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Ancient Greece occupies an inseparable position in the history of mathematics. The ancient Greeks attached great importance to mathematics and logic. The development history of Greek mathematics can be divided into three periods. The first period, from Ionian school to Plato school, lasted from the middle of the 7th century BC to the 3rd century BC. The second period is the pre-Alexandria period, from Euclid to BC 146, Greece was trapped in Rome. The third period was the later period of Alexandria, which was ruled by Romans and ended when 64 1 Alexandria was occupied by Arabs.

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origin

The origin of ancient Greek mathematics is not clearly documented. The first advanced civilizations developed in Greece and European countries were Minos and later Mycenae, both of which gradually flourished in 2000 BC. Although these two civilizations have writing ability and advanced level, they can be built.

The engineering technology of building a four-story palace with drainage system and honeycomb cemetery, but they did not leave any literature related to mathematics. Although there is no direct evidence to prove it, researchers generally believe that the neighboring Babylonian and Egyptian civilizations influenced the younger ancient Greek tradition.

From 800 BC to 600 BC, ancient Greek mathematics generally lagged behind ancient Greek literature, and there were very few materials related to ancient Greek mathematics during this period. Almost all the materials handed down were recorded by scholars in the late 4th century BC. The development of mathematics in ancient Greece can be divided into two stages: Athens and Alexandria.

scholar

Eratosthenes

Democritus

Euclid

Pythagoras

Thales

Archimedes

history

Athens period

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.

Alexander period

earlier stage

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.

later stage

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 produced the mathematical spirit, that is, the 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.