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Diophantus

Diophantus ( Alexandria of mathematician ) : Greek Neoplatonist philosopher, astronomer, and mathematician

Diophantus of Alexandria is a great Greek mathematician. He was born in between AD 201 and 215. He spent his life in Alexandria, Egypt. He has worked to solve the algebraic equations.

His work gave wide scope to number theory, Diophantus coined the term παρισότης (parisotes) which means almost equal. He was the first to declare that fractions are numbers. He used positive rational numbers for the coefficients and solutions. 

He probably died between AD 285 and 299. He died when he was almost 84 years old.

Diophantus
Diophantus

Diophantus Books

Few of the Diophantus Books:

  1. Arithmetica
  2. The Porisms (or Porismata)
  3. Books IV to VII of Diophantus’ Arithmetica: In the Arabic Translation Attributed to Qustā Ibn Lūqā Jacques Sesiano
  4. Diophantus of Alexandria: A Study in the History of Greek Algebra
  5. Diophantus and Diophantine Equations
  6. An Introduction to Diophantine Equations: A Problem-Based Approach

Many of his books has been lost. Few of his books are been still preserved in the libraries.

Contributions of Diophantus in Mathematics

Few of the notable contributions in Mathematics

  • He gave the structure of the number series.
  • He also gave names of the powers up to n6. 
  • n2 is called square number.
  • n3 is called cube number.
  • n4 is called square-square number.
  • n5 is called square-cube number.
  • n6 is called cube-cube number.
  • The term n1 however, is expressed as the side of a square number.

Interesting facts about Diophantus 

Interesting facts about him:

  1. He is considered the father of Algebra.
  2. He is considered the father of Polynomials.
  3. He is considered the father of Integer.

He was the one who has introduced symbols for square, square roots, cubes and cube roots.   

Mathematicians like Diophantus

Few Mathematicians like Thales of Miletus, Hero of Alexandria also Greek Mathematicians like him who have done notable work in Mathematics.

Quotes by Diophantus

If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term.

If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term. But, if there are on one or on both sides negative terms, the deficiencies must be added on both sides until all the terms on both sides are positive. Then we must take equals from equals until one term is left on each side.

Quotes By Other Mathematicians About Diophantus

Diophantus himself, it is true, gives only the most special solutions of all the questions which he treats, and he is generally content with indicating numbers which furnish one single solution. But it must not be supposed that his method was restricted to these very special solutions. In his time the use of letters to denote undetermined numbers was not yet established, and consequently the more general solutions which we are now enabled to give by means of such notation could not be expected from him. Nevertheless, the actual methods which he uses for solving any of his problems are as general as those which are in use to-day; nay, we are obliged to admit, that there is hardly any method yet invented in this kind of analysis of which there are not sufficiently distinct traces to be discovered in Him.

Leonard Euler

There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. He himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square.

Pierre de Fermat

FAQ About Diophantus 

What did Diophantus discover?

Diophantus discovered that fractions are numbers. His discovery ie Diophantine equations helped many mathematicians in doing great discoveries in mathematics.

What is Diophantus famous for?

Diophantus is known as the father of algebra, father of polynomials, father of Integer.

Who is the real father of algebra?

Diophantus is the father of algebra. He has contributed to the field of number theory and mathematical notation.

How old is Diophantus?

Diophantus died when he was 84 years old. He was born between AD 201 and 215 AD and died in between AD 285 and 299.

Why is Diophantus called the father of algebra?

Diophantus was the first mathematician who has done great contribution to mathematical notation and number theory, hence he is called the father of algebra.

Who is the father of polynomials?

Diophantus is called the father of polynomials

When was Diophantus born?

Diophantus was born in Alexandria in AD 201.

Who is the father of Integer?

Diophantus is called the father of Integers as he was the one who first considered fractions as numbers and for the coefficients and solutions he allowed the positive rational numbers to be used in it. 

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