Hindu Numerical System (Brahmi / Devanagari Numerical)

The Brahmi numerals at the basis of the system predate the Common Era. They replaced the earlier Kharosthi numerals used since the 4th century BC. Brahmi and Kharosthi numerals were used alongside one another in the Maurya Empire period, both appearing on the 3rd century BC edicts of Ashoka.

Buddhist inscriptions from around 300 BC use the symbols that became 1, 4 and 6. One century later, their use of the symbols that became 2, 4, 6, 7 and 9 was recorded. These Brahmi numerals are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, and there were rather separate numerals for each of the tens (10, 20, 30, etc.).

The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, and significantly younger than the Brahmi numerals.

The place-value system is used in the Bakhshali Manuscript. Although date of the composition of the manuscript is uncertain, the language used in the manuscript indicates that it could not have been composed any later than 400. The development of the positional decimal system takes its origins in Hindu mathematics during the Gupta period. Around 500, the astronomer Aryabhata uses the word kha ("emptiness") to mark "zero" in tabular arrangements of digits. The 7th century Brahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role of zero. The Sanskrit translation of the lost 5th century Prakrit Jaina cosmological text Lokavibhaga may preserve an early instance of positional use of zero.

These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti's Chronology of the scholars (early 13th century).

The numeral system came to be known to both the Persian Muslim mathematician Khwarizmi, who wrote a book, On the Calculation with Hindu Numerals in about 825, and the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Hindu Numerals (كتاب في استعمال العداد الهندي [kitāb fī isti'māl al-'adād al-hindī]) around 830. These earlier texts did not use the Hindu numerals. Kushyar ibn Labban who wrote Kitab fi usul hisab al-hind (Principles of Hindu Reckoning) is one of the oldest surviving manuscripts using the Hindu numerals. These books are principally responsible for the diffusion of the Hindu system of numeration throughout the Islamic world and ultimately also to Europe

The first dated and undisputed inscription showing the use of a symbol for zero appears on a stone inscription found at the Chaturbhuja Temple at Gwalior in India, dated 876.In 10th century Islamic mathematics, the system was extended to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953.

Various symbol sets are used to represent numbers in the Hindu numeral, all of which evolved from the Brahmi numerals.

The symbols used to represent the system have split into various typographical variants since the Middle Ages, arranged in three main groups:

• the widespread Western "Arabic numerals" used with the Latin, Cyrillic, and Greek alphabets in the table below labelled "European", descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb (There are two typographic styles for rendering western arabic numerals, known as lining figures and text figures).
• the "Arabic–Indic" or "Eastern Arabic numerals" used with Arabic script, developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals is used in Persian and Urdu. There is substantial variation in usage of glyphs for the Eastern Arabic-Indic digits, especially for the digits four, five, six, and seven.
• the Hindu numerals in use with scripts of the Brahmic family in India and Southeast Asia. Each of the roughly dozen major scripts of India has its own numeral glyphs (as one will note when perusing Unicode character charts). This table shows two examples:

• Kannada and Telugu  numerical system

0	1	2	3	4	5	6	7	8	9
0	౧	౨	౩	౪	౫	౬	౭	౮	౯

•  Assamese and Bengali numerical system

0	1	2	3	4	5	6	7	8	9
০	১	২	৩	৪	৫	৬	৭	৮	৯

• Malayalam Numerical system

0	1	2	3	4	5	6	7	8	9
൦	൧	൨	൩	൪	൫	൬	൭	൮	൯

As in many numbering systems, the numbers 1, 2, and 3 represent simple tally marks. 1 being a single line, 2 being two lines (now connected by a diagonal) and 3 being three lines (now connected by two vertical lines). After three, numbers tend to become more complex symbols (examples are the Chinese/Japanese numbers and Roman numerals). Theorists believe that this is because it becomes difficult to instantaneously count objects past three.