Logarithm

Multiplication is hard; addition is easy. John Napier spent twenty years creating tables that converted the former into the latter, publishing his Mirifici Logarithmorum Canonis Descriptio in 1614. The logarithm—from Greek logos (ratio) and arithmos (number)—transformed astronomical calculation from months of labor into hours.

Napier was a Scottish landowner, amateur mathematician, and theological controversialist. His motivation was practical: astronomy and navigation required multiplying and dividing numbers with six or seven digits, calculations so tedious that computers (the human kind) spent careers on them. Napier recognized that the properties of exponents offered a shortcut. If you could express any number as a power of some base, then multiplying those numbers meant merely adding their exponents.

The insight was that log(ab) = log(a) + log(b). To multiply 34,567 by 78,901, find their logarithms in a table, add those values, then look up the result in a reverse table. Multiplication becomes addition; division becomes subtraction. For calculations involving many operations—computing planetary positions, for instance—the time savings were revolutionary.

Henry Briggs, professor at Gresham College in London, traveled to Edinburgh in 1615 to meet Napier and propose an improvement: base-10 logarithms that would align with decimal notation. Napier agreed but died in 1617 before completing the work. Briggs published improved tables in 1624, establishing the common logarithm that dominated science and engineering for 350 years.

The cascade of applications was immediate. Johannes Kepler dedicated his 1620 Ephemeris to Napier. Edmund Gunter created the logarithmic scale in 1620. William Oughtred invented the slide rule around 1622, encoding logarithms mechanically. Navigation, surveying, engineering, and every mathematically intensive field adopted logarithmic calculation.

The slide rule remained standard equipment for engineers until electronic calculators appeared in the 1970s. Three and a half centuries of technological civilization computed with Napier's invention—every bridge, every spacecraft trajectory, every artillery table calculated by adding logarithms instead of multiplying raw numbers.