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.

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

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

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