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If we are going to start quoting individuals here is G.H Hardy one of the greatest Pure Mathematicians of the 20th century.
"... and there is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is 'mental' and that in some sense we construct it, others that it is outside and independent of us ... I believe that mathematical reality lies outside of us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations."
The whole point is that there is no definitive answer.
Steven
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