"Maths" for "Mathematics"; where does the S come from?

Abbreviations and contractions of words follow many conventions, take for example the word continued I have seen it abbreviated/shortened/contracted or clipped in three ways.

• cont
• cont.
• cont'd

Mathematics can be similarly contracted

• math
• math.
• (math's) maths

Perhaps, originally, the written form with the apostrophe, math's, was more common in Great Britain but over time the apostrophe became obsolete. In fact the apostrophe in math's has no effect on its pronunciation. Unfortunately, I don't have access to the Oxford English Dictionary to confirm my suspicion that the term math's was ever used. The Online Etymology Dictionary instead states that the American math first appeared in 1890 while the British maths is attested from 1911.
Wikipedia has this to say on contractions:

An abbreviation is a shortening by any method; a contraction is a reduction of size by the drawing together of the parts. A contraction of a word is made by omitting certain letters or syllables and bringing together the first and last letters or elements; an abbreviation may be made by omitting certain portions from the interior or by cutting off a part. A contraction is an abbreviation, but an abbreviation is not necessarily a contraction.

Further on, Wikipedia explains

In British English, according to Hart's Rules, the general rule is that abbreviations (in the narrow sense that includes only words with the ending, and not the middle, dropped) terminate with a full stop, whereas contractions (in the sense of words missing a middle part) do not.

Curious to see whether I could find the apostrophe version, I turned to Google Books and found to my surprise that math's existed in the US, this example is dated 1836, and predates Word Detective's claim that the first instance of math appeared in 1847.

Larry Trask who was professor of Linguistics in Sussex University (UK) mentions the most common shortened forms where the apostrophe still survives.

A few words which were contractions long ago are still conventionally written with apostrophes, even though the longer forms have more or less dropped out of use. There are so few of these that you can easily learn them all. Here are the commonest ones, with their original longer forms:

• o'clock, of the clock
• Hallowe'en, Halloweven
• fo'c's'le, forecastle
• cat-o'-nine-tails, cat-of-nine-tails
• ne'er-do-well, never-do-well
• will-o'-the-wisp, will-of-the-wisp

EDIT

Published in Richmond USA by William F. Richie, 1853-54, The Merit Roll of the Cadets of the Virginia Military Institute, July 1853 lists math's as the shortened form for mathematics twice!

Personal Reflections

As demonstrated in the excerpts I provided, it seems clear that the spelling convention for contracted words i.e., the use of the apostrophe for showing the omission of letters, was also used in the US. The shortened form math's was necessary in order to save space but for some reason the superfluous apostrophe and the letter -S were kept despite logic demanding that the word math was shorter. The question also arises whether this contracted word was ever actually spoken by Americans? My guess? Probably not, they chose not to say maths /maθs/ because it sounded plural and therefore opted for the clipped form, math /maθ/ in speech. The British, being renowned traditionalists, decided to keep the "silent" apostrophe in speech and thus favoured the longer form maths.