My thoughts on your three questions:
1. The word “maths” for mathematics is chiefly British usage, so it’s not only grammatically acceptable but also semantically airtight for, say, a UK career guidance counselor to tell you that “Maths is an essential tool for success” even if the logic of that advice may not be entirely defensible. But if the counselor saying that is a certified American from the Continental U.S., or else a Filipino math major who took advanced studies in the U.S., you can be 99.99% sure that his or her usage of “maths” is a mere affectation or just a lingering side effect of watching too many movies about British school life. Just keep in mind that in the American English Standard, which is the standard used in the Philippines, the undisputed usage is the whole word “mathematics” or the abbreviated “math” (without the suffix “-s,” and without a period as well).
2. A
number is an abstract count of things or an imaginary representation of how many there are of those things, while a
numeral is the way people express that number—that count—in writing. For instance, a count of five things can be expressed as the number “5” in the Hindu-Arabic numeral system, as “V” in the Roman numeral system, as “0101” in the binary numeral system, and as the word “
lima” in the Tagalog numeral system.
To give you a clear idea and an adequately broad intercultural context for the usage of the words “number” and “numeral,” let me quote from
“The Tree of Life,” an essay of mine that’s posted in the Forum: “The Chinese may have invented paper, the abacus, and gunpowder, and the Romans may have built their empire that extended all the way to Africa and to the banks of the Mesopotamian River in what is now modern Iraq, but I simply cannot conceive of the modern computer built from Chinese script or from the Roman
numeral system, with which no stable building taller than the Roman Coliseum could be built because the system simply could not multiply and divide
numbers properly.”
3. One of the denotations of the preposition “of” is “relating to” or “about.” This is the sense when “of” is used as lead word in such titles as
Of Mathematics,
Of Studies, and
Of Mice and Men. By some literary alchemy, using “of” instead of “relating to” or “about” makes such titles more engaging and momentous. How drab and commonplace those titles would sound if they were phrased instead as
Relating to Mathematics, Relating to Studies, or
About Mice and Men! Indeed, in literary prose, the choice of preposition can sometimes make a big world of difference in reader interest and readability.
