synthetic a priori truths

I'm reading Christopher Chase Rachels' new book "A Spontaneous Order", which makes the case for anarcho-capitalism and discusses praxeology and Austrian economics at length. In the first chapter, on praxeology, he claims that Misesian action axioms are the only examples of synthetic a priori truths, but it seems to me that the whole field of mathematics involves synthetic a priori statements. Mathematics is deductive, not inductive, but its a field of inquiry because not all mathematical statements are obvious from the basic definitions of mathematical operations and numbers; they require a lot of work to tease out the implications of these operational rules. Is there something fundamentally different between action axioms and mathematical reasoning?

link: http://bit.ly/1RPGD55