Ignore the reference books that say maxima is the standard plural of maximum and that maximums is a primarily American form. These books are behind the times. Maximums is the standard plural in 21st-century English, and it is far more common than maxima in most types of writing throughout the English-speaking world.
Strictly speaking, maxima is more common overall than maximums, but that’s just because the plural of maximum is most useful in the types of writing—scientific, medical, and mathematical—that typically preserve Latin plurals long after they’ve outstayed their welcome elsewhere. Online stats are also skewed by the use of maxima in numerous species names and in the Latin loan phrase mea maxima culpa.
The English plural, as used in these examples, is preferred outside scientific writing:
Afternoon maximums are muted, only in the upper 40s to low 50s. [Washington Post]
However, higher annual maximums come at a price, and may not be as important for many young pets as for older ones. [Vet Confidential, Louise Murray]
[H]is two bosses over the period showed an apparently relaxed attitude to daily trading maximums being exceeded. [Guardian]
But maxima is easy enough to find if you look in the right places—for example:
Computing the coordinate-wise maxima and convex hull of a planar point set are probably the most classic problems in computational geometry. [“Self-improving Algorithms for Coordinate-Wise Maxima and Convex Hulls,” on arXiv.org]
Simple, two-phase algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. [“Maxima-finding algorithms for multidimensional samples: A two-phase approach,” on ScienceDirect.com]
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