An ongoing debate:
A discussion (actually review of a John Barrow book) centering around the long-time debate over whether mathematics objectively exists in reality or is merely a creation of the human mind.
...And plenty more food-for-thought here:
Nice article at Wikipedia giving overview of "philosophy of mathematics;" includes many links:
...and similar "Foundations of Mathematics" article also at Wikipedia:
Relatedly, possibly worth mentioning a 2009 book from Jeremy Gray "Plato's Ghost: The Modernist Transformation of Mathematics," which narrates the evolution of mathematical thought from 1880 to the 1920s:
an online review here: