Over many centuries, scores of mathematicians have formulated a large number of theorems and, through experimentation, having been successful at proving them. Algebra, analytical geometry, differential calculus, prime numbers – the history of all of the main mathematical concepts can be seen to parallel the history of the sciences. Thus, being a teacher or lecturer of mathematics, requires of you, not only to lead your students through one of their most difficult subjects, but, also, exposes them to the greatest mathematicians of all time.
Although things are starting to change somewhat, sadly, most mathematics teachers (especially at high school level) and lecturers (at colleges and varsities) are male. So, even in today’s article, we explore mainly men who greatly contributed to our understanding of the discipline mathematics – Archimedes, Descartes, Euclid, Newton, Pythagoras and Thales.
Thales’ Theorem: All You Need to Know
Thales of Miletus was a Greek philosopher, statesman, astronomer and mathematician, whose famous theorem is still being taught in high schools today. One of the Seven Sages of Greece, he was born in Ionia, Asia Minor (now part of Turkey) in the year 625 BCE. He studied several sciences while in Egypt, at a time when these subjects were reserved for Babylonian and Egyptian priests.
From the Egyptians, Thales learned astronomy, geometry and philosophy. In truth, the pyramids of Egypt were frequently the theme for many scientific experiments conducted by the young apprentice.
After his Egyptian sojourn, Thales set sail for Miletus, firmly resolved to establish a school in Milan. While continuing research in various domains, Thales became a teacher carrying over to his followers many of the discoveries he had made while abroad. According to legend, Thales had set out to calculate what the height of a pyramid was, by comparing it to the shadow of his cane. It is believed that this led to the invention of his now-famous theorem, which states:
“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 was also an astronomer who discovered how sailors could make use of Ursa Minor (the Little Dipper) to navigate on the open ocean. He calculated the length of a year in relation to equinoxes and solstices and also worked out the trajectory of the sun between the tropics, among other things. Thales of Miletus died circa 547 BCE apparently from heat stroke.
Pythagoras and His Influence on the History of Mathematics
Any high school student will tell you that, Thales’ theorem is covered alongside that of Pythagoras. Pythagoras’ theorem is one of the most important markers in the development of geometry. Born close to the end of the 6th century, Pythagoras’ name translated means “announced by Pythia”. The history of Pythagoras is gleaned many from several works, which were written after his death. He was a very talented and athletic student, who participated in the Olympic Games, mainly in the category of combat.
As a student interested in history, the sciences and philosophy, he enrolled to become a student of Thales. Retracing his professor’s footsteps, he went off to immerse himself in the study of Babylonian and Egyptian sciences. On the conclusion of his studies, he returned to his island home, with the hope of establishing a school. He, unfortunately, did not receive the warm welcome his teacher did and was, as a result, was expelled from the city of his birth. He decided to flee to Greece, where he was better received and he established a school, called the School of Pythagoreans.
With the aid of his devotees, Pythagoras was able to prove his now-famous 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".
However, this was not his only contribution to the field of mathematics. Pythagoras’ table, the Pythagorean snail and his School for Pythagoreans impacted on the development of mathematics forever. Markedly upset by the death of several of his students, Pythagoras died in Italy, circa 490 BCE, by his own hand.
Euclid and His Influence on Mathematics
“Considering the fame of the author and of his best seller [the Elements], remarkably little is known of Euclid” – Carl Benjamin Boyer, historian.
Much of what we know about Euclid, one of most important mathematicians of all time, stems from the works of the Pappus of Alexandria and Procius, philosophers who lived many centuries later.
Euclid lived around 300 BC, before Archimedes, but after Plato and was active as a logician and geometer. He known chiefly for his treatise, Elements, a collection of postulates, definitions, mathematical proofs and propositions (constructions and theorems). The 13 books cover elementary number theory, incommensurable lines and solid and plane Euclidean geometry. Elements is the oldest existing large-scale explanation of mathematics. This seminal treatise and his other works, saw Euclid being called the ‘father of geometry’. His system. Euclidean geometry, involved innovations and a synthesis of theories of former Greek mathematicians, including Thales, Hippocrates of Chios and Eudoxus of Cnidus.
