HAMSIHAMSI

The History of Astronomical and Mathematical Sciences in India (HAMSI) Working Group is dedicated to fostering and disseminating research in the history of Indian exact sciences (including astronomy, mathematics, and related subjects), and integrating it into the history of mathematics in general.

How to read Devanāgarī numerals

The decimal place value system of numeration originated on the Indian subcontinent.  The earliest extant examples of these numerals are on copper plates dating from around the middle of the first millennium CE and epigraphic evidence suggests they might have emerged quite a bit earlier than this.  Indeed, indirect textual references in texts originating from the first century CE may indicate that a place value system was utilized at least as early the beginning of the first millennium CE.

The ingenuity of the decimal place value system lies largely in its simplicity.  Using only ten different digits, any number of whatever size can be expressed.

The generic representation of the Indian (Sanskrit) numerals written in Devanāgarī script in various palaeographic forms with their corresponding Indo-Arabic modern equivalents are presented below.


0123456789
RORI 5498
Makarandasāraṇī of Makaranda, RORI 5498


0123456789
ACC3225
Makarandasāraṇī of Makaranda, ACC 3225


0123456789
ACC
Mahādevīsāraṇī of Mahādeva, ACC 254


123456789
BORI 501
Karaṇakutuhalasāraṇī of Bhāskara II, BORI 501, 1895-1902


123456789
BORI 497
Mahādevīsāraṇī of Mahādeva, BORI 497, 1892-1895


123456789
BORI 546
Calendar of Makaranda, BORI 546, 1895-1902


The construction of numbers 10 and upwards are done by placing the unit-numerals in conjunction based on their decimal place value as is typical in our standard Indo-Arabic numeration system.

7431857392754544840
7  43  18  57  39  27  54  54  48  40


3447161993526313841
34  47  16  19  9  35  26  31  38  41