The Paper Trail: How Indian Numerals Came to Be Called Arabic

The digits in front of you are Indian. Not "probably Indian," not "Indian according to one tradition." The men who carried them west said so in writing, by name, at every stage, and the documents survive.

A Syriac bishop praised Indian computation done by means of nine signs in 662. A mathematician in Baghdad wrote a book around 825 whose title announced it was calculation with Indian numerals, and the Latin form of his name, Algoritmi, gave English the word algorithm. A Pisan merchant's son published a manual in 1202 that called the whole method modus Indorum, the way of the Indians. Arabic mathematicians named the subject hisab al-hindi, Indian reckoning. Arabic speakers still call the digits arqam hindiyya, Indian figures.

Calling them Arabic numerals in English is therefore not a theft. It is a shipping label: Europe named the cargo after the port it came through. The question worth asking is when a clear record stopped being taught, and the answer is later than most people assume, and in Europe's own classrooms.

A bishop on the Euphrates, 662

Severus Sebokht ran the monastery school at Qenneshre on the upper Euphrates and was among the most capable astronomers writing in Syriac. In 662 he set down a passage historians of mathematics have quoted for over a century, because it is the earliest datable notice of the Indian numerals from anywhere outside India.

His purpose was polemical, which is what makes the passage useful. Greek-speaking contemporaries had been telling him that science was Greek property. His reply was that learning belongs to everyone, that the Greeks took astronomy from the Chaldeans, and that the Indians had discoveries more ingenious than anything the Greeks managed, along with methods of calculation beyond describing. Then the sentence everyone cites: this computation is done by means of nine signs.

The text survives in a single Syriac manuscript in Paris, BnF Syriaque 346, copied in 1309, where it is labelled as part of Sebokht's correspondence with a priest named Basil in Cyprus. That ascription rests on the manuscript's headings, not on the text. François Nau published it with a French translation in the Journal Asiatique in 1910, and every English version traces back to him, which is why their wordings differ. The substance does not: nine signs, Indian, superior to what his Greek-praising correspondents offered.

Two details matter. Sebokht is not an Indian source asserting Indian priority; he is a Syriac Christian with no stake in the outcome, writing to irritate Greeks. And he counts nine signs, not ten. The zero mark existed as a placeholder but was not yet reckoned among the figures, and Fibonacci was still listing nine figures plus a separate sign for zero five hundred and forty years later.

The book that survives only in translation

Muhammad ibn Musa al-Khwarizmi worked in Baghdad in the first half of the ninth century, and two of his books changed the vocabulary of European mathematics. One, on restoration and balancing, al-jabr, gave English the word algebra. The other, written around 825, was a manual of practical arithmetic using the Indian figures: kitab al-hisab al-hindi, the book of Indian calculation.

The Arabic original is lost. Every copy of it. What reached Europe were four Latin reworkings, none a literal translation, and the one usually thought closest to al-Khwarizmi survives in a single fourteenth-century manuscript in Cambridge University Library, Ms. Ii.6.5. It opens with the words Dixit Algorizmi, "al-Khwarizmi said." That version is often associated with Adelard of Bath, who certainly translated al-Khwarizmi's astronomical tables in 1126, but the attribution of the arithmetic to him is not secure. When Baldassarre Boncompagni printed the Cambridge text in 1857 he had to supply a title, since none survived, and the one he supplied was Algoritmi de numero Indorum: al-Khwarizmi on the Indian numbers.

The book most often produced as evidence that Islamic mathematicians absorbed the credit is a book whose title says "Indian." Al-Kindi wrote on the same subject around 830 with the same attribution. Al-Uqlidisi, in Damascus in 952 or 953, wrote a book of chapters on Indian arithmetic, the oldest complete Arabic treatment to survive. Kushyar ibn Labban wrote on the principles of Indian reckoning. This was not a courtesy to a foreign source. It was the name of the subject.

How a man's name became a common noun

Al-Khwarizmi's name is a nisba, an adjective of origin: the man from Khwarazm, south of the Aral Sea. Latin scribes wrote it Algorizmi, Algoritmi, Alchorismus. Two thirteenth-century schoolbooks carried it into the universities, Alexander de Villa Dei's Carmen de Algorismo in verse and Johannes de Sacrobosco's Algorismus in prose, both copied in hundreds of manuscripts. The name came loose from the man and attached itself to the method. To do algorism was to calculate on paper with the figures rather than shuffle counters on a ruled board.

