Logarithms made lengthy calculations easier by converting multiplication and division into addition and subtraction. Before electronic calculators, mathematicians and astronomers could use logarithm tables to work through calculations that would otherwise take much longer. The history of logarithms is also a story about designing tools to reduce repetitive work.
John Napier and the first published logarithms
Scottish mathematician John Napier published his work on logarithms in 1614. His original system differed from the modern definition, but it introduced a way to simplify calculations using relationships between numbers and their powers.
In a modern base-10 example, multiplying 100 by 1,000 can be handled by adding their logarithms: log10(100) = 2 and log10(1,000) = 3, so the product has logarithm 5 and equals 100,000. This relationship helped make tables useful for large or repeated calculations.
Henry Briggs and base-10 tables
English mathematician Henry Briggs worked with Napier and helped develop common logarithms, which use base 10. These tables were convenient for decimal arithmetic and became important tools for calculation. Napier’s original construction and the modern definition should not be treated as identical; the history developed through further mathematical work.
The University of St Andrews biography of John Napier describes his 1614 publication and Briggs’s contribution.
Why logarithms still matter
Calculators have replaced printed tables for most routine arithmetic, but logarithms remain a core mathematical function. They help describe exponential relationships and appear in areas such as science, engineering, statistics and computing. Understanding their history shows how an abstract mathematical idea also served as a practical calculation tool.