The
HinduArabic
numeral system is a decimal
placevalue numeral system. It requires a
zero to handle the empty powers of ten
(as in "205").
Its glyphs are descended from the Indian
Brahmi numerals. The full system emerged by
the 8th to 9th century, and is first described in
AlKhwarizmi's
On the Calculation with
Hindu Numerals (ca.
825), and
AlKindi's four volume work
On the Use of the
Indian Numerals (ca.
830). Today the name
HinduArabic numerals is usually used.
Evidence of early use of a zero glyph may be present in
Bakhshali manuscript, a text of
uncertain date, possibly a copy of a text composed as early as the
3rd century.
Decimal System
Historians trace modern numerals in most languages to the
Brahmi numerals, which were in use around the
middle of the third century BC. The
place
value system, however, evolved later.
The Brahmi numerals
have been found in inscriptions in caves and on coins in regions
near Pune, Mumbai, and
Uttar
Pradesh. These numerals (with slight variations)
were in use over quite a long time span up to the 4th century AD
.
During the
Gupta period (early 4th
century AD to the late 6th century AD), the Gupta numerals
developed from the Brahmi numerals and were spread over large areas
by the Gupta empire as they conquered territory . Beginning around
7th century, the Gupta numerals evolved into the Nagari
numerals.
Positional notation
There is indirect evidence that the Indians developed a positional
number system as early as the
first
century CE. The
Bakhshali
manuscript (c. 3d c. BCE) uses a place value system with a dot
to denotethe zero, which is called
shunyasthAna,
"emptyplace", and the same symbol is also used in algebraic
expressions for the unknown (as in the canonical
x in
modern algebra).However, the date of the Bakhshali manuscript is
hard to establish, and has been the subject of considerable debate.
The oldest dated Indian document showing use of the modern place
value form is a legal document dated 346 in the
Chhedi calendar, which translates to
594 CE. While some historians have claimed that the date
on this document was a later forgery, it is not clear what might
have motivated it, and it is generally accepted that enumeration
using the placevalue system was in common use in India by the end
of the
6th century. . Indian books dated
to this period are able to denote numbers in the hundred thousands
using a place value system. Many other inscriptions have been found
which are dated and make use of the placevalue system for either
the date or some other numbers within the text , although some
historians claim these to also be forgeries.
In his seminal text of
499,
Aryabhata devised a positional number system
without a zero digit. He used the word "kha" for the zero
position.. Evidence suggests that a dot had been used in earlier
Indian manuscripts to denote an empty place in positional notation.
[214705]. The same documents sometimes also
used a dot to denote an unknown where we might use x. Later Indian
mathematicians had names for zero in positional numbers yet had no
symbol for it.
The use of
zero in these positional
systems are the final step to the system of numerals we are
familiar with today.
The first inscription showing the use of zero
which is dated and is not disputed by any historian is the
inscription at Gwalior dated 933 in
the Vikrama calendar (876
CE.) .
The oldest
known text to use zero is the Jain text from India entitled the
Lokavibhaga , dated 458
AD.
The first
indubitable appearance of a symbol for zero appears in 876 in India
on a stone tablet in Gwalior.
Documents on
copper
plates, with the same small o in them, dated back as far as the
sixth century AD, abound.
Adoption by the Arabs
Before the
rise of the Arab Empire, the
HinduArabic numeral system was already moving West and was
mentioned in Syria in 662 AD by the Nestorian scholar
Severus Sebokht who wrote the
following:
 "I will omit all discussion of the science of the Indians,
... , of their subtle discoveries in astronomy,
discoveries that are more ingenious than those of the Greeks and
the Babylonians, and of their valuable methods of calculation which
surpass description. I wish only to say that this
computation is done by means of nine signs. If those who
believe, because they speak Greek, that they have arrived at the
limits of science, would read the Indian texts, they would be
convinced, even if a little late in the day, that there are others
who know something of value."[214706]
According to alQifti's chronology of the scholars
[214707]:
 "... a person from India presented himself before the
Caliph alMansur in the year [776 AD] who was well versed in the
siddhanta method of calculation related to the movement of the
heavenly bodies, and having ways of calculating equations based on
the halfchord [essentially the sine] calculated in halfdegrees
... This is all contained in a work ... from which he
claimed to have taken the halfchord calculated for one
minute. AlMansur ordered this book to be translated into
Arabic, and a work to be written, based on the translation, to give
the Arabs a solid base for calculating the
movements of the planets ..."
The work was most likely to have been
Brahmagupta's
Brahmasphutasiddhanta (Ifrah)
[214708] (The Opening of the Universe) which
was written in 628
[214709]. Irrespective of whether Ifrah is
right, since all Indian texts after
Aryabhata's
Aryabhatiya used the Indian
number system, certainly from this time the Arabs had a translation
of a text written in the Indian number system.
[214710]
In his text
The Arithmetic of AlUqlîdisî (Dordrecht: D.
Reidel, 1978),
A.S. Saidan's studies were unable to answer in full
how the numerals reached the Arab world:
 "It seems plausible that it drifted
gradually, probably before the seventh century, through two
channels, one starting from Sind, undergoing Persian filtration and
spreading in what is now known as the Middle East, and the other
starting from the coasts of the Indian Ocean and extending to the southern coasts of the
Mediterranean."[214711]
AlUqlidisi developed a notation to
represent decimal fractions.The numerals came to fame due to their
use in the pivotal work of the
Persian mathematician
AlKhwarizmi, whose book
On the Calculation
with Hindu Numerals was written about
825,
and the
Arab mathematician
AlKindi, who wrote four volumes (see [2]) "On the
Use of the Indian Numerals" (Ketab fi Isti'mal al'Adad alHindi)
about
830. They, amongst other works,
contributed to the diffusion of the Indian system of numeration in
the
MiddleEast and the West.
Evolution of symbols
The evolution of the numerals in early Europe is shown below:The
French scholar J.E. Montucla created this table “Histoire de la
Mathematique”, published in 1757:
The Abacus versus the HinduArabic numeral system in Medieval
Pictures
Image:Gregor Reisch, Margarita Philosophica, 1508
(1230x1615).pngImage:Rechentisch.pngImage:Rechnung auff der Linihen
und Federn.JPGImage:Köbel Böschenteyn 1514.jpgImage:Rechnung auff
der linihen 1525 Adam Ries.PNGImage:1543 Robert
Recorde.PNGImage:Peter Apian 1544.PNGImage:Adam riesen.jpg
Adoption in Europe
 976. The first Arabic numerals in Europe
appeared in the Codex
Vigilanus in the year 976.
 1549. These are correct format and sequence of the
“modern numbers” in titlepage of the Libro Intitulado
Arithmetica Practica by Juan de Yciar, the Basque calligrapher and
mathematician, Zaragoza 1549.

