The figure on the left is counting with Boethian apices; the one on the right uses an additive abacus reckoning system
It was in India that all the crucial numerical ingredients came together to form our numbering system. From here, the decimal place-value system disseminated throughout the Eurasian continent before going on to conquer the world.
Brahmi numerals, 100 AD
The Hindu-Arabic numbers have their origin in India, based on the first nine numerals of Brahmi script, an ancient Indian writing which was probably derived from the Phoenician alphabet. The only numbers in Brahmi writing to have distinct signs were 1-9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and 1000. All other numerical signs were derived from these.
By 458 AD, there was evidence of Hindu numbers being written from left to right in descending powers of 10. Indian reckoners could have used counting boards with columns pre-inscribed with the number signs to calculate more easily. Each column indicated a different place-value (ones, tens, hundreds, etc.), with the “ones” column in the right of the board and then moving up the powers of ten leftward. This method of writing numbers caught, leaving the numbers going “from left to right” instead of the opposite direction.
Towards the mid-7th century BC people far away from India already knew about the Hindu numeral system. An interesting case is that of Abraham ben Meir ibn Ezra (Rabbi Ben Ezra), a Spanish scholar from Toledo. He borrowed the Indian place-value system, but instead of using the traditional number signs, he represented each with the first nine letters of the Hebrew alphabet (keeping the Indian sign for zero):
The Chinese, having been familiar with the base, only needed to borrow zero (0) from the Indians. Other cultures across Asia (Khmer, Malay, Cham, and Javanese) also took the Indian numbers and adapted them to their own scripts.
Al-Khowarizimi, founder of algebra. The word “algorism” derives from the Latinized version of his name
Arabs became acquainted with Indian scholarship through trade with and incursion into India. By around 770 the Hindu numerals made their way to the Caliph’s court in Baghdad when an Indian messenger transmitted the works of mathematician and astronomer Brahmagupta. Mohammed ibn-Musa al-Khowarizimi, a Persian scholar and eminent mathematician of his day, found great value in these numbers. Al-Khowarizimi in 825 wrote a book titled On the Calculation with Hindu Numerals. He utilized the numbers in treatises on mathematics and algebra, such as his book Hisab aljabr w’almuqabala, “The Book of Restoration and Equalization,” which was translated into Latin as Algebra et Almucabala.
First row, modern Hindu-Arabic numerals; second, gobar numerals; third, the Eastern Arabic version of the Hindu numerals
The Eastern Arabs were responsible for gradually altering the Hindu numerals to make them look more like Arabic script. Meanwhile, Arabs in Northern Africa possibly learned of the Eastern Arabic numerals around the 9th century and adapted them into a form we would recognize today. Our numbers are direct descendents of these “gobar numerals”:
The Western Arabs referred to their numbers as gobar numerals, an Arabic word meaning ‘dust’ because many of the Arabs wrote their works on sandy dusty slants. It is these dust numerals that are formally and historically considered the direct ancestors of the numerals we use today. (Source)
My Linguistics partner-in-crime Andres Garcia was responsible for the majority of the research in this part.
History of Numbers, Gulf Coast Community College
Very cool collection of graphics relating to the development of Hindu-Arabic numerals, Wikimedia Commons
Arabic numerals, Wikipedia
Brahmi numerals, Wikipedia
David Eugene Smith, Louis Charles Karpinski. The Hindu-Arabic Numerals.
Georges Ifrah, From One to Zero: A Universal History of Numbers.
Karl Menninger, Number Words and Number Symbols.
Peter Rudman, How Mathematics Happened: The First 50,000 years.