Diophantus

Q. Why were you known as the “father of algebra”?

A. I was one of the first mathematicians to work on developing algebra. My focus was on the solution of algebraic equations and on the theory of numbers. The title, “father of algebra”, was not one that I came up with myself, but given to me by historians and mathematicians. My work on Arithmetica has also been seen as a great contribution to the development of algebra.

Q. Can you tell me more about your best known work, Arithmetica?

A. Arithmetica is a collection of 130 problems that gives numerical solutions of determinate equations, which have a unique solution, and indeterminate equations.

Q. What are determinate and indeterminate equations?

A. Determinate equations have defined limits, that are not uncertain, but fixed. Indeterminate equations are the opposite, and do not have defined limits, and are uncertain.

Q. Do you agree with the statement that Aritmetica is the most outstanding work in Greek mathematics?

A. Yes, I would. This is because my work considers the solution of many problems which have to do with linear and quadratic equations. I am also responsible for the Diophantine analysis and Diophantine equation.

Q. Could you elaborate on the Diohpnatine analysis and Diophantine equation?

A. The Diophantine analysis is the method for solving problems that give numerical solutions of both determinate and indeterminate equations. The Diophantine equation is solved for integer solutions only. It is very difficult to tell if my equations are solvable. There are many equations, but a good example of one that is very challenging to solve is as follows: x2 – 94y2 = 1, the smallest solution for this equation is x = 2,143,295 and y = 221,064

Q. How would you describe the “Silver Age” in which you lived?

A. The Silver Age, also known as the Later Alexandrian Age, was a time when mathematicians were discovering many ideas that lead to our concept of mathematics today. This time period was called the Silver Age because it came after the Golden Age, which took place around the time of Eulicid.

Q. What were the most important events of your personal life, and when did they occur?

A. The major events of my personal life were my birth, my wedding, the death of my son, and my death. I like to keep historians guessing on the date of my birth, but I will tell you that it was around 200 BCE. I have no problem sharing age at the other major events of my personal life. As a result of a riddle published about me, historians and mathematicians have already discovered these ages. They concluded that I married at the age of 26, my son died when he was 42 years old, and when I was 80 years old. Four years later I died from unknown causes, at the age of 84. Here is that poem:

'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 ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage
After attaining half the measure of his father's life chill fate took him.
After consoling his fate by the science of numbers for four years, he ended his life.'