Medieval Arabic Numbers at World map
from Ptolemy, Cosmographia.
Ulm: Lienhart Holle, 1482

Libro Intitulado Arithmetica Practica,
1549


In the last few centuries, the European variety of Arabic numbers
was spread around the world and gradually became the most commonly
used numeral system in the world.
Even in many countries in languages which have their own numeral
systems, the European Arabic numerals are widely used in
commerce and
mathematics.
Impact on Mathematics
The significance of the development of the positional number system
is probably best described by the French mathematician Pierre Simon
Laplace (1749  1827) who wrote:
 "It is India that gave us the ingenuous method of
expressing all numbers by the means of ten symbols, each symbol
receiving a value of position, as well as an absolute value; a
profound and important idea which appears so simple to us now that
we ignore its true merit, but its very simplicity, the great ease
which it has lent to all computations, puts our arithmetic in the
first rank of useful inventions, and we shall appreciate the
grandeur of this achievement when we remember that it escaped the
genius of Archimedes and Apollonius, two of the greatest minds
produced by antiquity."
Tobias Dantzig, the father of
George
Dantzig, had this to say in
Number:
 "This long period of nearly five thousand years saw the
rise and fall of many a civilization, each leaving behind it a
heritage of literature, art, philosophy, and religion. But
what was the net achievement in the field of reckoning, the
earliest art practiced by man? An inflexible numeration so
crude as to make progress well nigh impossible, and a calculating
device so limited in scope that even elementary calculations called
for the services of an expert [...] Man used these devices for
thousands of years without contributing a single important idea to
the system [...] Even when compared with the slow growth of ideas
during the dark ages, the history of reckoning presents a peculiar
picture of desolate stagnation. When viewed in this light,
the achievements of the unknown Hindu, who some time in the first
centuries of our era discovered the principle of position, assumes
the importance of a world event."
See also
Notes
 HinduArabic Numerals
 Indian numerals
 HinduArabic Numerals
 Lamfin.Pdf
 Ifrah, Georges. 2000. The Universal History of Numbers: From
Prehistory to the Invention of the Computer. David Bellos, E. F.
Harding, Sophie Wood and Ian Monk, trans. New York: John Wiley
& Sons, Inc. Ifrah 2000:4171 9
 Kaplan, Robert. (2000). The Nothing That Is: A Natural
History of Zero. Oxford: Oxford University Press.
 AlUqlidisi biography by J. J. O'Connor and E.
F. Robertson
 Earliest Uses of Symbols for Fractions by Jeff
Miller
References