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ALGORITHM (a systematic technique for solving
a problem) was used by Gottfried Wilhelm Leibniz (1646-1716):
Ex cognito hoc velut Algorithmo, ut ita
dicam, calculi hujus, quem voco differentialem, omnes aliae aequationes
differentiales inveniri possunt per calculum communem, maximae que &
minimae, item que tangentes haberi, ita ut opus non sit tolli fractas aut
irrationales, aut alia vincula, quod tamen faciendum fuit secundum Methodos
hactenus editas. (From this rule, known as an algorithm, so to speak, of
this calculus, which I call differential, all other differential equations
may be found by means of a general calculus, and maxima and minima, as well
as tangents [may be] obtained, so that there may be no need of removing fractions,
nor irrationals, nor other aggregates, which nevertheless formerly had to
be done in accordance with the methods published up to the present.)
The citation above is from "Nova Methodvs pro maximis et minimis, itemque
tangentibus, quae nec fractas, nec irrationales quantitates moratur, &
singulare pro illis calculi genus, per G.G.L." (A new method for maxima
and minima, as well as tangents, which is not obstructed by fractional or
irrational quantities), Leibniz' first published account of the calculus
[Acta Eruditorum, vol. 3, pp. 467-473, October 1684], page 469.
Both terms "Algorithmo" and "differentialem" are italicized in the original.
The English translation is from Evelyn Walker's translation of extracts
from Leibniz' memoir found on p. 623 of Smith's Source Book in Mathematics
(1929), vol. 2.
Apparently the earliest English translation was carried
out by Joseph Raphson in The Theory of Fluxions, Shewing in a compendious
manner The first Rise of, and various Improvements made in that Incomparable
Method, London, 1715: "Now from this being known as the Algorithm, as
I may say of this Calculus, which I call differential, ..." (p.23). The
word was then taken up by Euler, for instance in his article 'De usu novi
algorithmi in problemate Pelliano solvendo', and its use was then firmly
established. [Julio González Cabillón, David Fowler]
The word algorithm is derived from the much older
word algorism, and "influenced by the Greek word arithmos
(number)," according to the OED2. However, according to Jan Hogendijk of
the Utrecht University it was not so influenced. Algorism (meaning
"the Hindu-Arabic system of numeration or calculations using it") is derived
from the Arabic al-Khowarazmi, the native of Khwarazm
(Khiva), surname of the Arab mathematician and astronomer Abu Ja'far Mohammed
Ben Musa (c. 780 - c.850).
According to the Theseus Logic, Inc., website, "The
term algorithm was not, apparently, a commonly used mathematical term in
America or Europe before Markov, a Russian, introduced it. None of the other
investigators, Herbrand and Godel, Post, Turing or Church used the term.
The term however caught on very quickly in the computing community."
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