Mathematics “has no generally accepted definition,” according to Wikipedia on September 15, 2020, with two references. On September 14, 2023, the assertion is, “There is no general consensus among mathematicians about a common definition for their academic discipline”; this time, there are no references.
I suggest that what really has no generally accepted definition is the subject of mathematics: the object of study, what mathematics is about. Mathematics itself can be defined by its method. As Wikipedia says also (as of either date given above),
it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.
I would put it more simply. Mathematics is the science whose findings are proved by deduction.
The right triangle whose legs are 3 and 4 has hypotenuse 5, because the square on it is
(4 − 3)2 + 2 ⋅ (4 ⋅ 3),
which is indeed 25 or 52. This is also
42 + 32.
Polytropy 