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I had a professor point out that it is odd we refer to more than one chain complex as "complexes." It seems that in most other definitions in math we stick to the typical latin plural, i.e. we say vertices instead of "vertexes", matrices instead of "matrixes". So why do we say "complexes" instead of complices when referring to more than one chain complex?

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    $\begingroup$ I don't think this belongs to history of science. This is a question about English language. $\endgroup$ – Alexandre Eremenko Mar 14 '17 at 23:53
  • $\begingroup$ Alexandre is correct, and this question has already been answered: english.stackexchange.com/questions/277945/… (and more amazingly, the question wasn't marked as off-topic!) $\endgroup$ – Tim Mar 15 '17 at 19:30
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Because unlike vertex, matrix or simplex, that came directly from Latin and have primarily mathematical uses, complex was borrowed through French around 1650s, with the meaning "a whole comprised of parts". By the time of entering mathematics as a noun it already had colloquially established plural in English, complexes.

It is similar with apexes, annexes, and most ironically syntaxes, regular speakers tend to ignore the pedantries of etymology. Appendices are an exception, possibly because appendixes is awkward to pronounce. Wiktionary does list complices as archaic plural. Here is from Wikipedia's English plurals:

"The general trend with loanwords is toward what is called Anglicization or naturalization, that is, the re-formation of the word and its inflections as normal English words. Many nouns (particularly ones from Latin) have retained their original plurals for some time after they are introduced. Other nouns have become Anglicized, taking on the normal "s" ending. In some cases, both forms are still competing".

Perhaps Latin being the language of science and mathematics for a long time made them more resistant to Anglicization than the general public.

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