What does fluxion mean?
Fluxion is a noun with its home ground in the history of mathematics. In Isaac Newton's formulation of the calculus, a fluxion was the rate at which a continuously varying quantity changes — what modern notation expresses as a derivative or, informally, an instantaneous rate of change. Newton called the changing quantity itself a 'fluent,' and he developed his theory of fluxions in the 1660s and 1670s, though he published it late. The word also has an older, broader sense as a flowing or continual change, inherited from Latin roots meaning 'to flow.' Today fluxion appears almost exclusively in formal, historical, or technical contexts: historians of science discussing the famous priority dispute between Newton and Leibniz, or writers on philosophy invoking perpetual flow. Its connotations are scholarly and precise rather than everyday. For anyone interested in how calculus got its names — and how notation shapes science — fluxion is a small word with a remarkable story.
nounA fluxion is, in the calculus developed by Isaac Newton, the rate of change of a continuously varying quantity — equivalent to what later notation calls a derivative. More broadly, it can denote any flowing or continuous change.
- In mathematics: the rate of change (derivative) of a continuously varying quantity in Newton's formulation of the calculus.
- In general or older usage: a flowing or continuous change; the act of flowing.
"In Newton's notation, the fluxion of the distance traversed by a falling body gives its instantaneous velocity."
"Leibniz's differential notation ultimately displaced Newton's fluxions throughout most of continental Europe."
"The philosopher argued that all reality is in a state of fluxion, forever flowing and never at rest."
Standard plural; historically used when referring to Newton's calculus collectively, e.g. in works describing his 'method of fluxions.'
"Continental mathematicians found Leibniz's differentials easier to work with than Newton's fluxions."
Before 'dx/dy' conquered mathematics, Isaac Newton described derivatives as 'fluxions' — and his bitter feud with Leibniz over whose notation was better helped split British and continental mathematics for a century.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of fluxion
Fluxion derives from the Latin fluxus ('flowing'), rooted in the verb fluere ('to flow'), and entered English in the mid-17th century, when natural philosophers were intensely interested in processes of flow and change. Isaac Newton adopted the term for the rates of change at the heart of his calculus, calling the varying quantities themselves 'fluents.' The word thus shares a lineage with cognates such as fluent, fluid, flux, and confluence, all descending from the same Proto-Indo-European root seen in Latin fluere.
Related word forms
How fluxion is actually used
The word is chiefly historical and technical today, encountered mainly in discussions of the history of calculus or in Newtonian terminology; the general sense of 'a flowing' is rare and largely archaic. It carries a formal, academic register.
Easily confused with fluxion
Flux is the broader term for flow or rate of flow (or a substance used in metallurgy), whereas fluxion specifically refers to Newton's calculus concept of a rate of change of a varying quantity.
Fluctuation describes irregular rising-and-falling variation, while a fluxion is the instantaneous rate of change of a quantity in Newton's calculus.