Minimum or Minima, and Other Irregular Plurals in English

There seems to be widespread confusion about the use of the words minimum and minima (along with maximum / maxima) in a mathematical context.

These and a number of other words, all borrowed from Latin or Greek, have potentially confusing singular and plural forms.

In fact, minimum is the singular form, just as in normal English usage, and minima refers to two or more. Thus we can talk about x = a being a local minimum of a function f(x), meaning that for x = a, f(x) has a value that is lower than for nearby values of x.

Graph illustrating local/global minima

A function will often have several local minima, however - that is, several dips in its graph. (A local minimum is actually the bottom of a dip.)

One of these dips/minima will be lower than all the rest. In the scenario in the diagram, this lowest local minimum is referred to as the global minimum. Note that global means "everywhere"; there can only be one global minimum for f(x). In particular, it doesn't make sense to talk about ??"a global minima" (because "a" implies singular, and "minima" implies plural) or to talk about "global minima" unless you are talking about minima of two or more different functions.

"Local minima" of a function makes sense (assuming the function has more than one local minimum), but ??"a local minima" and ??"a minima" still are not right, as once again, "a" implies singular, and "minima" implies plural.

Similar rules apply to maximum and maxima, extremum and extrema, and optimum and the less often used optima.

Other unusual singular/plural forms in mathematical English

SingularSingular examplePluralPlural example
criterionsatisfy a criterioncriteriaseveral criteria
automatonthis automatonautomata several deterministic automata
matrixthis matrix has eigenvalues ...matrices these symmetric matrices ...
vertexfind a vertex ...vertices a triangle has 3 vertices
datumthis single datumdatathis collection of data
schemahere is a schema for for-loopsschemata some schemata for for-loops and if-statements

A longer list of mostly technical terms with Greek/Latin style plurals

PluralSingular
abscissaeabscissa
addendaaddendum
algaealga
alumnaealumna
alumnialumnus
alveolialveolus
analysesanalysis
annuliannulus
antennaeantenna
appendicesappendix
aquariaaquarium
atriaatrium
automataautomaton
axesaxis
bacillibacillus
bronchibronchus
cacticactus
caesuraecaesura
calculicalculus
catharsescatharsis
cicatricescicatrix
colloquiacolloquium
colossicolossus
compendiacompendium
consortiaconsortium
continuacontinuum
corporacorpus
corrigendacorrigendum
craniacranium
crisescrisis
criteriacriterion
curriculacurriculum
datadatum
desideratadesideratum
diaeresesdiaeresis
diagnosesdiagnosis
dictadictum
directricesdirectrix
dodecahedradodecahedron
effluviaeffluvium
ellipsesellipsis
emphasesemphasis
encomiaencomium
ephemeridesephemeris
equilibriaequilibrium
errataerratum
esophagiesophagus
extremaextremum
focifocus
fungifungus
generagenus
geniigenius
honorariahonorarium
icosahedraicosahedron
incubiincubus
infimainfimum
lacunaelacuna
locilocus
magimagus
matricesmatrix
maximamaximum
mediamedium
memorandamemorandum
milleniamillenium
minimaminimum
minutiaeminutia
modulimodulus
mycobacteriamycobacterium
nebulaenebula
neurosesneurosis
nucleinucleus
nucleolinucleolus
octahedraoctahedron
operaopus
optimaoptimum
ovaovum
periphrasesperiphrasis
phenomenaphenomenon
phylaphylum
placentaeplacenta
pleuraepleura
podiapodium
polyhedrapolyhedron
psychosespsychosis
pudendapudendum
pupaepupa
quantaquantum
radicesradix
radiiradius
referendareferendum
rhombirhombus
rostrarostrum
sacrasacrum
sanatariasanatarium
sanatoriasanatorium
sarcophagisarcophagus
scapulaescapula
schemataschema
septaseptum
seraserum
simplicessimplex
simulacrasimulacrum
solariasolarium
spectraspectrum
spermatozoaspermatozoon
stadiastadium
sternasternum
stigmatastigma
stimulistimulus
stratastratum
substratasubstratum
succubisuccubus
syllabisyllabus
symposiasymposium
synopsessynopsis
synthesessynthesis
terminiterminus
testestestis
tetrahedratetrahedron
thesesthesis
thrombosesthrombosis
toritorus
tumulitumulus
ultimataultimatum
umbiliciumbilicus
verrucaeverruca
vertebraevertebra
verticesvertex

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