The word was in English well before Chaucer, and ordinary enough by the 1380s to carry a joke. Chaucer's clerk Nicholas, in the Miller's Tale, keeps his augrym stones neatly on a shelf at his bed's head, beside his astrolabe. Augrym is algorism worn down through French, and the standard gloss on the stones is that they are counters for a reckoning board, so the new word had attached itself to the old technology, which is roughly what most of Europe did with it for two hundred years.

The spelling algorithm is a later accident. In the 1690s the word was refashioned under the influence of the Greek arithmos, number, and that is where the intruding "th" came from. There is nothing Greek in the word. The letter is a scholarly mistake that hardened. The meaning widened to any step-by-step procedure, and from the 1930s to the sense the computing industry uses.

Zero took a similar route. The Sanskrit shunya, empty, was rendered into Arabic as sifr with the same meaning. Sifr entered Latin as cifra and as zephirum, then split. Cifra produced cipher, which in English meant the arithmetical zero from the late fourteenth century and did not mean a secret code until the 1520s, when codes commonly worked by substituting numbers for letters. Zephirum produced the Italian zefiro and then zero. Fibonacci spells the moment out: with the nine figures, and with the sign 0 which the Arabs call zephir, any number whatever can be written.

Three English words kept the receipt after the textbooks mislaid it: algorithm, a Persian mathematician's hometown, and cipher and zero, one Arabic word twice over.

What Fibonacci did, and what he did not

Leonardo of Pisa, called Fibonacci, is routinely credited with introducing these numerals to Europe. That claim is widespread, it appears in a great many otherwise careful places, and it is wrong.

The Codex Vigilanus, copied at the monastery of Albelda in the Rioja in 976, contains the earliest known drawing of the Indian figures in a Latin manuscript, with a note beside them. We should know, the scribe says, that the Indians have a most subtle intelligence, that other peoples yield to them in arithmetic and geometry and the other liberal disciplines, and that this shows in the nine figures with which they designate each rank. That is two hundred and twenty-six years before Liber Abaci, in Christian Spain, with India named on the page.

Gerbert of Aurillac, who spent three years in the Catalan monasteries from 967 and became Pope Sylvester II in 999, is associated with an abacus whose counters, called apices, were marked with the figures. That went nowhere and deserved to: it kept the shapes and discarded the reason for them, since a counting board with labelled tokens gains nothing from place value.

What Fibonacci did was different and much bigger. Liber Abaci, first issued in 1202 and revised in 1228, was a working manual for merchants: currency conversion, the alloying of metals, profit sharing, the pricing of goods. The 1202 text does not survive, and what modern readers have, including Laurence Sigler's 2002 English translation, descends from the 1228 revision.

The prologue says plainly where he learned the method. His father was a Pisan official at the customs house at Bugia, modern Béjaïa in Algeria, and sent for his son so the boy could be taught calculation. Fibonacci describes a marvellous instruction in the art of the nine Indian figures, then lists them, 9 8 7 6 5 4 3 2 1, with the sign 0. He had traded through Egypt, Syria, Greece, Sicily and Provence, studied the methods used in each, and judged the Indian one best. The Latin he uses for it is modus Indorum. He learned it from Arabic-speaking teachers in North Africa, and passed on the attribution they had given him.

The medieval resistance that mostly did not happen

One story usually told at this point should be set aside: that medieval Christendom feared zero as diabolical, that a war raged between abacists and algorists, and that Florence banned the numerals in 1299 out of superstition. C. Philipp E. Nothaft took that narrative apart in the British Journal for the History of Mathematics in 2020, tracing it to a 1905 article by Leo Jordan whose speculation about an abacist-algorist quarrel was repeated until it looked like evidence. The 1299 Florentine ruling was real but dull: a money changers' guild rule requiring debits and credits to be written out legibly rather than in figures, the sort of anti-fraud provision any accounting regime produces.

Where the credit was lost, and where it was not

Say the important thing first, because the order matters. Everything above is a record of open acknowledgement. Arabic and Persian mathematicians called the subject Indian reckoning for centuries and never stopped. Al-Biruni travelled to India, learned Sanskrit, read the astronomical literature and finished a long book on the country around 1030. The Latin translators kept the attribution in their titles. A monk in tenth-century Spain wrote that the Indians surpassed all other peoples in arithmetic. Any account that opens by blaming Arabs or Muslims for the theft of Indian mathematics has the documents exactly backwards.

