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“A world of ideas exists, created by human beings, existing in their shared consciousness. These ideas have properties which are objectively theirs, in the same sense that material objects have their own properties. The construction of proof and counterexample is the method of discovering the properties of these ideas. This is the branch of knowledge which we call mathematics.”
Reuben Hersh
“The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?... Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.”
Reuben Hersh

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What Is Mathematics, Really? What Is Mathematics, Really?
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18 Unconventional Essays on the Nature of Mathematics (Volume 0) 18 Unconventional Essays on the Nature of Mathematics
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