Why is "math" always pluralized in British English but singular in American English?

Math or Maths are shortenings of "mathematics". As mathematics is a plural it is generally held that the abbreviation should be a plural (except in the US). Thus "maths"

Although "math" is widely adopted It isn't correct.

It seems to me that mathematics is plural in form but used as a singular. The English abbreviation is essentially a reduplicated plural which in my mind is redundant and doesn't make much sense considering how both the English and Americans use it (that is, "math is fun, maths is fun" and not "math are fun, maths are fun").

The abbreviation should at least have a verbal agreement and because its use is singular; it should be used with a singular verb without a reduplicated plural.

The subject (singular) 'mathematics' incorporates many different types of calculations and equations etc. (plural), and therefore the correct abbreviation is 'maths'. However the word 'math' would be okay if used as an abbreviation for 'mathematical' (singular). An example would be "my math may be wrong", where the person means "my mathematical calculation may be wrong".

It's really quite simple but the American approach does have a certain elegance to it, they've taken proper English and dispensed with the somewhat unnecessary letters that really have no meaning, such as 'silent' letters like the u in colour or harbour. We Brits can hardly complain though because for some bizarre reason, there's no u in the number forty, which really ought to mean that a structure is similar to a fort (fortress)!

According to Merriam-Webster's Eleventh Collegiate Dictionary (2003) the short-form word math for mathematics goes back to circa 1847, whereas the "chiefly Brit" short-form word maths for mathematics goes back only to 1911.

Google Books and Elephind searches, however, turns up some interesting details about usage of Math. and Maths. from an earlier period when the words seem to have been written abbreviations of mathematics, not spoken short-form words in their own right. As you might expect, the earliest instances of both Math. and Maths. appear explicitly in the context of abbreviations for mathematics in tables, summaries, or general text where certain other words are likewise severely shortened. In all of these instances, a period follows the abbreviation.

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Early 'Math.'

From The Ladies Diary: Or, Women's Almanack, for the Year of Our Lord 1795 (1795) [combined snippets]:

If the earth's diameter be 7957 ¼, its circumference will be 25ooo; therefore 25000 : 360° :: 20 : 17' 16" ⅘, the arc of a great circle on the earth in the given distance of 20 miles. But, by Doctor Hutton's Math. Tables, 2d edit. the versed sine of 17' 6" ⅘, to radius 1, is .0000126; and therefore .0000126 x 3978.875 = .0501338 mile = 88.235488 yards, the versed sine or height of the segment seen, = the height of the eye above the earth's surface; ...

From The Cambridge University Calendar for the Year 1822 (1822):

Assistant-Tutors,

Wm. Whewell, M.A. Math. | R. W. Evans, M.A. Class. | G. Peacock, M.A. Math.

From The Massachusetts Register and United States Calendar (1824):

PROFESSORS

Prof. of Math. & Nat. Phil. James Dean, A.A.S.

Prof. of Learned Languages, Lucas Hubbell, A.M.

Lecturer on Surgery and Theory & Prac. of Physic, Nathan R. Smith, M.D.

The first two instances of Math. above are from England; the third is is from the United States.

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Early 'Maths.'

From a column headed "In what branch deficient," in a table titled "Report of the Progress, Aptitude, and Habits of certain Cadets of the Fourth Class," in Regulations for the Military Academy by the President of the United States (1839):

Mathematics. | Mathematics. | Maths. and French. | Maths. and French. | Maths. and French. | French. | French. | Maths. and French. | Maths. and French. | Maths. and French.

The "Teachers' Bulletin" section at the back of American Educational Monthly (February 1864) uses the abbreviation "Maths." dozens of times over the course of a three-page advertisement Here is a brief excerpt from this ad:

Ladies — English, Mathematics, French, Latin, Drawing, etc.

1—Grad. Van Norman Inst.; expr. 1 year; Eng. branches and French; salary depends on duties.

2—Expr. 2 years; Eng. and Maths.; salary depends on duties.

3—Ed. at Miss Ward's Sem.; expr. 6 years; Eng., Maths., French, and Drawing; Episcopalian; salary depends on duties.

4—Grad. Phipps's Sem.; expr. 8 years; Eng., Maths., French, and German; salary depends on duties.

From "St. Andrew's College, Bradfield," in School Inquiry Commission, volume 11, South-Eastern Division (1868):

8. Edward Wilkinson.—Scholar of Ex. Coll., Oxford, 1860, ; 2nd Class in Mods. (Maths.), 1862 ; 2nd Class in Final Classical School, 1864.

...

11. William Targett Fry, Exeter College, Oxford.—2nd Class in Mods. (Maths.), 1862 ; 2nd class in Final Schools (Maths.), 1864.

...

18. Frederick Hume Talbot.—Junior student (Maths.) of Ch. Ch., 1865.

From Francis Drake, Dictionary of American Biography (1876):

Chauvenet, William, LL.D., mathematician, b. Milford, Pa., 1820; d. St. Paul, Minn., 13 Dec., 1870. Y.C. 1840. He was first employed in taking meteor. observations at Girard Coll. Obs.; became in 1841 instr. in maths. at the U.S. Naval Asylum, Phila.; prof. of astron. and maths. at the Naval Acad., Annapolis, 1845–59; prof. of astron. and maths. at Wash. U., St. Louis, 1859–62; chancellor of the U., 1863–9.

In this group of four instances of Maths., the first, second, and fourth instances are from the United States; the third is from England.

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Emergence of the short forms in regular speech

From a series of journal entries by John Maury written in October 1860, reprinted in John Johnson, The University [of Virginia] Memorial (1871):

"Monday, Oct. 15. Up until 2 o'clock to-night, studying Math."

"Wednesday, Oct. 17. Rose this morning at half-past 8. Rather later than usual. Joe did not wake me up."

From "Rallying Round a Candidate," in the [New York] Sun (June 4, 1893), reprinted from the St. Louis [Missouri] Globe-Democrat:

With scarcely an exception every Federal officer now living who had fought against Kirby Smith has made a personal appeal for his daughter. Soldiers of Bull Run and Manassas scrawled out letters of recommendation, while the Cove people in the mountains added their testimonials to the worth of Kirby Smith's daughter in characteristic dialect, such as is found in Craddock's stories of the hills. The students of the institution where the general had so long taught "math" sent their endorsements, couched in elegant diction and sophomoric phrases.

From "A Protest Against Modern Foot-Ball," in the Richmond [Virginia] Dispatch (November 19, 1897):

If the boys received pay for playing [football], it might alter the case a little, but not much. I am speaking especially to our home college. If Professor Boatwright's chaps can't find enough exercise and mental training playing golf, tennis, gymnastics, and studying "Math.," why not buy several acres of ground and make those boys go to ploughing and planting potatoes and corn? If they continue to play ball they will have to go back on the farm, and it would be well for them to know one thing well.

From "Straight Tips," in Blue and Gold: Being a Record of the [University of California] College Year (1901):

Miss L. I. DE Yo–That I have an ardent male admirer studying Math. in Switzerland, and that I wear a chess pin and an engagement ring.

The preceding four instances of math come from U.S. sources in the context of school studies. What distinguishes them from their Math. predecessors is the conversational context in which they appear, as well as the absence of other abbreviations nearby. These instances give the impression of reflecting real-world spoken use of math as a short-form alternative to mathematics. In contrast, the earlier instances seemed to be reducing the word mathematics to a single syllable simply to fit a narrow space or a constricted citation style.

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From a letter by Charles Sorley of November 24, 1912, in The Letters of Charles Sorley (1919):

I am quite befoozled. I have just finished my weekly hour's course of Walter Pater. That creature has been foisted on me by Gidney and I have to read an essay of his every week. This is only the second week so I really ought not to give an opinion, but I think he is the dullest and most stilted author I have ever read. ... It is a bore because otherwise I have found I have learnt more by giving up maths. than in the whole time I did them, as instead of maths. I do English with Gidney and (except when he is obsessed by Pater) he is a very inspiring teacher.

From a brief item in the [Sydney, New South Wales] Evening News (July 10, 1920):

Dr. Mannix to Teach "Maths"

NEW YORK, Friday. It is announced that Dr. Mannix has been appointed De Valera Professor of Mathematics at Maysooth College, Ireland.

From Oliver Onions, A Case in Camera (1921):

He knew very little about himself—hardly seemed aware that there was anything of importance to know. It was all Maxwell—"Bobby was the whole show," And I had a very keen sense of the honor the dead man had done himself in denying this. "Frightfully hot stuff on maths," said Smith ; and the world is full of men who are "frightfully hot stuff on maths," in that sense ; but it is rarely that you find one of these not too absorbed in the technique and detail of his own activities to be aware of a vision beyond.

Sorley and Onions were both British. Sorley attended Oxford; Onions, what later became the Royal College of Art.

Also, from a letter to the editor of the Sydney [New South Wales] Morning Herald (November 14, 1921) by Kathleen Oxley:

Mathematics, trigonometry, Latin, and Greek have been condemned by some of the writers as unnecessary waste of time for women, but a knowledge of some of these subjects is necessary for any girl who wishes to take up certain professions. It has been admitted even by the conservatives that architecture is a suitable profession for women, but for this she needs higher mathematics, and mathematics must be studied in school days. It is too late to begin and study maths, at 17, after a girl has decided that she wishes to be an architect. Then, many a woman has a keen love of literature, and to such a one a sound knowledge of Latin and Greet would be an inestimable blessing. I speak from experience. My work is all In my home, but I would give much to have the knowledge of Latin, Greek, and mathematics possessed by many of tho girls growing up to-day. That knowledge will never prevent them excelling in domestic arts. I have seen my kitchen filled with university girls in their vacation, all keen on concocting dainty dishes for little suppers, and they have done it well, too. In Australia since we have had compulsory military training every boy Is fitted for the duty of defending his country by n system which in no way interferes with his general education. No one dreamt of suggesting that instead of Latin, Greek, and maths, he should be taught the use of arms. Why cannot we have a similar system of compulsory domestic training for girls, so that those who have homes of their own will know how5- to manage them? No more time need be devoted to tho learning of actual domestic work than Is devoted by the boys to their military training, and then the girls' general education could be as free as the boys'.

Of these four instances, two are from Britain and two from Australia. The same observations about conversational style apply to these instances as to the instances of math cited in this section of my answer: even when a period persists in the orthographic representation of maths, the context strongly suggests that the word is spelled as it is to reflect a short-form word in spoken use, not merely a convenient written abbreviation designed to save space on the page.

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Conclusions

The prehistory (as it were) of math and maths prior to their emergence as common short-form alternatives to mathematics is more complicated than I had expected. The abbreviation Math. goes back to at least 1795, and the abbreviation Maths. to at least 1839, but occurrences do not strictly follow today's regional preferences: the two earliest instances of Math. that I found are from England, and the two earliest instances of Maths. are from the United States.

Nevertheless, the modern preference in the United States for the short-form word math in casual discourse appears to have taken hold by the 1890s, and the corresponding modern preference in Britain and Australia for maths seems to have become well established by 1920. I have not found any persuasive explanation of why these differing preferences emerged.