What do mathematicians dispute about, or on the ontological status of the objects of mathematics

In this article the author considers various conceptions concerning ontological status of the objects of mathematics. The relation is show between these problems and a dispute over universals, and then Platonism, conceptualism and nominalism as the fundamental standpoints on the question o f mathematical objects are presented. Examples are given of concrete (specific) theories w ith in these standpoints and their implications (also epistemological ones) are shown.In this article the author considers various conceptions concerning ontological status of the objects of mathematics. The relation is show between these problems and a dispute over universals, and then Platonism, conceptualism and nominalism as the fundamental standpoints on the question o f mathematical objects are presented. Examples are given of concrete (specific) theories w ith in these standpoints and their implications (also epistemological ones) are shown