Chinese and western ancient mathematics are two completely different systems. China's ancient mathematics focused on structure and mechanical algorithm system, while the western mathematics represented by ancient Greece focused on logical deduction system.

Mathematics in ancient Greece began around 600 BC and lasted for nearly 1300 years until 64 1 year. The early period began in 600 BC, and finally Greece was merged into the Macedonian Empire in 336 BC, and its activities were mainly concentrated near the Dojo. Later, from the period of Alexander the Great, the activity place was in Alexandria. In 64 1 year, Alexandria was occupied by Arabs, and the era of ancient Greek civilization came to an end. China's mathematics originated in the distant Stone Age and experienced the pre-Qin embryonic period (from ancient times to 200 BC). Early Han and Tang dynasties (from 200 BC to 1000), the heyday of Yuan and Song Dynasties (from 1000 to14th century), and the importation of western learning in Ming and Qing Dynasties (14th century to19/kloc-0).

Comparison of the earliest records of mathematics

The earliest Greek mathematical record is a handwritten copy of Byzantine Greek (with some modifications), which was recorded between 500 years and 1500 years after the original Greek was written. The reason is that the original Greek manuscript has not been preserved. The earliest books are the Outline of Mathematics written by Pappus in the 3rd century and the Outline of Old Small and Medium-sized Enterprises written by Procras in the 5th century. The Outline of Odysseus is based on a book written by Odysseus (a fairly complete historical overview of Greek geometry before 335 BC, but it has been lost).

China's earliest mathematical monographs include Du Zhong Arithmetic and Xu Shang Arithmetic (contained in Han Shu's Literature and Art Annals), but both of them have been lost. Arithmetic book is the earliest one that can be seen in China at present, and it is also a relatively complete mathematical monograph. This book was found in a large number of bamboo slips unearthed in Zhangjiashan, Jiangling, Hubei Province in 1984+ 10. According to experts' research, The Arithmetic Book was copied in the early years of the Western Han Dynasty (about the 2nd century BC) and should have been written earlier, about the Warring States Period. In the form of problem sets, Arithmetic Book has more than 60 subheadings and more than 90 topics, including four operations such as integer and fraction, proportion, area and volume.

Conclusion: China is one of the four ancient civilizations, and all cultural creations originated in China. Generally speaking, China's achievements in mathematics are later than those in ancient Greece.

Second, the comparison of classic works The classic work of ancient Greek mathematics is Euclid's masterpiece "The Elements of Geometry". Euclid, a great mathematician in Alexander's early days, completed an epoch-making work-transforming the empirical science established by experiments and observations into deductive science, and systematically introducing logical proofs into mathematics. The axioms and theorems adopted by Euclid in the Elements of Geometry have been carefully considered and screened, and the contents are arranged according to a rigorous scientific system to make them systematic and theoretical.

More than all his previous works. The Elements of Geometry is divided into thirteen chapters and contains 467 propositions. The main contributions of Geometry Elements to world mathematics are:

1. Establish an axiom system and clearly put forward the axioms, postulates and definitions used. A series of theorems are revealed from the simple to the deep, so that hundreds of theorems can be proved with a small number of axioms.

2. Introducing logical proof into mathematics systematically, emphasizing that logical proof is a basic method to establish the authenticity of mathematical propositions. 3. Methods of geometric proof: analysis, synthesis and reduction to absurdity.

The Elements of Geometry brilliantly summarizes the mathematical achievements accumulated by human beings for a long time and constructs a scientific mathematical system. It provides subjects and materials for future generations to continue to study and study mathematics, and makes the development of geometry full of vitality. For two thousand years, it has been recognized as the basic textbook of elementary mathematics.

China's classic is Nine Chapters of Arithmetic. The difference is that Nine Chapters of Arithmetic was not written by one person at a time. It has undergone many reorganizations, deletions and revisions, and is the crystallization of the painstaking efforts of several generations. It was written in the early years of the Eastern Han Dynasty (1st century A.D.). "Nine Chapters Arithmetic" takes the form of problem sets. The book is divided into nine chapters, citing 246 mathematical problems, and after some problems, describing the solutions of such problems. The main contribution of arithmetic in Chapter 9 to world mathematics is: 1. Square root, which reflects the superb calculation level of China's mathematics and shows China's unique algorithm system.

