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Algebra Through The Ages

Algebra is such a staple in Mathematics today. It is so prevalent that the concept of algebra i.e. representing unknown values as abstract symbols rather than numbers feels so natural. It is one of the simplest and most utilised weapons in a mathematician’s toolkit. In this article, we will explore the roots of algebra and discover the many contributions to its formalisation all over the world. The earliest known usage of algebra is by the Babylonians around 2000 BC. Using tables and clever geometry – a Babylonian mathematical – the Babylonias could solve quadratic equations. Their methods consisted of step-by-step instructions in dealing with equations of certain forms. The Babylonians actually managed to derive the quadratic formula albeit a very informal version without any of the symbols we use today. There is also evidence of algebra from ancient Egyptian texts circa 1650 BC. Texts from that time, such as the Rhind papyrus, showed that the Egyptians could solve linear equations an
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The 7 Bridges of Königsberg

Königsberg was a Prussian city (presently Kalingrad, Russia) in the 18 th century. The city had seven bridges connecting four landmasses as shown in the diagram.   According to folklore, the following question was a popular mathematical puzzle at the time: Could one take a walk through the city in such a way that each bridge would be crossed once? Though many had attempted the problem, they could not prove that their answer was indeed correct. Enter Euler. Euler tackled this problem in 1735, proving exactly why his answer was correct and subsequently creating the field of graph theory. Leonhard Euler (1707-1783) was an extremely prolific mathematician. Most people will know of his constant e, from high school mathematics as well as his multitude of other accomplishments. Euler had such a huge mathematical influence that Pierre-Simon Laplace quoted "Lisez Euler, lisez Euler, c'est notre maître à tous." Which some of you French learners/speakers will know roughly translate

Pythagoreanism

Pythagoras of Samos is most famously credited for discovering the theorem relating the three sides of a right angled triangle (though evidence suggests that this theorem was not discovered by Pythagoras and was actually in use in many parts of the world before Pythagoras’s birth). However, few know about the Pythagorean Brotherhood - a cult formed by Pythagoras in Croton in Southern Italy in the 5 th Century BC that lasted almost 200 years after his death. Though the Pythagoreans shared many ritualistic features with other cults such as wearing robes, observing sexual purity, maintaining utmost secrecy and loyalty, and not touching beans, it was unique in its worship of numbers and their metaphysical. Pythagoreans believed in the metaphysics of number and that reality was mathematical in nature. They also believed that spiritual purity could be achieved through the study of philosophy and mathematics. ALL IS NUMBER - Pythagorean Motto Pythagoreans believed in the concept of tetraktys,

Fermat's Last Theorem

You may be familiar with Pythagoras’ Theorem. This simple yet significant theorem is a staple in secondary education around the world and oftentimes your best friend when it comes to geometry problems. This simple theorem is backed up with many simple and elegant proofs easily understandable by anyone who can understand the theorem itself. This is exemplified by this rearrangement proof: See how the the yellow areas in the first diagram can be rearranged to form the second diagram and how this proves Pythagoras’ Theorem. Now, there are some integers that satisfy Pythagoras’ Theorem. These are referred to as Pythagorean Triples and there is an infinite amount of them (Why?). Some small examples include (3,4,5), (5,12,13) and (8,15,17).   Finding Pythagorean Triples is an example of solving a Diophantine equation – equations which have positive integer solutions for all variables. Unsurprisingly, Diophantine equations are named after Diophantus who developed methods for solving such equa