The Sumerians in Mesopotamia were the first to develop a counting system to keep an account of their goods—cattle, horses, and donkeys, for example.
The Sumerian system was based on position; that is, the placing of a particular symbol in a particular place showed its value. The Sumerian system was handed down to the Akkadians around 2500 BC and then to the Babylonians in 2000 BC. It was the Babylonians who first thought of a mark to signify that a number was absent from a column; just as 0 in 1025 signifies that there are no hundreds in that number. Although zero’s Babylonian ancestor was a good start, it would still be centuries before the symbol of zero as we know it appeared.
The renowned mathematicians among the Ancient Greeks, who learned the basics of their math from the Egyptians, did not have a name for zero, nor did their system have a placeholder as did the Babylonian one. They may have pondered it, but there is no definite evidence to say the symbol even existed in their language. It was the Indians who began to understand zero both as a symbol and as an idea.
Brahmagupta, around 650 AD, was the first to formalize arithmetic operations using zero. He used dots underneath numbers to indicate a zero. These dots were alternately referred to as ‘sunya’, which means empty, or ‘kha’, which means place. Brahmagupta wrote standard rules for reaching zero through addition and subtraction as well as the results of operations with zero. The only error in his rules was division by zero, which would have to wait for Isaac Newton and G.W. Leibniz.
But it would still be a few centuries before zero reached Europe. First, the great Arabian voyagers would bring the texts of Brahmagupta and his colleagues back from India along with spices and other exotic items. Zero had reached Baghdad by 773 AD and would be developed in the Middle East by Arabian mathematicians who would base their numbers on the Indian system. In the ninth century, Mohammed ibn-Musa Al-Khowarizmi was the first to work on equations that equaled zero, or algebra as it has come to be known. He also developed quick methods for multiplying and dividing numbers known as algorithms (a corruption of his name). Al-Khowarizmi called zero ‘sifr’, from which our cipher comes. By 879 AD, zero was written almost as we now know it, an oval—but in this case smaller than the other numbers. And thanks to the conquest of Spain by the Moors, zero finally reached Europe; by the middle of the twelfth century, translations of Al-Khowarizmi’s work had arrived in England.
The Italian mathematician, Fibonacci, built on Al-Khowarizmi’s work with algorithms in his book Liber Abaci, or “Abacus book,” in 1202. Until that time, the abacus had been the most common tool to perform arithmetic operations. Fibonacci’s developments were quickly noticed by Italian merchants and German bankers, especially the use of zero. Accountants knew their books were balanced when the positive and negative amounts of their assets and liabilities equaled zero. But governments were still suspicious of Arabic numerals because of the ease with which it was possible to change one symbol into another. Though forbidden, merchants continued to use zero in secret messages, thus the origin of the word ‘cipher’, meaning code, from the Arabic ‘sifr’.
27 Từ vựng Nâng cao
- To hand down (phr. v) – /hænd daʊn/ – to give or leave something to people who will live after you – Truyền lại, để lại (cho thế hệ sau).
- To signify (v) – /ˈsɪɡ.nɪ.faɪ/ – to be a sign of something; to mean – Biểu thị, có nghĩa là.
- Absent (adj) – /ˈæb.sənt/ – not in a place because of illness or other reasons; not existing – Vắng mặt, không tồn tại.
- Ancestor (n) – /ˈæn.ses.tər/ – a person related to you who lived a long time ago; an early type of animal/machine that later developed into something else – Tổ tiên; vật khởi nguyên.
- Renowned (adj) – /rɪˈnaʊnd/ – famous for something – Nổi tiếng, lừng danh.
- Placeholder (n) – /ˈpleɪsˌhəʊl.dər/ – a symbol in a mathematical expression that may be replaced by the name of any element of a set – Ký hiệu giữ chỗ (trong toán học).
- To ponder (v) – /ˈpɒn.dər/ – to think carefully about something, especially for a noticeable length of time – Suy ngẫm, trầm tư.
- Definite (adj) – /ˈdef.ɪ.nət/ – fixed, certain, or clear – Rõ ràng, chắc chắn, xác định.
- To formalize (v) – /ˈfɔː.mə.laɪz/ – to make something official or standardized – Chính thức hóa, chuẩn hóa.
- Arithmetic operations (n. phr.) – /əˈrɪθ.mə.tɪk ˌɒp.ərˈeɪ.ʃənz/ – the basic mathematical processes of addition, subtraction, multiplication, and division – Các phép toán số học.
- To indicate (v) – /ˈɪn.dɪ.keɪt/ – to show, point, or make clear in another way – Chỉ ra, cho thấy.
- Alternately (adv) – /ɒlˈtɜː.nət.li/ – in a way that involves two things happening or existing one after the other repeatedly – Luân phiên, xen kẽ.
- Voyagers (n) – /ˈvɔɪ.ɪ.dʒərz/ – people who go on long journeys, especially by sea or in space – Nhà du hành, người đi biển (hành trình dài).
- Exotic (adj) – /ɪɡˈzɒt.ɪk/ – unusual and exciting because of coming from a distant, foreign country – Ngoại lai, kỳ lạ (đến từ nơi xa).
- Equations (n) – /ɪˈkweɪ.ʒənz/ – a mathematical statement that says two amounts or values are equal – Phương trình.
- Algebra (n) – /ˈæl.dʒə.brə/ – a part of mathematics in which letters and other general symbols are used to represent numbers and quantities – Đại số học.
- A corruption of (n. phr.) – /ə kəˈrʌp.ʃən ɒv/ – a word that has been changed from its original form in some way – Một dạng biến thể/trại đi của (từ ngữ).
- Conquest (n) – /ˈkɒŋ.kwest/ – the act of taking control of a country, city, etc. by force – Cuộc chinh phạt, sự xâm chiếm.
- Translations (n) – /trænsˈleɪ.ʃənz/ – something that is translated, or the process of translating from one language to another – Các bản dịch, sự phiên dịch.
- To build on (phr. v) – /bɪld ɒn/ – to use a success or achievement as a base from which to achieve more success – Xây dựng/phát triển dựa trên (nền tảng đã có).
- Developments (n) – /dɪˈvel.əp.mənts/ – new events or achievements in a continuing situation – Những bước phát triển, những thành tựu mới.
- Assets and Liabilities (n. phr.) – /ˈæs.ets ænd ˌlaɪ.əˈbɪl.ə.tiz/ – a company’s assets are the things it owns, and its liabilities are the amounts of money it owes – Tài sản và nợ phải trả.
- Suspicious (adj) – /səˈspɪʃ.əs/ – feeling doubt or a lack of trust – Nghi ngờ, khả nghi.
- Numerals (n) – /ˈnjuː.mə.rəlz/ – a symbol or a group of symbols that represents a number – Chữ số, ký hiệu số.
- Forbidden (adj) – /fəˈbɪd.ən/ – not allowed, especially by law – Bị cấm.
- Cipher (n) – /ˈsaɪ.fər/ – a secret way of writing; a code – Mật mã.
- Origin (n) – /ˈɒr.ɪ.dʒɪn/ – the beginning or cause of something – Nguồn gốc, khởi nguyên.
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