exponens

Exponens in Latin is the present participle of exponere (to put forth, to set out, to display), from ex- (out) + ponere (to put, to place). The mathematical use emerged in the seventeenth century. Michael Stifel, in his Arithmetica Integra (1544), used the concept of exponents for powers of numbers, and Nicolas Chuquet had used exponential notation even earlier in 1484. But the word 'exponent' for the superscript number was standardized later.

Rene Descartes introduced the modern exponential notation in his La Geometrie (1637) — writing x³ instead of xxx or other cumbersome notations. The superscript number set forth how many times the base appears as a factor. This notation was so much cleaner than predecessors that it was adopted almost immediately. Descartes gave mathematics its most compact notation for repeated multiplication.

Exponential growth became one of the most important concepts in science and economics. Thomas Malthus argued in 1798 that population grows exponentially while food production grows linearly — a mismatch that would inevitably produce famine. The concept of exponential growth (2, 4, 8, 16, 32...) versus linear growth (2, 4, 6, 8, 10...) is now taught in every introductory science course. The word 'exponential' entered common speech meaning 'very fast,' which is imprecise but captures the spirit.

The word 'exponent' also means 'advocate' — an exponent of a theory is someone who puts it forth, explains it, champions it. This is the original Latin meaning. The mathematical meaning and the rhetorical meaning are both about putting something forward. The number puts forth multiplications. The advocate puts forth ideas. The root exponere holds both.