When we study mathematics we are standing on the shoulders of the great thinkers. Because of the life work and legacy of these great men and women, we continue further in our study of the language of God and truth through his beautiful creation. Let’s explore one such great man: Diophantus.
At the dawn of the Later Alexandrian Age, about 250 AD — 350 AD, we find the leading Greek algebraist, Diophantus. Diophantus, like so many mathematicians and philosophers before him; lived, studied, and taught in Alexandria. Throughout all of history no other city has hosted the hub of mathematical discovery for as long a period as Alexandria, which boasted Euclid around 300 BC and Hypatia in 415 AD. Diophantus’ great work was his Arithmetica, which is a collection of over 150 problems. Diophantus’ equations in his text were not focused on finding all possible solutions to a problem but finding a value that would make his equation true. His solutions were integers and therefore led to mathematicians generalizing equations with integer solutions as Diophantine equations. Diophantine equations are often formed from riddles because they do so often contain multiple solutions. For example: Mrs. Adams made 84 truffles for her party. If each guest gets the same number of truffles to eat, then how many guests can Mrs. Adams host at her party?
Other Diophantine problems form what we call systems of simultaneous equations. Interestingly, Diophantine never solved these with two variables. Instead, he chose to define one variable in terms of the other. Diophantine, while often called the father of Algebra, is one man who shaped the future of mathematics from the halls of Alexandria.
Try the following Diophantine Problem:
My farm has dogs and chickens. Each dog has five toes on each of his front feet and four toes on each of his back, while the chickens have 5 toes on each foot. If the sum of toes for my dogs and chickens is 364, and the sum of dogs and chickens on the farm is 30 animals. How many dogs do I have on the farm?