**GALOIS GROUP** is found in 1899 in the *Bulletin of the American
Mathematical Society* (OED).

**GALOIS THEORY** is found in 1893 in the *Bulletin of the New
York Mathematical Society.*

The term **GAMMA FUNCTION** was introduced by Legendre (Kline, page
424).

The term **GASKET** was coined by Benoit Mandelbrot. On page 131,
[Chapter 14] of "The Fractal Geometry of Nature", Benoit Mandelbrot says:

And on page 142, Mandelbrot adds:Sierpinski gasketis the term I propose to denote the shape in Plate 141.

I call Sierpinski's curve aThe citation above was provided by Julio Gonz嫮ez Cabill鏮.gasket,because of an alternative construction that relies upon cutting out 'tremas', a method used extensively in Chapter 8 and 31 to 35.

The word **GAUGE** (in gauge theory) was coined by Hermann Weyl (1885-1955).

**GAUSSIAN CURVE** (normal curve) appears in a 1902 paper by Karl
Pearson [James A. Landau].

**GAUSSIAN DISTRIBUTION** and **GAUSSIAN LAW** were used by Karl
Pearson in 1905 in *Biometrika* (OED2).

**GAUSSIAN INTEGER** is found in the title, "Sums of fourth powers
of Gaussian integers," by Ivan Niven (1915-1999), *Bull. Am. Math. Soc.*
47, 923-926 (1941).

**GAUSSIAN LOGARITHM** appears in 1874 in *Rep. Brit. Assoc.*
(1873) (OED2).

The term **GEODESIC** was introduced in 1850 by Liouville and was
taken from geodesy (Kline, page 886).

The term **GEODESIC CURVATURE** is due to Pierre Ossian Bonnet (1819-1892)
[University of St. Andrews website].

**GEOMETRIC MEAN.** The term *geometrical mean* is found in
the 1771 edition of the *Encyclopaedia Britannica* [James A. Landau].

The term **GEOMETRIC PROGRESSION** was used by Michael Stifel in
1543: "Divisio in Arethmeticis progressionibus respondet extractionibus
radicum in progressionibus Geometricis" [James A. Landau].

**GEOMETRIC PROPORTION** appears in 1706 in *Synopsis Palmariorum
matheseos* by William Jones: "In any Geometric Proportion, when the
Antecedent is less than the Consequent, the Terms may be express'd by *a*
and *ar* (OED2).

**GEOMETRIC SERIES** is found in English in 1837 (OED2).

The term **GEOMETRY** was in use in the time of Plato and Aristotle,
and "doubtless goes back at least to Thales," according to Smith (vol.
2, page 273).

Smith also writes (vol. 2, page 273) that "Plato, Xenophon, and Herodotus use the word in some of its forms, but always to indicate surveying."

However, Michael N. Fried points out that Smith may not be entirely correct:

In theSmith (vol. 2, page 273) writes, "Euclid did not call his treatise a geometry, probably because the term still related to land measure, but spoke of it merely as theEpinomis(whose Platonic provenance is not completely clear), it is true that Plato refers to mensuration or surveying as 'gewmetria' (990d), but elsewhere Plato is very careful to distinguish between practical sciences concerning sensibles, such as surveying, and theoretical sciences, such as geometry. For instance, in thePhilebus(of undisputed Platonic provenance), one has:

"SOCRATES: Then as between the calculating and measurement employed in building or commerce and the geometry and calculation practiced in philosophy-- well, should we say there is one sort of each, or should we recognize two sorts?

