A method used for one problem could not be used to solve even another very similar problem. Diophantus wrote many books but unfortunately only a few lasted. He did a lot of work in algebra, solving equations in terms of integers. Some of his equations resulted in more than one answer possibility. It was none other than Diophantus who started the use of a symbol to specify the unidentified quantities in his equations.
He also used fractions as numbers. This had an enormous influence on the development of number theory. View one larger picture. Biography Diophantus , often known as the 'father of algebra', is best known for his Arithmetica , a work on the solution of algebraic equations and on the theory of numbers. However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived. There are a few limits which can be put on the dates of Diophantus's life.
On the one hand Diophantus quotes the definition of a polygonal number from the work of Hypsicles so he must have written this later than BC. On the other hand Theon of Alexandria, the father of Hypatia , quotes one of Diophantus's definitions so this means that Diophantus wrote no later than AD.
However this leaves a span of years, so we have not narrowed down Diophantus's dates a great deal by these pieces of information. There is another piece of information which was accepted for many years as giving fairly accurate dates.
Heath [ 3 ] quotes from a letter by Michael Psellus who lived in the last half of the 11 th century. Psellus wrote Heath's translation in [ 3 ] :- Diophantus dealt with [ Egyptian arithmetic ] more accurately, but the very learned Anatolius collected the most essential parts of the doctrine as stated by Diophantus in a different way and in the most succinct form, dedicating his work to Diophantus. Psellus also describes in this letter the fact that Diophantus gave different names to powers of the unknown to those given by the Egyptians.
This letter was first published by Paul Tannery in [ 7 ] and in that work he comments that he believes that Psellus is quoting from a commentary on Diophantus which is now lost and was probably written by Hypatia.
However, the quote given above has been used to date Diophantus using the theory that the Anatolius referred to here is the bishop of Laodicea who was a writer and teacher of mathematics and lived in the third century. His symbol to depict the numeral was a dot underneath a number. Hypatia , born c. She is the earliest female mathematician of whose life and work reasonably detailed knowledge exists.
One of the earliest known mathematicians were Thales of Miletus c. Diophantus was the first Greek mathematician who recognized fractions as numbers ; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.
Syncopated algebra, in which some symbolism is used , but which does not contain all of the characteristics of symbolic algebra. For instance, there may be a restriction that subtraction may be used only once within one side of an equation, which is not the case with symbolic algebra. The Indian mathematician Brahmagupta CE appears to be the first to articulate the result that the product of two negative numbers is a positive number.
He of course also gave the much easier result that the product of a positive number and a negative number is a negative number. Mathematician Richard Dedekind asked these questions years ago at ETH Zurich, and became the first person to define real numbers.
John Stillwell. Bruce C. Timothy Gowers. Additionally, his use of mathematical notations, especially the syncopated notation played a significant role in cementing his position as a notable mathematician. He was the first one to incorporate those notations and symbolism in his work. Prior to that everyone made use of complete equations which was often time-consuming. Introduction of algebraic symbolism with abridged notation for recurring operations proved to be quite useful tool in solving problems.
However, his symbolism technique lacked the expression of more general operations in algebra like the general number n. It only goes to show that his work was more focused on particular problems while ignoring the general ones.
0コメント