/ˈlɒɡərɪðəm/
[noun] A mathematical value that shows how many times you must multiply a certain base number by itself to get another number. For example, the logarithm of 1000 in base 10 is 3, because 10 × 10 × 10 = 1000.
Logarithm was invented as a word before the maths behind it was fully understood — a name chosen to sound ancient, but coined brand new in 1614.
The word 'logarithm' is, unusually in the history of language, almost entirely a human invention rather than a slow evolution through centuries of usage. It was created deliberately in 1614 by the Scottish mathematician John Napier, who published a landmark work called *Mirifici Logarithmorum Canonis Descriptio* — 'A Description of the Wonderful Table of Logarithms'. Napier needed a name for a genuinely new mathematical concept he had spent twenty years developing, and so he reached into the ancient Greek treasury and assembled one from parts.
Napier combined two Greek words: 'logos' (λόγος), meaning 'ratio' or 'reckoning', and 'arithmos' (ἀριθμός), meaning 'number'. Together they gave him 'logarithmos' — essentially 'ratio-number' or 'reckoning number'. The word entered English almost immediately from Napier's Latin text, arriving as 'logarithm' by the early 1600s with almost no changes in spelling or meaning. It is one of the rare cases in etymology where you can name the precise person, the precise year, and even the precise book in which a word was born.
The root 'logos' is one of the most philosophically loaded words in all of ancient Greek. It carried meanings ranging from 'word' and 'speech' to 'reason', 'proportion', and 'account'. From this single powerful root, Greek gave Latin 'logica', which passed through Old French as 'logique' before arriving in English as 'logic'. The same root gave us 'logical', 'logistics', and the suffix '-logy' found in words like 'biology' (Greek 'bios', life + 'logos', study) and 'geology'. Napier chose 'logos' specifically in its mathematical sense of 'ratio', reflecting how his original logarithms were built around the relationship between two sequences of numbers — one arithmetic, one geometric.
The second half of the word, 'arithmos', has its own distinguished history. It is the source of the English word 'arithmetic', which travelled the route Greek 'arithmetike' → Latin 'arithmetica' → Old French 'arismetique' → Middle English 'arsmetrik' before settling into its modern spelling. The Greek 'arithmos' itself is thought to derive from a Proto-Indo-European root meaning 'to fit together' or 'to count', which also connects distantly to the word 'rhyme' — originally spelled 'rime' in Old English, connected to the sense of ordered counting or matching sounds. This surprising link between mathematical counting and poetic rhythm reflects how the ancient mind saw number and pattern as deeply related.
Napier's invention was revolutionary not because of the word, but because of what it named. Before calculators or computers, multiplying enormous numbers — essential for navigation, astronomy, and banking — was agonisingly slow. Logarithms transformed multiplication into addition, effectively doing in seconds what took skilled mathematicians hours. The great astronomer Johannes Kepler called Napier's tables a gift from God. Within a decade, the English mathematician Henry Briggs refined Napier's system into the familiar base-10 version, and the word 'logarithm' rapidly spread across Europe in scientific texts. Today, a shortened form — 'log' — is used casually in classrooms and calculators worldwide, a tiny syllable that still carries the ghost of Napier's carefully chosen Greek construction.
Perhaps the most remarkable thing about 'logarithm' is what its history reveals about how scientific language works. Most words arrive in English worn smooth by centuries of use across many tongues and mouths. Logarithm arrived fully formed, constructed by one man sitting in a Scottish castle, borrowing the prestige of ancient Greek to give weight and permanence to a new idea. The strategy worked: the word has sat unchanged in the language for over four hundred years, as stable and precise as the mathematics it describes.