PROTARCHUS: On the strength of what has been said I should give my vote for there being two" (57a).This distinction reoccurs in Proclus' neo-platonic commentary on Euclid's

Elements.There Proclus writes: "But others, like Geminus... think of one part [of mathematics] as concerned with intelligibles only and of another as working with perceptibles and in contact with them... Of the mathematics that deals with intelligibles they posit arithmetic and geometry as the two primary and most authentic parts, while the mathematics that attends to sensibles contains six sciences: mechanics, astronomy, optics, geodesy, canonics, and calculation. Tactics they do not think it proper to call a part of mathematics, as others do, though they admit that it sometimes uses calculation... and sometimes geodesy, as in the division and measurement of encampments" (Friedlein, p.38).Even Herodotus does not identify geometry and geodesy, but only claims that the origin of the former might have had it origin in the later (

the Histories,II.109).

*Geometry* appears in English in 14th century manuscripts. An anonymous
14th century manuscript begins, "Nowe sues here a Tretis of Geometri wherby
you may knowe the heghte, depnes, and the brede of mostwhat erthely thynges"
(Smith vol. I, page 237). The OED shows another 14th century use.

The term **GEOMETRY OF NUMBERS** was coined by Hermann Minkowski
(1864-1909) to describe the mathematics of packings and coverings.

**G淗EL'S INCOMPLETENESS THEOREM.** The term *G鐰el's theorem*
was used by Max Black in 1933 in *The Nature of Mathematics* (OED2).

In 1955 K. R. Popper in P. A. Schilpp Philos. of R. Carnap (1963) refers to his "two famous incompleteness theorems" (OED2).

**GOLDEN SECTION.** According to *Greek Mathematical Works I -
Thales to Euclid* (which is Loeb 335): "This ratio is never called the
Golden Section in Greek mathematics. The name appeared in print for the
first time, as the goldene Schnitt, in *Die reine Elementar-Mathematik*
by Martin Ohm (1835)." This citation is from a footnote on page 510 [John
Conway].

According to an Internet web page, Euclid used *Reliqua Sectio*
and Leonardo used *Sectio Aurea.*

According to Schwartzman (page 100) *golden section* was apparently
first used in print in 1835 by Georg Simon Ohm.

According to Smith (vol. 2, page 291), "This term seems to have come
into general use in the 19th century. It is found in the *Archiv der
Math. und Physik* (IV, 15-22) as early as 1844."

The term **GOODNESS OF FIT** is found in the sentence, "The 'percentage
error' in ordinate is, of course, only a rough test of the goodness of
fit, but I have used it in default of a better." This citation is a footnote
in "Contributions to the Mathematical Theory of Evolution II Skew Variation
in Homogeneous Material," which was in *Philosophical Transactions of
the Royal Society of London* (1895) Series A, vol 186, pp 343-414 [James
A. Landau].

**GOOGOL** and **GOOGOLPLEX** are both dated 1938 in MWCD10. Both
terms were coined by Milton Sirotta, nephew of American mathematician Edward
Kasner (1878-1955), according to *Mathematics and the Imagination*
(1940) by Kasner and James R. Newman:

Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out.This quotation was taken from the article "New Names for Old" found in

**GRAD** or **GRADE** (hundredth of a right angle). *Gradus*
is a Latin word equivalent to "degree."

Nicole Oresme called the difference between two successive *latitudines*
a *gradus* (Smith vol. 2, page 319).

*Grade,* defined as a hundredth of a right angle, is found in 1898
in *Houston Elec. Dict.,* in which both spellings are given. [Joanne
M. Despres of Merriam-Webster Inc.] The term may have been used in the
unpublished French *Cadastre* tables of 1801.

**GRADIENT** was introduced by Horace Lamb (1849-1934) in *An Elementary
Course of Infinitesimal Calculus* (Cambridge: Cambridge University Press,
1897):

It is convenient to have a name for the property of a curve which is measured by the derived function. We shall use the term "gradient" in this sense.Sylvester used the term in a different sense in 1887 (OED2).

The *DSB* says that Maxwell introduced the term in 1870; this seems
to be incorrect.

**GRAHAM'S NUMBER.** The term "Graham-Spencer number" appears in
N. D. Nenov and N. G. Khadzhiivanov, "On the Graham-Spencer number," *C.
R. Acad. Bulg. Sci.* 32 (1979).

