Diophantus: The Father of Algebra

Diophantus was an Alexandrian Greek mathematician who was believed to have been born between AD 201 and 215 in Alexandria, Egypt, and died at around the age of 84. There is not much information about his life, and whatever is known today is derived from a  fifth century Greek anthology of number games that was created by Metrodorus. According to one of the puzzles, Diophantus had married at the age of 26. He had a son who died at the age of 42, four years before the death of Diophantus, who died at the age of 84. Historians have estimated his life span and other things based on these statements. 

Arithmetica by Diophantus

Diophantus wrote several books on mathematics, and the series of his books was titled Arithmetica. It is considered that Greek mathematics is inadequate without the contributions made by Diophantus through his work in this book. Arithmetica is a collection of 130 problems that give the numerical solutions to determinate and indeterminate equations. 

Originally, there were a total of 13 books in this series. However, out of those, only six have survived through the years. Some people believe that there were four Arabic books discovered in 1968 that were written by Diophantus. Some of the Diophantine problems from his book Arithmetica have been found in some Arabic sources. 

Diophantus⏤The Father of Algebra

In the late-16th century, a great deal of inclinations was found among the mathematicians, and it was Diophantus’s work that inspired them. Because of this and his great contributions to number theory, he is referred to as the “father of algebra.”

Diophantus made significant advances in mathematical notions and is regarded as one of the first mathematicians to introduce symbolism into algebra using an abridged notion for the frequency of occurring operations. In addition to that, an abbreviation for the unknown and the powers of the same. 

Over the years, his work was observed, and it was found that Diophantus had refrained from applying the general method of solving the problems in his equations. Many mathematicians have even commented that his work is generally devoid of the general method of solving each problem. Rather, each one of them was solved with a unique method. 

Contributions of Diophantus

• Diophantus was the first person who used algebraic notions and symbolism in his work and made a mark. Before him, almost everyone made use of a complete form of equations, which was very time-consuming. In today’s world, when we solve a mathematical question or an equation, we generally put the letter x as the unknown quantity in that algebraic equation. In the oldest copies of the Arithmetica, the unknown quantities were represented by a similar character in Greek that looked like the letter sigma.

• When we talk about his contribution to number theory, it is important to note that he was one of the first mathematicians who recognized fractions as numbers in their right and allowed positive rational numbers for the coefficients and solutions in his equations. In modern use, the Diophantine equations are usually algebraic equations with integer coefficients for which integer solutions are sought. Diophantus would apply himself to some of the most complex algebraic problems, which are popularly known as Diophantine analysis. These would deal with finding the integer solutions to the types of problems that would lead to equations in multiples unknown. 

• The year that is usually associated with syncopated algebra is 275, as Diophantus was probably the first mathematician who took steps towards an algebraic notation. The shift from rhetorical to syncopated and then, ultimately, to symbolic is referred to as a transition. Diophantus has tried to indeterminate problems of the second degree. He did not restrict the solution to integers and rather tried rational solutions. An example of syncopated notation in algebra would be to write as “unknown cubed 1, unknown squared 13, unknown 5”. 

• Diophantus’s famous work Arthmetica has inspired some of the most famous mathematicians, like Leonhard Euler and Pierre de Fermat, to make new and significant discoveries in this subject. A heavy influence of Diophantus can be seen in Fermat’s Last Theorem, which has become quite famous in recent years. Through his work, Diophantus has established a great foundation for algebra and its evolution over the years. This even left a great impression on the minds of the great mathematicians. This is without a doubt one of the biggest contributions that one can make from his or her work. 

Diophantus played a major role in the evolution and propagation of algebra. Today, it is a well-established concept to study mathematics with multiple branches and applications in different sectors. How we learn algebra today is greatly influenced by his work. We make use of the unknowns in solving several algebraic problems that he has taught the world. Read some more articles on the BYJU’S FutureSchool blog about other famous mathematicians and academicians. Then, leave a comment to let us know how you feel.