The loss came later, in Europe, and it looks structural rather than malicious. The history of mathematics that hardened into nineteenth and early twentieth century European teaching ran from Egypt and Babylon to Greece to Rome, then through a long silence to the Renaissance. India and the Islamic world entered that story, when they entered it at all, as a corridor where Greek learning was warehoused and later handed back. A narrative with that shape has no slot for an Indian invention adopted wholesale by Europe. So the invention quietly became a set of symbols, symbols need no inventor, and the label that stuck described the last leg of the journey rather than the first.

Specialists were never confused. David Eugene Smith and Louis Charles Karpinski published a book-length study in 1911 and titled it The Hindu-Arabic Numerals. What failed was the passage from scholarship into the ordinary classroom, a duller offence than theft and a more consequential one, since the classroom is where almost everyone learns what they will believe for life. George Gheverghese Joseph made that the central charge of The Crest of the Peacock in 1991.

Georges Ifrah's The Universal History of Numbers is the most widely read popular account of this material, but historians of mathematics have criticised its handling of sources sharply. Read it for orientation and verify specifics elsewhere. For the Indian material, Kim Plofker's Mathematics in India is the safer reference.

What actually crossed the border

The thing transmitted was not a set of shapes. Shapes are the cheap part, and they kept changing. The Brahmi forms, the eastern Arabic forms still used from Egypt to Pakistan, and the western Arabic forms of Spain and North Africa from which European digits descend all look different, and the lineage of individual glyphs is still argued over. The western forms are often called ghubar, dust figures, after the sand board they were traced on, though Paul Kunitzsch argued against the label because it once carried a theory of separate origin the evidence does not support. What crossed was not a font but a procedure.

Positional notation with a zero means the value of a symbol depends on where it sits. That single move turns arithmetic into a fixed sequence of steps performed on written symbols instead of a manipulation of physical objects. It is why al-Khwarizmi's book was a book of procedures, and why his name came to mean procedure.

Zero is the load-bearing piece. Brahmagupta's Brahmasphutasiddhanta, composed in 628, treats zero as a number rather than a gap, defines it as what is left when a quantity is subtracted from itself, and in its algebraic chapter gives rules for arithmetic with zero and with negative quantities, which he calls debts. He also attempts division by zero, lets a fraction with zero in the denominator stand, and declares that zero divided by zero is zero. That is wrong, and the failure belongs here, because a tradition reported only when it is correct is being flattered rather than studied.

The oldest surviving Indian inscription using a circular zero as a place-value digit is at the Chaturbhuj temple in Gwalior fort, dated 876, in a land grant of 270 hastas and an endowment for 50 daily garlands. Earlier evidence exists, and each piece carries a caveat. Aryabhata's verse notation and number-words in 499 are generally read as implying decimal place value, though that is an inference from how the system works rather than a statement in the text, and no symbol is displayed. The Bakhshali manuscript uses a dot for zero, but its date has been argued over for a century: the Bodleian's 2017 radiocarbon tests returned three widely separated dates from three folios, and Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk replied that year that the bark of the oldest folio does not date the text.

Around 771 to 773 an embassy from Sind brought Sanskrit astronomical material to Baghdad, where it was translated as the Sindhind and became a foundation of Islamic mathematical astronomy. That episode is real. The storybook detail attached to it, the name Kanaka for the visiting scholar, comes from much later reports, and the astronomer's identity is unknown.

Kerala, and the question left open

In December 1832 Charles Matthew Whish, an East India Company civil servant in Malabar, presented a paper to the Royal Asiatic Society. He died the following April, aged thirty-eight, and it was printed posthumously in 1834. He reported that Sanskrit and Malayalam texts of the Kerala school, among them Nilakantha's Tantrasangraha and Jyesthadeva's Yuktibhasa, contained infinite series for the circumference-to-diameter ratio and for the sine and cosine, long predating the European ones.

The mathematics is now settled. Madhava of Sangamagrama, working around 1400, had series that European mathematicians reached two centuries later.

Whether any of it travelled is a separate question, and it is open. The hypothesis is that Jesuit missionaries in Kerala carried the material back to Europe, which is not absurd: they were in the right places at the right time, several were mathematically trained, and they were collecting local calendrical knowledge. But surveys of Jesuit correspondence and archives have not produced a document showing the series moving, and Plofker's published assessment of those attempts amounts to the judgement that the case has not been made. Until a text turns up, the honest position is that Kerala reached these results first and that transmission remains undemonstrated.

For the numerals no such gap exists. A reader who doubts it can open Nau's edition, the Cambridge manuscript, the Codex Vigilanus or Sigler's Fibonacci and read the attribution in the transmitters' own words.