History

Mesopotamia

By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC), the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.[8] The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60), looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them. India

The concept of zero as a number and not merely a symbol for separation is attributed to India, where, by the 9th century AD, practical calculations were carried out using zero, which was treated like any other number, even in case of division.[9][10] The Indian scholar Pingala (circa 5th-2nd century BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code.[11][12] He and his contemporary Indian scholars used the Sanskrit word śūnya to refer to zero or void. The use of a blank on a counting board to represent 0 dated back in India to 4th century BC.[13] In 498 AD, Indian mathematician and astronomer Aryabhata stated that "sthānāt sthānaṁ daśaguņaṁ syāt"[14] (literally, "place to place in ten times in value"),[citation needed] i.e. "from place to place each is ten times the preceding"[14] which is the origin of the modern decimal-based place value notation. The oldest known text to use a decimal place-value system, including a zero, is the Jain text from India entitled the Lokavibhâga, dated 458 AD, where shunya ("void" or "empty") was employed for this purpose.[15] The first known use of special glyphs for the decimal digits that includes the indubitable appearance of a symbol for the digit zero, a small circle, appears on a stone inscription found at the Chaturbhuja Temple[disambiguation needed] at Gwalior in India, dated 876 AD.[16][17] There are many documents on copper plates, with the same small o in them, dated back as far as the sixth century AD, but their authenticity may be doubted.[8] China

Since the 4th century BC, counting rods were used in China for decimal calculations including the use of blank spaces.[vague] The Nine Chapters on the Mathematical Art of 213 B.C.[18] instructed "[when subtracting] subtract same-signed numbers,[vague] add differently signed numbers, subtract a positive number from zero to make a negative number, and subtract a negative number from zero to make a positive number."[19] The word wúrù (無入) (rendered here as zero, its standard translation by mathematical historians) literally means "no entry" or "null enters".[vague] Along with negative numbers, Chinese mathematicians understood zero[when?], and some of them indicated it with wúrù (無入 "no entry"), kōng (空 "empty") and the frame-like symbol[vague] 口/囗,[vague] Gautama Siddha introduced the symbol 0[vague] in the 8th century.[20][21] Ch’in Chu-shao's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol for zero,[22] and Chinese authors were familiar with the idea of negative numbers well before the fifteenth century[when?] when they became well established in Europe.[22] The Arab world

The Hindu-Arabic numerals and the...