Diophantus of Alexandria

In the history of mathematics Diophantus of Alexandria is known as the father of master algebra for his works and the contributions he left to this science of numbers. By his skill in calculation, he managed to produce a large collection of problems of this type and solve them without making use of Euclidean geometry . All these problems were compiled in his work “Arithmetic” , which consisted of thirteen books, of which only six of them are known. For this great contribution, he is credited with introducing algebraic calculus in mathematics .

Personal information

  • When was he born: Between the years 200 and 214
  • Where he was born:  Alexandria, Egypt
  • When he died: Between the years 284 and 298
  • Where he died:  Alexandria, Egypt

Who was Diophantus of Alexandria?

Diophantus of Alexandria was a Greek mathematician born between 200 and 214 AD in Alexandria recognized as the father of master algebra . His best known work is “Arithmetic” , which consisted of thirteen books of which only six are preserved and a part of the seventh. These books contain a treatise on equations, the determinate and indeterminate systems of equations presented through a collection of problems with their solutions. His death is calculated between 284 and 298 AD at the age of 84.

  • Biography of Diophantus of Alexandria
  • Contributions of Diophantus of Alexandria
  • Works of Diophantus of Alexandria
  • Importance

Biography of Diophantus of Alexandria

Little is known of Diophantus’ life. It is known to belong to the ancient world, specifically to the city of Alexandria. His birth is calculated between the years 200 and 215 .

Some historians claim that he married at age 26 and had a son who lived to be 42 years old.

Diophantus of Alexandria’s death is believed to have been at the age of 84 between the years  284 and 298 .

Contributions of Diophantus of Alexandria

Diophantus’ contributions to the development of algebraic calculus were so significant in the field of mathematics that he is known as the father of modern algebra.

His best known works such as: “Arithmetic” , “Polygonal Numbers” , “Porismas” and “Moriastica” were of great importance for the development of mathematics among the Arabs in the 10th century. His works were translated into Latin and Greek between the fourteenth and seventeenth centuries.

In later centuries, his writings were translated into more than 33 languages ​​and are studied in many schools of basic education and in many university careers such as engineering, physics , mathematics, accounting, statistics, etc. 

Works of Diophantus of Alexandria

Among the most outstanding works of Diophantus we can mention the following:

  • Arithmetic is the most representative work and the one most translated into other languages ​​by Diophantus. This book is made up of thirteen volumes of which only six remain. In this work Diofanto brings together a collection of equation problems with variables that take rational values. This type of equations will later be called Diophantine equations and will have a very important value in the study of mathematics. What currently exists of the work known as Arithmetic is divided into books that are mentioned below:
    • Book I , is composed of 39 problems, 25 are equations of the first degree and 14 of the second degree.
    • Book II , contains 35 algebraic problems.
    • Book III , consists of 21 problems. In this book the best known problem is 19 because it is necessary to go to knowledge of geometry to solve it.
    • Book IV , this one contains 40 problems that are mostly about cubes.
    • Book V , consists of 30 problems, most of them are equations of the second and third degree.
    • Book VI , composed of 24 problems related to right triangles.
  • Mathematical notation is a significant contribution to the field of mathematics in which Diophantus uses symbols for the unknown variable and for subtraction.
  • Diophantine analysis is a type of study designed by this mathematician who seeks solutions to diophantine or polynomial equations with integer coefficients. In this work Diophantus of Alexandria presents 3 types of equations of the second degree.
  • Los Porismas is a work that contained a collection of mottos raised by Diophantus on arithmetic. This book is lost and is believed to have been one of the volumes of Arithmetic.
  • Polygonal numbers and geometric elements are writings of Diophantus on these subjects that were of great interest to Pythagoras and his followers.


The work of Diophantus of Alexandria represented a great contribution to the improvement of algebra in his time and today .

Many careers worldwide related to the study of mathematics such as physics, engineering, accounting, statistics, chemistry, among others, study the works of Diophantus as an indispensable subject in their courses .

In addition to this, the work carried out by Diophantus of Alexandria, introduced very significant discoveries such as the use of symbols – which are currently not known – to represent unknown variables and for subtraction.

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