C’est parce que la simplicité, parce que la grandeur est belle, que nous rechercherons de préférence les faits simples et les faits grandioses, que n… - Henri Poincaré

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.

C'est même des hypothèses simples qu'il faut le plus se défier, parce que ce sont celles qui ont le plus de chances de passer inaperçues.

The axioms of geometry, therefore, are neither synthetic a priori judgments nor experimental facts.
They are conventions; our choice among all possible conventions is guided by experimental facts; but it remains free and is limited only by the necessity of avoiding all contradiction. . . .
In other words, the axioms of geometry (I do not speak of those of arithmetic) are merely disguised definitions.
Then what are we to think of that question: Is the Euclidean geometry true?
It has no meaning.
As well ask whether the metric system is true and the old measures false.