Chapter 4: Systems Based on Numbers

Section 1: The Notion of Numbers

History of digit sequences

On an abacus or similar device numbers are in effect represented by digit sequences. In antiquity however most systems for writing numbers were like the Roman one and not based on digit sequences. An exception was the Babylonian base 60 system (from which hours:minutes:seconds notation derives). The Hindu-Arabic base 10 system in its modern form probably originated around 600 AD, and particularly following the work of Leonardo Fibonacci in the early 1200s, became common by the 1400s. Base 2 appears to have first been considered explicitly in the early 1600s (notably by John Napier in 1617), and was studied in detail by Gottfried Leibniz starting in 1679. The possibility of arbitrary bases was stated by Blaise Pascal in 1658. Various bases were used in puzzles, but rarely in pure mathematics (work by Georg Cantor in the 1860s being an exception). The first widespread use of base 2 was in electronic computers, starting in the late 1940s. Even in the 1980s digit sequences were viewed by most mathematicians as largely irrelevant for pure mathematical purposes. The study of fractals and nesting, the appearance of many algorithms involving digit sequences and the routine use of long numbers in Mathematica have however gradually made digit sequences be seen as more central to mathematics.

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From Stephen Wolfram: A New Kind of Science [citation]