One of the debates that interests me is scientific realism vs anti-realism.
To summarise:
Realism: Science/maths represents a deeper platonic reality. For example a realist would say that the space-time continuum is something that actually, physically exists.
Anti-realism: Science works. Who cares about the rest? Arguing over whether space-time 'actually exists' (whatever that means) is pointless. All that matters is that you can use a theory to make predictions.