Meaning
Mathematicians use special languages for talking about strange things, out of this world.
What does it all mean?
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Ontology
What are these strange things that mathematicians talk about?
Do they really exist?
How can we tell?
Does it matter?
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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?
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Application
How can knowledge of abstract mathematics be applied in the real world?
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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.
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Computing
What are the implications for mathematics of the information revolution?
What can mathematics contribute?
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