سوال ۱۲ کنکور ارشد ریاضی ۱۴۰۴

PASSAGE 1

The traditional view of the nature of mathematics, which goes back at least as far as Plato and which is still current in mathematics departments today, is that mathematics is the purely rational study of immaterial forms. Mathematics, on this view, is concerned exclusively with objects like numbers, shapes, and functions which do not occur in the physical world, although they may have imperfect instances in the physical world. Thus, the geometer studies straight lines and perfect circles, but the lines he draws on the blackboard are not straight and the circles he draws are not perfect. Since the objects the mathematician studies are not physical, there is no way for him to have empirical knowledge about those objects. Thus, mathematics is an a priori discipline, independent of all experience. The Euclidean methodology, though rarely applied in practice, is still the ideal in principle. Mathematicians should deduce <u>their</u> theorems by logical inference from self-evident axioms. Any other source of mathematical knowledge may be heuristically useful, but is not strictly correct. As Plato says in The Republic (Book VI, 510), the objects that mathematicians study are “ideals which can be seen only by the mind”.

12. The underlined word “their” in the passage refers to …………………… .