When we say force is the cause of motion, we are talking metaphysics; and this definition, if we had to be content with it, would be absolutely fruit… - Henri Poincaré

Point set topology is a disease from which the human race will soon recover.

What we call objective reality is, in the last analysis, what is common to many thinking beings, and could be common to all; this common part, we shall see, can only be the harmony expressed by mathematical laws. It is this harmony... which is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.

John Stuart Mill understood the word existence in a material and empirical sense; he meant that in defining a circle we assert that there are round things in nature.
In this form his opinion is inadmissible. Mathematics is independent of the existence of material objects. In mathematics the word exist can only have one meaning ; it signifies exemption from contradiction.