Leibniz on Number Systems

In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Springer. pp. 167-197 (2024)
  Copy   BIBTEX

Abstract

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that were exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life.

Author's Profile

Lloyd Strickland
Manchester Metropolitan University

Analytics

Added to PP
2023-05-25

Downloads
796 (#19,290)

6 months
486 (#3,220)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?