Many of today’s courses with a math tutor – algebraic reasoning, fractions, equations, logarithms, Euclidian division, Euclid’s axioms and Euclidian geometry – have been structured around Euclid’s research. Euclid, who became a professor of mathematics at the School of Alexandria, gained inspiration for many of his discoveries from regular visits to the library and the Museum of Alexandria.
We owe a lot of what we learn about mathematics, even at primary school level, to this great mind: Euclidian division (with the four main elements being a dividend, divisor, quotient and remainder) and the highest common factor (HCF). It is presumed that Euclid died in Alexandria in 265 BCE.
To help improve understanding and boost grades, consider hiring an online mathematics tutor who can provide personalized instruction and support.
What do we Know About Sir Isaac Newton
One of world’s most important mathematicians was Sir Isaac Newton (1642 – 1727). Also a physician, astronomer and philosopher, he was born in Woolsthorpe, Lincolnshire, England. Raised, mainly, by his grandmother and father, although he appeared a rather distracted learner, Isaac was very gifted at building all kinds of machines.
The world is the richer for one professor who convinced Newton’s mother to allow him sign Isaac up at Cambridge University, when she wanted him to leave school to help out on the family farm. The main mathematical concepts he studied there included arithmetic, trigonometry and geometry. He also studied optics and astronomy and graduated in the year 1665. He is, first and foremost, known for having discovered the phenomenon known as gravitation. According to legend, he figured out this phenomenon by observing apples falling from the trees in an orchard. Newton, in the field of mathematics, introduced derivatives and the binomial theorem, which is used extensively in the areas of statistics and probability.
Newton became an accomplished professor and, when not lecturing, studied the way light behaved, by and large, optics. In particular, he studied the way that white light behaved when shone through a transparent prism, unearthing that light separates into a number of beams and into different colours. His experiences with light saw him invent the world’s first telescope reflector, which was well-received by scientists around the world at that time.
What do we Learn from Rene Descartes?
The study of Rene Descartes is a very important step, if one is to grasp an understanding of how mathematics has developed over time, particularly the operation of equations. Born in Haye, France in 1596,he was raised by his grandmother in a well-to-do family, his father being a provincial government advisor. Rene drafted numerous scientific articles, starting with “The World or Treatise on Light”, which explains many daily physical phenomena, including the earth’s revolution around the sun.
His most celebrated work, however, still is his 1637 “Discourse on Method”. This work is best known as the source of Descartes famous quotation: “I think, therefore I am” (Je pense, donc je suis). It was written entirely in French and published many mathematically developments for the first time. One of them being the use of letters to denote unknown quantities in an equation. Because of this work, we, today utilise the letters x, y and z (or a, b and c) to represent quantities that are not known. Descartes formulated a way to write powers and invented analytic geometry. We also owe thanks to Descartes for developing refined calculations and Cartesian equations that all mathematics students learn at high school.
Archimedes: Mechanic and Mathematician (287 – 212 BCE)
One of the greatest mathematicians of antiquity, Archimedes was renowned for inventing machines. In Alexandria, where he continued his studies, after he had studied astronomy under his father, he rubbed shoulders with many of the great minds of his age, inspiring him to develop numerous mathematical theories. He, for instance, discovered the value of Pi, which represents the relationship between the diameter of a circle and its circumference. Archimedes also enjoyed calculating areas, as he did with that of a parabola, as well as other figures.
In science, he also explained, after experimentation, the “principle of flotation”, which explains the force that is exerted on a solid body submerged in a fluid, be it gas or liquid. This knowledge helped him design, and have built, the largest ship in Antiquity, the Syracusia. At the end of his career, Archimedes designed several war machines to help the city of Syracuse defend itself against attack. The art of war and several innovations, particularly catapults and powerful boats, were all markedly influenced by Archimedes, inventor and one of the world’s most important mathematicians. He also developed the Archimedean Screw, still in use today, which moves a liquid (like water) from one altitude to a higher one. He died in Syracuse during a Roman invasion. Archimedes’ legally influenced many subsequent famous mathematicians, inventors and scientists, including Leonardo da Vinci.
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