The place-value decimal numeral system with zero — the system in which "105" means one hundred, zero tens, and five units, with position determining value — was developed in India between roughly the 5th and 7th centuries CE, building on much earlier Indian mathematical traditions. Transmitted to the Islamic world by the 9th century (where it was called "Hindu numerals") and to medieval Europe by the 12th century (where it was called "Arabic numerals"), it is now the universal numeral system of global mathematics, science, commerce, and daily life. It is arguably the most consequential single mathematical contribution in human history.
Before the Indian numeral system spread worldwide, different cultures used radically different and far less practical number systems. Roman numerals (I, V, X, L, C, D, M) have no place value — XLVIII cannot be multiplied by XII using any simple rule, and long division is essentially impossible without an intermediate system. The Indian place-value system, where each digit's value depends on its position, makes arithmetic with large numbers straightforward enough to teach to children — which is why it replaced every competing system it encountered.
The digits 0–9 as used worldwide are often called "Arabic numerals" in the Western tradition, because Europeans received them via Arabic-language manuscripts. But Arabic scholars who transmitted the system were explicit about its origin: the 9th-century mathematician al-Khwarizmi (whose works introduced the system to the Islamic world and whose name gave us the word "algorithm") called them "Hindu numerals." The correct attribution is Indian, and the system is more accurately called the Hindu-Arabic numeral system — or simply the Indian numeral system.
The earliest Indian numerical notation, the Brahmi numeral system, appears in inscriptions from roughly the 3rd century BCE onward (including edicts of Emperor Ashoka). Brahmi numerals were not place-value — they had separate symbols for 1–9, 10, 20, ..., 100, 1000, and so on, somewhat like Roman numerals. The transition to a place-value system was a development of the first millennium CE.
The Bakhshali manuscript, a mathematical text discovered in 1881 near Peshawar (now Pakistan), contains some of the earliest known uses of a dot symbol to represent zero in a place-value context. Radiocarbon dating published in 2017 dated portions of the manuscript to 224–383 CE, though the full manuscript spans multiple centuries and the dating of individual leaves remains contested among scholars.
Āryabhaṭa's Āryabhaṭīya (499 CE — see the Aryabhatiya entry) uses a sophisticated place-value system (encoded alphabetically) for large astronomical calculations, demonstrating that place-value arithmetic was well established in Indian mathematics by the late 5th century. The explicit zero as a written symbol in the modern sense appears clearly in the Gwalior inscription (876 CE) and is implicit in Brahmagupta's Brahmasphutasiddhanta (628 CE — see that entry), which gives the first known complete rules for arithmetic operations involving zero.
Al-Khwarizmi's Kitab al-mukhtasar fi hisab al-jabr wal-muqabala (c. 825 CE) and his separate treatise on Indian arithmetic introduced the Hindu numeral system to Arabic-speaking scholars. European transmission came primarily through 12th-century Latin translations, including Fibonacci's Liber Abaci (1202 CE), which championed the Hindu-Arabic system over Roman numerals for commercial calculations — though widespread adoption in Europe took several more centuries.
Brahmagupta's Brahmasphutasiddhanta (628 CE) contains the first known explicit, systematic rules for arithmetic with zero treated as a number: zero plus a positive number equals that number; zero minus a positive number equals a negative number; zero times any number equals zero. He also attempted rules for division by zero (arriving at 0/0 = 0, which is not how modern mathematics handles it, but the attempt to treat zero/zero as a definite quantity was a significant conceptual step). These rules — especially the treatment of zero as a genuine arithmetic object rather than merely an absence — mark a fundamental conceptual advance over all prior numeral traditions.
The Babylonians had a place-value system (base 60, the ancestor of modern timekeeping) but used a space rather than a symbol for zero, creating ambiguity. The Maya independently developed a place-value system with a zero symbol, but this did not influence the main line of mathematical development that led to the modern system. The Egyptian, Greek, and Roman systems were all non-place-value and became progressively more cumbersome for large-number arithmetic. The Indian system's combination of base 10, genuine place value, and a written zero symbol made all four arithmetic operations (addition, subtraction, multiplication, division) uniformly simple for numbers of any size — an ergonomic and conceptual advantage decisive enough that it supplanted every alternative it encountered.
It is difficult to overstate the downstream impact of the Indian numeral system on the history of mathematics and science. Decimal fractions (Stevin, 1585), logarithms (Napier, 1614), the development of algebra as a computational discipline, double-entry bookkeeping, actuarial tables, scientific notation, and ultimately the binary representation underlying all digital computing — all are built directly on the foundation of a place-value system with zero. The Indian mathematicians who developed this system in the first millennium CE created the numerical infrastructure that makes all quantitative science possible.