2. Equation theory, the emergence of multiple simultaneous linear equations, equivalent to gauss elimination's summary, is unique in the world. 3. The introduction of negative numbers, especially the establishment of addition and subtraction rules of positive and negative numbers, is a great contribution.

In 263 AD, Liu Hui annotated Nine Chapters of Arithmetic. His main contribution is to sort out the achievements of ancient mathematics in China and comment on them with his own understanding, especially to refine some mathematical methods, which has reached the peak of mathematics in China.

Nine Chapters Arithmetic systematically summarizes the great achievements of China's mathematics from the Western Zhou Dynasty to the Qin and Han Dynasties. It is an important symbol of the formation of China's mathematical system, with rich and colorful contents, reflecting the highly developed ancient mathematics in China. The influence of Nine Chapters Arithmetic on the development of mathematics in China is as profound as that of Euclid's Elements of Geometry on western mathematics. Conclusion: Nine Chapters of Arithmetic and Elements of Geometry are the most important mathematical classics in the world. Nine Chapters Arithmetic is famous for its practicality and algorithm, while Geometry Elements is popular in the whole scientific community for its logical deduction. The two complement each other, rather than one covering up the other.

3. Comparison of mathematical characteristics between ancient Greece and China.

The characteristics of ancient Greek mathematics are as follows:

1. The Greeks abstracted mathematics and made it a science, which has immeasurable significance and value. The Greeks insisted on using deductive proof and realized that truth can only be obtained through deductive reasoning. To get the truth, we should start from the truth and not take unreliable facts as our own knowledge. Starting from the axiom 10 in the Elements of Geometry, we can get quite a few theorems and propositions.

2. The contribution of the Greeks to mathematics content is mainly to create plane geometry, solid geometry, triangle between plane and sphere, number theory, and popularize arithmetic and algebra, but it is only preliminary, with shortcomings and even mistakes;

3. The Greeks attach importance to the aesthetic significance of mathematics, and think that mathematics is a kind of beauty and a harmonious, simple, clear and orderly art;

The Greeks believe that the ultimate truth about the structure and design of the universe can be seen in mathematics, which makes mathematics closely linked with nature, and that the universe is designed according to the laws of mathematics and can be recognized by people.

The characteristics of China's mathematics are as follows:

1. The most basic feature of China's mathematics is its distinctive sociality. Throughout the contents of China's classical mathematics works, almost all of them are closely related to the actual needs of social life at that time. Starting from "Nine Chapters Arithmetic", China's arithmetic classics were basically written according to the style of problem set solution, and their contents reflected some practical needs of social politics, economy, military affairs and culture at that time, with strong applied mathematics color;

2. Mathematics education and research in China has been under the control of the government to meet the needs of the ruling class;

3. The mathematical works of mathematicians in China are deeply influenced by various social thoughts, philosophical schools and even religious theology in history, with various social traces.

4. China's mathematics is based on the mutual infiltration of geometric method and algebraic method, and it is the combination of shape and number. It is calculated by decimal system. At the same time, a set of "programming language" is used to reveal the calculation method, and the calculation program is concise and ingenious. 5. China's mathematical theory is manifested in the operation process, that is, "the unity of reasoning and calculation". Chinese mathematicians are good at abstracting profound mathematical concepts from complex mathematical phenomena and extracting general mathematical principles as the basis for studying many mathematical problems.

Conclusion: Ancient Greek mathematics belongs to the axiomatic deduction system, and it focuses on "reason"-first, axioms, postulates and definitions are given, and then a series of theorems are proved from simple to complex and orderly; China mathematics belongs to the mechanized algorithm system; Focus on "calculation"-classify problems and then use a fixed equation to solve the calculation of a class of problems.