The phrase "a system of mathematics" is correct and usable in written English.
You can use it when discussing a structured approach or framework within the field of mathematics.
Example: "In this course, we will explore a system of mathematics that emphasizes problem-solving and critical thinking."
Alternatives: "a mathematical framework" or "a mathematical structure".
And the reason for focusing on the language of set theory is that it is a universal language in the sense that any system of mathematics is mutually interpretable with a theory formulated in the language of set theory; for example, PA is mutually interpretable with ZFC−Infinity.
Hilbert also saw (again, dimly) that the consistency of a system of higher mathematics entails that this system is at least partially arithmetically sound.
But the plot soon proves as elusive as the boffin, rapidly abandoned in favour of increasingly bizarre left turns and hilarious digressions, including a hilarious routine about devising a new system of mathematics.
That a general answer is necessary is clear from the demands of Hilbert's proof theory, i.e., it is not to be expected that given a formal system of mathematics (or even a single sequence of formulas) one can "see" that it is consistent (or that it cannot be a genuine derivation of an inconsistency) the way we can see, e.g., that 11 + 111 = 111 + 11.
Or maybe just as Eddie Lampert has always touted that he has found a new form of retailing, perhaps the same can be said about his coming up with a new system of mathematics.
Mathematics- Research an ancient system of mathematics.
Self-referential statements also profoundly influenced Gödel in his famous incompleteness theorems that destroyed the hope of a complete axiomatised system of mathematics.
Translated into an Aristotelian manner of discourse, meaningful interactions between individuals could be transferred to an equally rational closed system of mathematics: an arithmetic for simple transactions, an algebra for solving certain well-delimited puzzles, a calculus to simulate changes, rates and flows, and a geometry for purposes of illustration and model construction.
I know adult numeracy is a problem – but under no system of mathematics that I am aware of does 22 out of 46 represent 80 per cent". A spokesman for Cable's department said his figures were based on statements from universities and press reports.
The main subject was his own system of mathematics, which he has been evolving for nearly half a century, and which underlies all his work in other fields.
