This period began with the Ionian school headed by Thales, whose contribution was to create the proof of proposition and take the first step to establish the geometric deduction system. Later, a school headed by Pythagoras, a mysterious political, religious and philosophical group, took "everything counts" as its creed, abstracted mathematical theories from concrete things and gave mathematics a special independent position.
After 480 BC, Athens became the political and cultural center of Greece, and various academic ideas contended in Athens, which can be seen everywhere in speeches and debates. In this atmosphere, mathematics began to jump out of the closed walls of individual schools and come to a wider world.
Zhi Nuo of Elijah School put forward four famous paradoxes (dichotomy, tortoise chasing, still flying arrow, playground problem), which forced philosophers and mathematicians to think deeply about endless problems. Homo sapiens put forward three difficult problems in geometric drawing: turning a circle into a square, folding a cube in half and bisecting any angle. The interest of the Greeks lies in solving these problems theoretically, which is another step for geometry from practical application to deductive system. It is precisely because the three difficult problems cannot be solved with a ruler that researchers often break into unknown areas and make new discoveries: conic curve is the most typical example; The problem of "turning a circle into a square" also led to the discussion of pi and exhaustive method.
The philosopher Plato founded the famous Plato Academy in Athens, and trained a large number of mathematicians, which became the link between the early Pythagorean school and the long-term active Alexandria school. Eudoxus is one of the most famous figures in this college. He founded the proportional theory which is suitable for incommensurable measure and incommensurable measure. Plato's student Aristotle is the founder of formalism, and his logical thought opens the way for arranging geometry in a strict logical system in the future.
Second, the Alexandria period (300 BC-6465438 AD).
This stage is divided into two periods, which is bounded by the annexation of Greece by the Roman Empire in 30 BC.
The golden age of Greek mathematics appeared in the early days of Alexandria, represented by three famous geometricians: Euclid, Archimedes and Apolloni.
Euclid summed up classical Greek mathematics, arranged geometry with axiomatic method, and wrote 13 volume "The Original". The significance of this epoch-making historical masterpiece lies in that it sets the earliest example of establishing deductive mathematics system by axiomatic method.
Archimedes was the greatest mathematician, mechanic and mechanic in ancient times. He organically combined the empirical research method of experiment with the deductive reasoning method of geometry, making mechanics scientific, with both qualitative analysis and quantitative calculation. Archimedes is also involved in a wide range of pure mathematics. One of his great contributions is to establish accurate quadrature methods for the area of various plane figures and the volume of rotating bodies, which includes the idea of calculus.
Eratosthenes, the librarian of Alexandria Library, was also a famous scholar in this period. "Conic Curve" written by Apolloni Uss systematically sorted out the knowledge of conic curve obtained by predecessors, made new contributions, and had a great influence on the development of mathematics in17th century.
Alexander's later period was under Roman rule. Fortunately, the Greek cultural tradition has not been destroyed, and scholars can continue to study it. However, it has lost the majestic momentum of the previous period. Outstanding mathematicians in this period include Helen, Plume, Diophantine and Pappus. Diophantine algebra is unique in Greek mathematics; Papos's work is a summary and supplement to previous research results. After that, Greek mathematics was at a standstill.
In 4 15 AD, Hipatia, a female mathematician and leader of Neo-Platonism, was brutally killed by Christians. Her death marked the decline of Greek civilization, and the days when Alexandria University was full of creativity are gone forever.
In 529 AD, Justinian, the emperor of the Eastern Roman Empire, ordered the closure of schools in Athens, prohibiting the research and dissemination of mathematics, and the development of mathematics was once again dealt a fatal blow.
In 64 1 AD, the Arabs captured Alexandria, and the library was burned down again (the first time was in 46 BC), thus ending the long and splendid history of Greek mathematics.
In a word, the achievements of Greek mathematics are brilliant. It has created great spiritual wealth for mankind, which is second to none in the world in terms of quantity and quality. More important than the concrete achievements made by Greek mathematicians, Greek mathematics has produced mathematical spirit. That is, deductive reasoning method of mathematical proof. The abstraction of mathematics and the belief that nature is designed according to mathematical methods have played a vital role in the development of mathematics and even science. And a series of thoughts such as rationality, certainty, eternity and irresistible regularity produced by this spirit occupy an important position in the history of human cultural development.