I'm reading a very interesting book by a Bill Barton right now called, The Language of Mathematics; telling mathematical tales (ISBN 978-0-387-92937-8). He's describing attempts at creating a maths curriculum for Maori schools.
The book got me thinking about whether there is an English word for "mathematics". The word is of Greek origin: μάθημα máthēma, “knowledge, study, learning” but there seems to be no word in the English language for "mathematics". The etymology of "arithmetic" is even more convoluted covering, it seems, the whole Indo-European language family except English. There is tælcræft, lit. "tell-craft" that seems to have been rejected early on.
In the synopsis of the book it says "Simple English language statements are expressed quite differently in some other languages, not simply represented with different vocabularies or an underlying base of the number system". What he means here is that some languages may treat numbers as if they were verbs: the bottles are three-ing on the table; my fingers five (p. 5) - all very well in linguistics analysis though it may sound a bit strange in everyday English. But these are grammatical functions (ie, not -emically different than treating numbers as adjectives as English does: five, little ducks, for eg) not to be confused with statements like when he claims that 1 + 1 = 2 may not necessarily be "true" in other languages.
I'm just in the beginning of the book, but he says that he'll "challenge the idea that mathematics is the same for everyone, that it is an expression of universal human thought - and explain the questions about the bridge and 1 + 1 posed incredulously above" (p. 8). Tælcræft, I look forward to it.
Understandably, he tells of a Maori woman demanding a change in some constructed word that was being "misused" by children that she overheard (upwards talk) for the word "praise". But I think this is confusing the "grammaticalization" problem with the "lexicalization" problem. Let me try and explain:
I was talking to a very excellent friend of mine a few years ago when he described to me that some Inuit children were starting to simplify the words for "deep" and "shallow" (in Inuktitut, one says itijuq for "it is deep" and ikkattuq for "it is shallow") using the word for "deep" as the base and inserting the negation [-nngit-] and dimunitive [-kuluk-] to denote "shallow" = *itinngittukuluk.
This is a lexical error but not a grammatical error, strictly speaking. It is like over-extending the prefix [de-] (as in demoralizing) to other words that may not readily accept the prefix: *decontinued rather than discontinued.
The problem with constructing neologisms, especially specialist terms, is that it is often forgetten or neglected to define the newly minted term in logically productive terms, let alone provide an explanation that the new term is different from common usage of the root, that it means something highly specific in highly specific context (providing examples where the new term is acceptable and where it is not acceptable, say).
This is a huge problem in Inuktitut terminology exercises where explanatory phrases tend to be used rather than lexicalized root nouns or verbs that are grammatically/logically productive. An over-used example: the now-accepted term for "uranium" nungusuittuq which loosely translates as "that which never depletes, or never-ending (source of energy)", which makes sense in some way but is not entirely true or accurate enough for productive discourse. In an ideal situation, one could have looked into the notion of "radioactivity"/"beta-decay" and constructed and defined a better, more useful term: say, tangiingajuq or some other invented term (doesn't really matter as long as we can define it specifically; in fact, the more removed from common usage the constructed term the better to minimize confusion), and describe what the new term means or denotes and how it fits in the larger scheme or framework of quantum chemistry.
Now, back to the question: Is there a word for "mathematics" in English? -the answer is yes and no. The original Greek term does not make any outward reference to the notions of "number", "numeral manipulation" or "quantology" for that matter, but the English usage is common enough to be understood by laity (though specialists would argue that their field of study should rightly be called "set theory" "algebra" "geometry", etc, etc.)- like nungusuittuq I guess.