Miletus with the hope of establishing the school of Milan. There, Thales became a professor and started to teach all of the discoveries he had made abroad to his disciples, all the while continuing his research in different domains. The discovery of the theorem that we know today, according to legend, has it that Thales wanted to calculate the height of a pyramid in relation to the shadow of his cane. It was through this inquiry that Thales invented his now-famous theorem:

“if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle"

Thales’ knowledge also extends to cover the field of astronomy, where he discovered how to use the little dipper, or ursa minor, to guide sailors in the open ocean; how to calculate the duration of a year in relation to solstices and equinoxes; identified the trajectory of the sun between the two tropics, etc. Thales died in approximately 547 BCE in Miletus.

## The Influence of Pythagoras over the History of Math

As every student can recall, Thales’ theorem is covered in curriculum alongside Pythagoras’ theorem. A concept covered early on in the academic career of high-schoolers, Pythagoras’ theorem marks one of the most important chapters in the development of geometry. Pythagoras, which translates to “announced by Pythia,” was born on the island of Samos in Greece at the end of the 6th century BCE. The history of the infamous scientist is derived from only some works written before Pythagoras’ death. Pythagoras was a very gifted and athletic student. Most notably, he participated most in the Olympic games for the category of combat. Interested by philosophy, history and the sciences, he became a student of Thales. Following in his professors footsteps, Pythagoras left home to learn Egyptian and Babylonian sciences. After finishing his studies, he returned to his island with the idea of starting a school, exactly as Thales had done. Pythagoras, however, did not receive the same welcome as his teacher had and was consequently expelled from his native city. He fled to greater Greece, where he was finally able to create his school named School of Pythagoreans.

With his disciples, the mathematician managed to demonstrate his now infamous theorem:

“the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Or a2+b2=c2"

The influence of Pythagoras on the discipline of mathematics doesn’t end there. The Pythagorean snail, Pythagoras’ table, along with his School for Pythagoreans changed the field of mathematics forever. Pythagoras died in approximately 500 BCE.

## Euclid and His Discoveries in Mathematics

The life of Euclid and his discoveries changed altered the approach to teaching mathematics. Trigonometry, algebraic reasoning, equations, fractions, logarithms, Euclid's’ axioms, Euclidean division, Euclidean geometry, Euclidean algorithms – many of today’s maths courses are structured with regards to Euclid’s’ research. Born in Athens around 330 BCE, Euclid became a professor at the School of Alexandria. His mathematical discoveries were inspired by his frequent visits to the library and to the Museum of Alexandria. The mathematician is now celebrated in the world over for his seminal work named Elements, written around 300 BCE. Considered as the Mathematics Bible, this book has, like the Bible, continued to be sold since its inception. Divided into thirteen books, Elements develops several theories concerning the geometric plane and general arithmetic (triangles, right angles, circles, etc.). Through these works, Euclid managed to prove Pythagoras’ theorem and to develop the function of the greatest common divisor (GCD) in Euclidean divisions. Euclidean divisions are nothing but the simple division taught in elementary school. This division involves the four main elements: a dividend, divisor, quotient and remainder. Euclid also explained how to find the HCF (highest common factor), a procedure that involves finding the greatest number common to two numbers that they are both divisible by. Finding the HCF allows division to be accomplished much more easily. Euclid died in 265 BCE in Alexandria.

## Everything to Know About Sir Isaac Newton

Isaac Newton (1642-1727) is not just a simple mathematician. Physician, philosopher and astronomer, Isaac Newton was born in Woolsthorpe in Lincolnshire in the UK. Raised mainly by his father and his grandmother, he was characterized as being at once a distracted student but also very gifted in building machines of all types. When his mother decided to take Newton out of school so he could aid the family farm, one professor convinced her to let him sign up at the University of Cambridge. There, he studied arithmetic, geometry, trigonometry, astronomy and optics – and subsequently graduated in 1665. Isaac Newton is known first and foremost for having discovered the phenomenon called gravitation. Legend has it that Isaac Newton must have discovered gravity in observing apples fall in an orchard. In the field of mathematics, Newton introduced derivatives as well as binomials, helping prove that the formula [(a+b)n] functions no matter what the value of n is. While Newton became an accomplished professor, he also used his free time to study the behaviour of light and, more largely, optics. More specifically, he studied the behaviour of white light on a transparent prism and realized that light separates itself into many beams and different colours. He used his experiences with light to invent the first telescope reflector, which ended up as a success within his contemporary scientific community around the world.

## Why do we Study Rene Descartes?

Studying Rene Descartes in maths is an unmissable step in the journey of understanding the history of mathematics and, more precisely, the operation of equations. Born in France in 1596 in the town of Haye, Rene Descartes was raised by his grandmother in an upper-class family. His father was an advisor to the Parliament of Brittany. Rene Descartes wrote many scientific works during his career. He started most notably with “The World, or Treatise on Light,” which describes many of the physical phenomena of daily life, including the movement of the earth around the sun. However, his most celebrated work remains 1637’s “Discourse on Method.” Written entirely in French, Descartes produced many mathematical developments, the most significant of which was his utilization of letters to signify the unknowns in an equation. It is because of this work that we started to utilize the set of letters x,y,z or a,b,c to do the same. Descartes also wrote powers in a method that went against the traditions of the era – writing x4 instead of xxxx. Descartes also invented analytic geometry, which consists in representing figures by their algebraic calculations derived from a system of coordinates. Refined calculations, Cartesian equations, we owe thanks to Descartes for developing all of these great chapters of math taught at high school! Look up for a math tutor here.

## Archimedes: the Mathematician and Mechanic

Great mathematician and physician of antiquity, Archimedes, alive between 287-212 BCE, is one scientist most known in the field of inventing machines. After having studied astronomy with his father, Archimedes continued his studies at the prestigious School of Alexandria. There, he rubbed elbows with the greats of the time, which inspired him to develop his numerous mathematical theories. Mathematics as a discipline owes many of its tools to Archimedes, one of which is the number Pi. He calculated the relationship between the circumference of a circle and its diameter and discovered that the number he found is always the same, no matter the size of the circle. Archimedes also took pleasure in calculating areas, like the area under a parabola, and other figures. His various mathematical contributions don’t stop there, science also benefited from his knowledge and experiments by his explanation of what is today called the “principle of flotation.” This theorem provides an explanation of the force exerted by onto a solid body submerged in a fluid, being liquid or gas. This resulted in the construction of the biggest boat of Antiquity: the Syracusia. Archimedes finished his career in the service of the city of Syracuse in order to expand upon war machines. Catapults, powerful boats - the art of war and its innovations have all been influenced by Archimedes. Amongst all of his machines, he developed also the screw, which was utilized to move liquid from a lower altitude to a high one. Archimedes died in Syracuse during the Roman invasion. His legacy continued to influence some of the world’s biggest scientists, including Leonardo de Vinci.

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