Meaning
Mathematicians use special languages for talking about strange things, out of this world.
What does it all mean?

Ontology
What are these strange things that mathematicians talk about?
Do they really exist?
How can we tell?
Does it matter?


Epistemology
Mathematics has often been presented as a pardigm of precision and certainty, but some writers have suggested that this is an illusion.
How can we know the truth of mathematical propositions?

Application
How can knowledge of abstract mathematics be applied in the real world?


Foundations
Mathematics is a highly structured logical science, but dig deep enough and you can find some sand.
Making the best foundations for mathematics involves philosophy.

Computing
What are the implications for mathematics of the information revolution?
What can mathematics contribute?

