Foundation of Arithmetics

3 min read

China is the centre of the world’s maths development, where numerous theorems, algorithms and solutions have been put forth or solved at the earliest time. In the early ancient time 3,000 years ago, China invented the decimal system, the most advanced way of numbering worldwide then. In the early Western Zhou dynasty, the Chinese people had already learned such mathematic knowledge as the Pythagorean theorem and concepts of circle and square figures. In the Spring and Autumn period, at the latest, people already had a good command of the world’s best calculating instruments of the time such as the rod-arithmetic and abacus, and representation of negative numbers, decimal fractions, factional numbers, quadratic or higher degree equations and systems of linear equations, as well as proficiency in the1-9 multiplication tables and arithmetic calculations for Writings on Reckoning,a integral numbers. In the mathematic litcpure. Warring States period, China Hubei province contributed to the main parts of Writngs on Reckoning, Arithmetical Classic of the Gnomon and the Circular Paths of Heaven, and Nine Chapters on Mathematical Art; and for the earliest time Mohist Canon put forth to the world the mathematic concepts and definitions for circle, line, plane, end, and the power of n. It is indicated that the early ancient time already witnessed constitution of the basis of Chinese traditional maths(arithmetic).

During the period from Eastern Han to Sui and Tang dynasties in the middle ancient time, Nine Chapters on Mathematical Art by Liu Hui and Commentary on Arithmetical Classic of the Gnomon and the Circular Paths of Heaven by Zhao Shuang further laid theoretical basis for Chinese traditional maths, Zu Chongzhi’s seven-digit numerical value of the ratio of the circumference to the diameter of a circle, the four fundamental operations of arithmetic for fractions, calculation of extraction of square and cubic roots, pioneering of new studies of a problem of 100 chickens, solution to congruence, etc., caused Chinese arithmetic to enter a period of rapid development. Song and Yuan dynasties were the prime periods for development of Chinese traditional maths when the concept of unknown numbers was introduced, followed by the emergence of many other mathematic concepts such as the solution to equations of higher degrees, the law of the expansion of a binomial raised to any high power, summation of the highest common arithmetical progression, and the solution to the multiple high-order equation. All of these took a significant lead in the world. 200 years after the early Ming dynasty, Chinese arithmetic stagnated for a long time and did not have any further gradual development till the arrival of learning from the West.

Chinese traditional maths gives priority to arithmetic (i.e. algebra) with markedfeatures of constitution, calculation, plasticity, programming, and mechanization, among the front ranks of the world for thousands of years.

However, the traditional maths still lacked some concepts that led to some missing spots in the discipline. For instance, without the concept of angles, there was no trigonometry, and w ithout systematic theories and rigid and accurate requirements, it would be impossible to develop the practical arithmetic into modern and contemporary maths.

In contrast, the ancient Greek maths, which was represented by Euclid’s Elements, was apt at theoretical discussion, based on which they established a set of deduction systems comprising definition, postulation, axiom and theorem, which grew to be the origin of modern maths. Nonetheless, the ancient Greek maths lacked the place value system, the concept of negative numbers, let alone any good calculation methods and solution to numbers raised to certain great powers. For a considerably long run of history, such blank spots obstructed thedevelopment of Western maths. On the other hand, they were China’s strength. As a matter of fact, China’s ancient arithmetic was introduced to Europe via the Arabian countries. Consequently, it consolidated greatly the Europeans’ ability in calculation and helped open up a vast expectation in local maths in terms of the combination of algebra with geometry to bring about the emergence of analytic geometry, invention of logarithm, and in particular the creation of calculus due to the possibility of extending limited calculation to infinity. So the Western maths not only originated from both the ancient Greek maths and ancient Chinese maths, but were actually the outcome of the integration of the two varieties of maths-the maths of theoretical speculation represented by the Euclidian geometrical elements of ancient Greece and the practical arithmetic system of ancient China giving priority to algebra.