Diophantus



Diophantus was born and raised in Alexandria, Egypt. He lived during the "Silver Age", or called the "Later Age of Alexandrian." The information of his early and personal life is very scarce because not much was recorded on his actual life, just on his work. However, there is record of his death, given in a puzzle. The puzzle is:"Here lies Diophantus." The wonder behold- Through art algebraic, the stone tells how old: "God gave him his boyhood one-sixth of his life, One-twelfth more as youth while whiskers grew rife; And then yet one-seventh eve marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage Met fate at just half his dad's final age. Four years yet his studies gave solace from grief; Then leaving scenes earthly he, too found relief." (Diophantus, "Father of Algerbra"). The answer to the riddle is 84, so he lived to be 84 years old.

Diophantus always had a the ability for learning and loved solving problems. He never stopped until he achieved the final answer and then he would move on for a more difficult and challenging one. Math was more of a hobby, then a school subject. All of his hard work and endless efforts allowed him to attend the University of Alexandria in Egypt. At the University, he learned many of his skills and this took his talents to a whole new level. Diophantus was always at the head of the class in every possible category.

After obtaining all of his extraordinary knowledge from school Diophantus did not miss a beat after he graduated. Diophantus later wrote a collection of thirteen books called, "Arithmetica". His books consist of difficult and somewhat complicated equations in algebra. The books are not to be thought as of text books, but as an application of algebra. Almost all the books have survived throughout their life-time except for seven of them leaving six. They were thought to be vanished, or maybe even destroyed. No one really ever knew what happened to the rest of Diophantus's books. In all of the books there a 130 problems total.

Diophantus's first work was with polygonal numbers, on which he wrote a short essay about in the Arithmetica. He explained this through a method where numbers are represented by line segments. In his books Diophantus illustrateds how to solve linear equations, (this would be the beginning of them). In the same readings, Diophantus also showed how to solve quadratic equations. The 130 thirty problems that were in the Arithmetica mainly included equations that were determinate and indeterminate. Since no one was very familiar with his work at the time, they didn't understand well and it was very complex to most people.

A determinate equation is an equation that has defined limits, or that is established, definite. It is an equation that has a definite answer that is not infinite and only has one possible solution. An example of this would be: 5-3=2. The example problem in determinate because it only has one solution, which is 2. The equation 5-3=2 cannot be derived any other way because it is determinate and only has one single solution. This is not only for this problem, but all determinate equations.

An indeterminate equation is the exact opposite of a determinate equation. An indeterminate one is a group, or one equation with an infinite amount of solutions to the equation. An example of this would be: a //x + // b //y=c. // The solutions to this particular equation is infinite because there are no values for a,b,x, and y. This allows anyone to give their own values to the variables. These equations can never be solved down to one final, definite answer. 

These were the first forms of algebraic expressions, and he also included integers. These infinite solution equations were also able to be simplified down to one answer. Since Diophantus was the first to deal with the indeterminate equations he was lucky enough to have them named after him. They are currently known as the //Diophantine Equations. //  Diophantus was also the first mathematician to actually treat a fraction as a number. These new thoughts and thinking processes gave a whole twist on math and what it was going to be.

Diophantus wrote other books from the Arithmetica collection. One in particular was called, "The Porisms". This book also disappeared with the other books in the Arithmetica. Some people have an impression that this could have been one of the lost books in the Arithmetica. The book, "The Porisms" was generally written about rational numbers and how they are to be used. There is another book that was authored by Diophantus, and that was, "Preliminaries to the Geometric Elements". This book was originally thought to be written by the Hero of Alexandria, another mathematician in Diophantus's time. Then, researchers show that the credit was falsely given to Hero and it really belonged to Diophantus. 

Diophantus accomplished many mathematical tasks in his lifetime. This was only made possible because he decided to explore terms and theories no one ever thought of. From his courageous doings, and great efforts toward algebra he earned himself the name, "Father of Algebra". He developed so many beginning steps to algebra and a lot of different techniques. In his time the algebra was very raw and untouched, then he molded it and was the person most responsible for the algebra we have and use today. The equations of determinate and indeterminate and methods to them were also made from Diophantus and his work. Diophantus was a very accomplished mathematician, and did it in a time period where everyone did not have the great knowledge as we do today.

=
Diophantus should be looked upon as the ultimate creator of algebra. The books and material we learn in class would have never been fully developed without Diophantus and his amazing work. He fully deserves the nickname given to him because of all of his achievements in his work.The mathematics today would not be the same without Diophantus's discoveries. His books were very informational not leaving a single detail, hopefully one day his other books will be found. In conclusion, Diophantus was a very great and accomplished mathematician and will be remembered as the "Father of Algebra". ======