The term "Graham's number" appears the 1985 *Guinness Book of World
Records,* and it may appear in earlier editions of that book.

The number is discussed in M. Gardner, "Mathematical Games," *Sci.
Amer.* 237, Nov. 1977.

**GRAPH (older sense, noun)** is due to Sylvester, according to the
OED2, which states that he shortened the word *graphic* and applied
it to mathematics. The OED2 shows a use of the term by Sylvester in 1878
in *American Journal of Mathematics* I. 65.

The phrase *graph of a function* was used by Chrystal in 1886 in
*Algebra*
I. 307: "This curve we may call the graph of the function" (OED2).

**GRAPH (verb)** is found in 1898 in Perry, *Applied Mechanics*
21: "Students will do well to graph on squared paper some curves like the
following" (OED2).

**GRAPH (in graph theory)** "appears to have been coined by A. Cayley,"
according to an Internet web page.

However, Martin Gardner wrote in *Scientific American* in April
1964, "In the 1930s, the German mathematician D幯es K霵ig made the first
systematic study of all such patterns, giving them the generic name 'graphs.'"
K霵ig published *Theorie der endlichen und unendlichen Graphen* in
Leipzig in 1936.

*Graph theory* appears in English in W. T. Tutte, "A ring in graph
theory," *Proc. Camb. Philos. Soc.* 43, 26-40 (1947).

**GREAT CIRCLE** was used by John Davis in *Seamans Secrets,*
which was written in 1594: "Navigation consiseth of three parts, ... The
third is a great Circle Navigation, which teacheth bow upon a great Circle,
drawn between any two places assigned (being the only shortest way between
place and place) the Ship may be conducted and to performed by the skilful
application of Horizontal and Paraboral Navigation."

**GREATEST COMMON DIVISOR** in Latin books was usually written as
*maximus
communis divisor.*

Cataneo in 1546 used *il maggior commune ripiego* in Italian.

Cataldi in 1606 wrote *massima comune misura* in Italian.

In 1881 G. A. Wentworth uses the phrase "highest common factor" in *Elements
of Algebra,* although the phrase "G. C. M. of *a* and *b*"
is found, where the context shows he is referring to the greatest common
divisor [James A. Landau].

*Greatest common divisor* is found in English in "A New Definition
of the General Abelian Linear Group," Leonard Eugene Dickson, *Transactions
of the American Mathematical Society,* Vol. 1, No. 1. (Jan., 1900).
The term may also occur much earlier.

**GREEN'S THEOREM** appears in the 1902 *Encyclopaedia Britannica*
[James A. Landau].

**GROEBNER BASES.** Bruno Buchberger introduced Groebner bases in
1965 and named them for W. Gr鐽ner (1899-1980), his thesis adviser, according
to *Ideals, Varieties, and Algorithms* by Cox, Little, and O'Shea
[Paul Pollack].

The term **GROUP** was coined (as *groupe* in French) by Evariste
Galois (1811-1832). According to Cajori (vol. 2, page 83), the word group
was first used in a technical sense by Galois in 1830. The modern definition
of a group is somewhat different from that of Galois (Hans Wussing, "Die
Genesis des abstrakten Gruppenbegriffes," Berlin 1969; translated as "The
Genesis of the Abstract Group Concept," M.I.T. Press 1984.). [Ken Pledger]

The term **GROUP OF AN EQUATION** was used by Galois (Kramer).

**GROUP THEORY** is found in English in 1898 in *Proc. Calf. Acad.
Science* (OED2).

**GRUNDLAGENKRISIS** (foundational crisis). Walter Felscher writes,
"As far as I am aware, 'Grundlagenkrisis' was a term invented during the
Hilbert-Weyl discussion between 1919 and 1922, occurring e.g. in Weyl's
*鈁er
die neue Grundlagenkrise der Mathematik,* Math.Z. 10 (1921) 39-79."