0 is an extremely important number symbol, and the concept of 0 thinking has existed in other regions for a long time.

According to historical records, the Mayans had a mathematical system called "the most brilliant product of human mind". Maya (or their Omek ancestors) independently developed the concept of zero, and Mayan civilization first invented the special font 0. In Mayan numerals, 0 is represented by a pictographic symbol like a shell. And uses a binary number system; This number is represented by a dot (-) as 1 and a bar (-) as 5. Inscriptions show that they sometimes use hundreds of millions. ?

The zero mentioned here is not the Arabic numeral 0 we use, but it should be the earliest digital symbol containing the concept of 0.

In ancient Egypt, as early as 2000 BC, some people used special symbols to record zeros in bookkeeping.

There are 0 seeds in ancient Babylonian literature. But unlike now, the symbol of 0 is represented by spaces. For example, to represent 10 1, Babylon wrote 1 1.

The concept of 0 has a long history in China and has been recorded in many documents. In ancient China, counting chips was used for calculation. In counting chips and abacus, spaces were used to indicate 0. In the 4th century BC, mathematicians in China had understood the concepts of negative numbers and zero. (However, in China's ancient knotting notation, "zero" appeared in the negation of "yes", indicating "no". )

The Nine Chapters of Arithmetic in the 1 th century AD said: "The pros and cons are: the points with the same name and the benefits of different names, the positive ones are not responsible, and the negative ones are not correct. Its synonyms are divided, the same name is beneficial, and there is no positive or negative. " Subtraction: When you meet numbers with the same sign, subtract their values; when you meet numbers with different signs, add their values. The difference between zero MINUS positive numbers is negative, and the difference between zero MINUS positive numbers is positive. " ) The concept of "Buru" in the above text is usually considered as zero by mathematical historians. (For the full text, see Wikipedia's "Nine Arithmetic Chapters". Even so, there was no symbol to represent zero at that time. There is no "zero" symbol at the beginning of digital calculation, and it will be empty when it meets "zero". For example, "6708" can be expressed as "┴〧? ╥ "(Because seven has no corresponding symbol, it is replaced by quotient code; After all, the quotient code is calculated. There is no "zero" in the number, so it is easy to make mistakes. So later, someone put the copper coins in the empty space to avoid making mistakes, which may be related to the appearance of the symbol "Ф". It was not until the early 7th century in India that the great Indian mathematician Graf Magpuda first explained the nature of 0, that is, any number multiplied by 0 is 0, and any number can be obtained by adding or subtracting 0. Unfortunately, he didn't mention the example of calculating with the symbol of life position.

However, most people believe that the invention of the mathematical symbol "0" should be attributed to Indians in the 6th century. Indian civilization can be traced back to 2000 BC, but they didn't have mathematics before 800 BC. After about the 3rd century BC, numerical symbols appeared in India, typically Brahman numerals. The outstanding feature of Brahman number is that it gives each number of 1 to 9 a separate label, and there is no zero-sum and carry notation. They first used a black dot () to represent zero, and then gradually became an "O".

However, it is said that around 2500 BC, the symbol "0" was used in the Vedas, the oldest document of Brahmanism in India. At that time, zero represented an empty position in Indian Brahmanism (but they didn't have mathematics before 800 BC, so this statement is doubtful. According to this statement, in China's ancient knot notation, zero appeared in the negation of "yes", indicating "no". You can also forget it). -I have doubts about the last paragraph, if it is true; So why did Indians still use black spots as a symbol of "zero" in the 6th century? As for when the dot became round, it is impossible to verify the exact time. (This book started in Zhan Jing, published in 7 18 AD, with a volume of 104 and a page of 1089, and translated nine Indian calendars; At that time, Indians' zeros were still black spots. )

Around the third century BC, the ancient Indians completed the invention of the digital symbol 1 to 9, but there was no "0" at this time. The symbol of "0" appeared in the Gupta dynasty of India after the invention of digital symbols from/kloc-0 to 9 1 000 years. It was not round when it first appeared; It is represented by a black dot. As for when to turn from a point to a circle, the specific time is impossible to verify. Until 876 AD, people were in Gualior, India. Found a stone tablet engraved with the number "27o". This is also the earliest record of the symbol "0" found by people, but the symbol of this zero is a circle O smaller than zero; Nor is it like the modern symbol "0".

But if you say symbols, there are already spaces in China's calculation; Later, copper coins were used to represent the symbol of zero in calculation. Since then, copper coins have evolved into zero as a symbol of zero; Is a very normal thing. In 690; Wu Zetian promulgated "Handwriting of Zetian", in which one word is "é" (earlier than the Indian small circle symbol O 186); Although it didn't mean zero at that time. When China recorded "Ф" in mathematics in ancient times, it was expressed by "Ф", on the one hand, to distinguish numbers; More importantly, it was written by China's ancient substitute brush. As for Lian Bi's habit of writing with a brush, it is much more convenient to write "Ф" than "Ф", so zero gradually becomes a counterclockwise painting "Ф"; This is China's zero. The Ming calendar of Jin Dynasty 1 180 has numbers such as "403" and "309".

According to the research of Dr. Lee Yue Se, a famous British expert in the history of science, "0" originated from China and Indian culture, and it was the value system first used by China that promoted the emergence of zero. Indians created "0" under the influence of China's calculation and value system. As early as the Shang Dynasty more than 3,000 years ago, China adopted this value system. There are numbers such as "600 and 50 and 9 (659)" in Oracle Bone Inscriptions, and decimals are clearly used.

And how did a black spot in India become a symbol of zero? I wonder if there is any evidence of evolution. Moreover, there was no decimal system in ancient India, and China had the earliest decimal system in the world. Although ancient Egypt was decimal, there was no position system. Although Babylon has a warehouse system, Babylon is a 60-base system; Only China has a decimal numerical system that satisfies both decimal and positional systems. However, the earliest time when the symbol of "0" in China literature indicates "0" is also impossible to verify. In the Song Dynasty, Cai Shen's New Works of Jurisprudence (1135-1198) indicated the vacancy with a square "ai". The Ming calendar of Jin Dynasty 1 180 has numbers such as "403" and "309". In A.D. 1247, Qin used the symbol "zero" to represent the concept of zero in nine chapters of his works. There is a "0" image in question 14 of Ye Li's Circle Survey of the Sea Mirror (1248).

In short, the origin of zero is still inconclusive, but in any case, zero has a very strong vitality since its appearance, and it is now widely used in all fields of society.