We don't know that Diophantine was active around 250 AD. His book Arithmetic and his works on so-called polygon numbers (shape numbers) are the earliest systematic mathematical papers in the world.
Arithmetic *** 13, with 6 volumes. This book can be classified as algebra. Algebra is different from other disciplines in that it introduces unknowns and operates them.
According to the conditions of the problem, it is included in the equation, and then the unknown number is obtained by solving the equation, such as the calculation of the age of Diophantine in front of us.
There are also unknowns in arithmetic, and this unknown is the answer. All operations are only allowed with known numbers. Since we want to operate on the unknowns in algebra, we need to use some kind of symbol to represent them.
Diophantine naturally named his achievements in this field arithmetic, so he was called "the father of algebra" by later generations.
Since Pythagoras school, the interest center of Greek mathematics is geometry, and they think that only propositions that have been proved by geometry are reliable. For the sake of logical rigor, algebra also puts on the coat of geometry.
Therefore, all algebraic problems, even the solution of simple linear equations, are also included in the rigid geometric model. It was not until the emergence of Diophantine that algebra was liberated and the fetters of geometry were freed.
For example, the relation of (a+b) 2 = a2+2ab+b2 is an important geometric theorem in Euclid's Elements of Geometry, but it is only the inevitable result of simple algebraic operation in Diophantine arithmetic.
Diophantine thinks that algebraic method is more suitable for solving problems than geometric deductive statement. It shows a high degree of originality and originality in the process of solving problems, which is unique in Greek mathematics.
If Diophantine's works were not written in Greek, people wouldn't think it was the result of the Greeks, because it didn't have the style of classical Greek mathematics, and the thinking method and the whole subject structure were brand-new.
Without Diophantine's job, people might think that this Greek didn't know algebra at all, and some even speculated that he was a Hellenistic Babylonian.
In arithmetic, Diophantine not only describes algebraic principles, but also lists many problems belonging to various indefinite equations, and points out the methods to solve these equations, recognizing that real roots and rational numbers may be "roots" and positive roots.
In order to represent the number of knowledge, its power, reciprocal, equation and subtraction, he simplified letters, used parallel writing to represent the addition of two quantities, and used Arabic numerals to represent the coefficient of quantity after the symbol of quantity.
The sum and difference of two numbers are multiplied by the sign rule. He also introduced the concept of negative number and realized that the square of negative number equals to positive number.
Diophantine has made outstanding contributions in the fields of number theory and algebra, and opened up a broad research road. This is an unusual leap in human thought, but this leap has sprouted in early Greek mathematics.
Diophantine's works became the starting point for many mathematicians such as Fermat, Euler and Gauss to study number theory. Two parts of number theory are named after Diophantine, namely Diophantine equation theory and Diophantine approximation theory.
Although Diophantine Arithmetic still has many shortcomings, it is still an epoch-making work connecting the past with the future.
Let's talk about Papos, another scientist in ancient Rome. His most valuable work is "Mathematical Assemblies". It is in this situation that pappas began to collect and sort out the achievements of predecessors, and compiled them into an important book: Mathematical Compilation.
Mathematical assembly occupies a special position in history, not only because it has many inventions, but more importantly, it records a lot of predecessors' work and saves a lot of works that can't be seen elsewhere now. It and Proklose's Abstract are two original materials to study the history of Greek mathematical science, which have made great contributions.
Papos also wrote books on geography, music, hydrostatics and so on, and annotated Ptolemy and Euclid's works. He reads widely.
And his main contribution, which we introduced, is to collect, summarize, supplement and comment on academic works in almost the whole Greek period, so that they can be inherited and carried forward. These contributions are indelible.
Let's start with a scientist, Hipatia. We introduce her here only because Hipatia is the first female scientist and philosopher recorded in history.
Hipatia studied with her father in her early years. Her achievements in mathematics are mainly to help her father comment on Ptolemy's famous mathematical work "The Great Assembly" and to help her father edit Euclid's "Elements of Geometry".
According to an ancient dictionary, Hipatia also commented on the arithmetic of Diophantine and the conic curve of Apolloni, but these comments have been lost.
Hipatia also engaged in scientific and philosophical activities in Alexandria, teaching mathematics and neo-Platonism. Her philosophical interest tends to study academic and scientific issues, rather than pursuing mystery and exclusiveness.
Around 400 AD, Hipatia became the leader of the Neo-Platonism School in Alexandria. Because of her academic reputation, even some Christians worship her as a teacher.
However, early Christians regarded science as heresy to a great extent and persecuted the spread of Greek traditional culture as heresy. In 4 15, Hipatia was lynched by a group of Christian thugs.
Her tragic life experience has become the theme of some literary works, and the famous writer Kingsley wrote about her in the novel Hipatia. Hipatia in the novel is smart, beautiful, articulate and open-minded.