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Math as synthetic a priori

I just had my first lecture on Kant. My teacher of course talked about the synthetic a priori, but only went on to talk about it in regard to Kant's description of space and time.

I remember reading about Kant asserting that synthetic a priori knowledge also presents in the form of math, for example. My teacher stated during the lecture that math is analytic a priori, as David Hume claims. I stayed behind after the lesson and asked him about it, but he didn't seem to agree that math can be viewed as a synthetic a priori.

Doesn't Kant indeed say that math IS synthetic a priori, and if so, is that view accepted in contemporary philosophy?
gpt
For Kant, mathematical judgments have an intrinsic connection to space and time.  He thinks of math as involving geometry and arithmetic, and the basis of geometry being the quantity we apprehend as extension in space while the basis of arithmetic is the quantity we apprehend as extension in time.  Accordingly, for Kant the question about the nature of math's bases becomes the question about the nature of our apprehension of the quantities of spatial and temporal extension.

So, on the basis of taking space and time to have an *a priori* source he infers that mathematics has an *a priori* source.  But the nature of this *a priori* source, on his view, is not merely one of recognizing the content of concepts we already possess (like when we judge that a bachelor is unmarried), but rather has its basis in our capacity to synthesize spatial or temporal extension in order to arrive at propositions describing geometric or arithmetic quantities.  So, by taking mathematical judgments to be acts of syntheses involved our apprehension of space and time, he takes them to be synthetic *a priori*.

I don't think that there's any consensus about the foundations of mathematical judgments these days; it was a heated dispute in the early twentieth century.  On one hand, there was definitely opposition to this Kantian account, which argued in favor of an analytic *a priori* basis for math, and this has had a wide influence on how philosophers think of mathematics.  On the other hand, one of the major proposals during the crisis about math's foundations, which remains a significant though minority interest among people working in this area, was deliberately modeled after Kant's view, which was articulated in a systematic way as a basis for thinking about and doing (it had some consequences for how math is done) mathematics--this is Brouwer's "intuitionism."