The plural(s) of 'index' in U.S. dictionaries
Both Merriam-Webster's Eleventh Collegiate Dictionary (2003) and The American Heritage Dictionary of the English Language (2010) give indexes and indices as acceptable plurals of index—but both of them list indexes first and indices second, which their way of indicating that indexes is the more common (or the preferred) plural, according to their assessment.
Today, the online versions of these dictionaries continue to support the preferences given in print a decade or more ago.
index noun | plural indexes or indices
index n. pl. indexes or indices
Having said that, I note that an Ngram chart plotting relative frequency of indexes (blue line) and indices (red line) for the period 1750–2019 shows a widening advantage for indices in the published works included in the Google Books database over the past thirty years or so:
I note that the results for "indexes" tracked in this Ngram chart include instances where "indexes" appears as a singular verb (as in "She indexes academic books for a living"), as well as instances where it appears as a plural noun; in contrast, the results for "indices" include only instances of the word as a plural noun. So the advantage for indices over indexes as a plural of index in the Google Books database is probably somewhat (although not a lot, to judge from my spot-checking of the actual matches underlying the data plots in the chart) larger than the chart suggests.
A further point of interest is that one of the six definitions of index covered in Merriam-Webster's entry for index as a noun includes a remark that the plural for index when used in this particular sense is usually rendered as indices:
index n ... 4 pl usu indices : a number or symbol or expression (as an exponent) associated with another to indicate a mathematical operation to be performed or to indicate use or position in an arrangement
None of the other definitions in the MW entry for index—and none of the six entries for index as a noun in AHDEL—indicate a "usu" plural form of index as between indexes and indices.
Discussions of 'indexes' versus 'indices' in U.S. style guides
Bryan Garner, Garner's Modern American Usage, third edition (2009) may have had the order of plural entries for index in MW and AHDEL in mind when he addressed the issue of indexes versus indices:
Index. A. Plurals. For ordinary purposes, indexes is the preferable plural, not indices [examples omitted].
Indices, though less pretentious than fora or dogmata, is pretentious nevertheless. Some writers prefer it to indexes in technical contexts, as in mathematics and the sciences. Though not the best plural for index, indices is permissible in the sense "indicators"—e.g., "Various indices, from satellite photos of crops in the Third World to emergency room reports of overdoses in America's inner cities, [...]"
Garner goes on to note that some writers at least occasionally use the harder-to-defend forms indeces (plural) and indice (singular).
Kenneth Wilson, The Columbia Guide to Standard American English (1993) notes that both plural forms are currently standard in English and then focuses on the idea of "foreign plurals" versus "regular English plurals":
index (n.) has two Standard plurals: indexes (pronounced IN-deks-iz) and indices (pronounced IN-di-SEEZ). See FOREIGN PLURALS [where Wilson makes the following relevant observations: "But when loan words cease to deem foreign, and if their frequency in English increases, they very often drop the foreign plural in favor of a regular English -s. Thus at any given time we can find some loan words in divided usage, with both the foreign plural (e.g., indices) and the regular English plural (e.g., indexes) in Standard use."]
Wilson seems to take the view that, all things else being equal, indexes will eventually win out over indices as index becomes less and less a foreign loan word and more and more a naturalized English word. This same expectation probably underlies Garner's view that insisting on retaining a word's original "foreign plural" form is pretentious once the word (in its singular form) has been fully subsumed into everyday English.
Other style guides offer more perfunctory treatment of the issue. For example, from Frank Vizetelly, A Desk-Book of Errors in English, revised edition (1920):
indices : A plural form of index, generally and more properly reserved for use in science and mathematics. In other cases the plural indexes should be used.
From Roy Copperud, American Usage and Style: The Consensus (1980):
indexes, indices. The first is the Anglicized form, the second the Latin form. Indexes is recommended.
From The New York Times Manual of Style and Usage, revised edition (1999):
indexes (not indices).
From Bill Bryson, Bryson's Dictionary of Troublesome Words (2002):
indexes, indices. Either is acceptable, though some dictionaries favor indices for technical applications.
British and Canadian commentators' views of 'indices' versus 'indexes'
Thus far I have focused on U.S. style guides, but British and Canadian style guides have also weighed in on the question. From H.W. Fowler, A Dictionary of Modern English Usage (1926/1937):
LATIN PLURALS ...More often the Latin & English forms are on fairly equal terms, context or individual taste deciding for one or the other: dogmas, formulas, indexes, hiatuses, & gladioluses, are fitter for popular writing, while scientific treatises tend to dogmata, formulae, indices, hiatus, & gladioli. ... All that can safely be said is that there is a tendency to abandon the Latin plurals, & that when one is really in doubt which to use the English form should be given the preference.
From Eric Partridge, Usage and Abusage: A Guide to Good English (1947):
indices; indexes. The former is obligatory in Mathematics and Science; indexes is correct for 'an index of names, subjects, etc.'; in all other senses, indices is now the more usual plural.
From Margery Fee & Janice MaAlpine, [Oxford] Guide to Canadian English Usage, second edition (2007):
Latin plurals Most English words derived from Latin form their plurals in the regular way, by adding -s or -es, and this is the safest choice if you are in doubt[cross-reference omitted]. However, there are some Latin borrowings that still form their plurals according to the rules of Latin, at least in formal contexts:
– singular ends in -ex or -ix, plural in -ices: appendix, appendices; cortex, cortices, index, indices; matrix, matrices
Style guides seem to agree generally that the plural of index in a mathematical or scientific setting is commonly—and arguably properly—rendered as indices. As for the plural in nonspecialist settings, many sources—especially in the United States—endorse indexes as the plural, but most acknowledge that neither form is incorrect.
At the management consultancy where I've been working for the past several years, the general house style rule is to follow the spelling preferences laid out in the latest edition of The American Heritage Dictionary of the English Language. As I noted earlier, AHDEL gives the nod to indexes—but in this instance the consultancy's house style guide overrules that preference and opts for indices:
indices (not indexes)
Whether this decision reflects pretentiousness, a desire to look as scientific as possible, or simple affection for Latin plural forms, I can't say. But it is symptomatic of a striking and sustained effort (evident in the Ngram chart above) among U.S. and British English writers to resist the Anglicization of indices to indexes—even though such Anglicization is, as Henry Fowler noted almost a century ago, the usual tendency in dealing with a foreign plural as the singular form of the word becomes naturalized into common English.