Nine Symbols and a Dot That Changed Everything A Story of Numbers

Reema finds an old paper covered in strange wedge-shaped Mesopotamian numerals, and her father unfolds the whole story of how numbers came to be written the way they are today. Ancient Indian texts like the Yajurveda Samhita already named numbers at a staggering scale, powers of ten reaching into the trillions and far beyond, and the Bakhshali manuscript (around the 3rd century CE) contains some of the earliest known uses of a dot to mark zero. This knowledge, refined by Aryabhata (499 CE), eventually travelled through the Arab world (Al-Khwarizmi and Al-Kindi, around 800-830 CE) and reached Europe through figures like Fibonacci around 1200 CE -- prompting the mathematician Pierre-Simon Laplace to later praise the Indian number system as one of the most useful inventions in the history of thought, precisely because of how elegantly it combined place value with a genuine zero.

The most basic way to record an amount is a direct one-to-one mapping, a stick or mark for every single object counted, with no shortcuts at all. A second method uses sounds, borrowing the letters of an alphabet to stand for numbers. A third method, symbols, is the direction every major numbering system eventually took, each one facing the exact same underlying challenge: how to represent very large amounts without needing an impossibly long string of individual marks.

The Ishango Bone (roughly 20,000-35,000 years old, discovered in the Democratic Republic of Congo, with notches arranged in columns possibly indicating a calendrical system) and the even older Lebombo Bone (roughly 44,000 years old, discovered in South Africa, considered one of the oldest known mathematical artefacts) both carry deliberately grouped tally notches, some of the earliest physical evidence of human counting. Some cultures, like certain groups in Papua New Guinea, counted using body parts directly rather than abstract symbols. The Gumulgal people of Australia counted in twos (one, two, two-and-one, two-twos, and so on), and strikingly, entirely separate cultures with no known contact -- the Bakairi of South America and the Bushmen of South Africa -- independently developed remarkably similar counting-in-twos systems, a genuinely puzzling historical convergence worth pausing on.

Roman numerals build every number from a small set of landmark symbols (I=1, V=5, X=10, L=50, C=100, D=500, M=1000): 27 becomes XXVII (10+10+5+1+1), and larger numbers like 2367 combine these landmarks correctly as 1000+1000+100+100+100+50+10+5+1+1, written as MMCCCLXVII. Addition and even multiplication of Roman numerals can be done directly, without first converting to the Hindu system, though the process grows increasingly unwieldy as numbers get larger, precisely because Roman numerals carry no place value and no zero at all.

Ancient Egyptian numerals (around 3000 BCE) used base 10 with dedicated symbols for each landmark power of ten, but still without any place-value system -- a number like 324 needed 100+100+100+10+10+4 worth of separate symbols laid out together. Building an entirely new base-5 system from scratch, using landmark numbers 1, 5, 25, 125 (powers of 5 instead of 10), makes the very idea of 'a base' concrete: 143 groups as one 125, three 5's, and three 1's. The medieval abacus (11th century) mechanised decimal counting directly, using beads or counters on lines representing each place value.

The Mesopotamian system (using a base of 60, the ancestor of today's 60 minutes and 60 seconds) was a genuine place-value system, though it long struggled with representing an empty place clearly. The Mayan system used a base close to 20 (with a curious exception: its third landmark number was 360, not 400, likely tied to their calendar). Chinese rod numerals alternated between two symbol orientations (Zong and Heng) specifically to avoid ambiguity between adjacent place values. The Hindu system finally combined true place value with zero playing two genuinely distinct roles at once: a placeholder marking an empty position, AND a real number in its own right that can be added to, subtracted from, and reasoned about -- a synthesis credited to Aryabhata (499 CE) and formalised further by Brahmagupta (628 CE, in his Brahmasphutasiddhanta).