Kant, from the Prolegomena to Any Future Metaphysics:
One might well at first think: that the proposition 7 + 5 = 12 is a purely analytic proposition that follows from the concept of a sum of seven and five according to the principle of contradiction. However, upon closer inspection, one finds that the concept of the sum of 7 and 5 contains nothing further than the unification of the two numbers into one, through which by no means is thought what this single number may be that combines the two. The concept of twelve is in no way already thought because I merely think to myself this unification of seven and five, and I may analyze my concept of such a possible sum for as long as may be, still I will not meet with twelve therein. One must go beyond these concepts, in making use of the intuition that corresponds to one of the two, such as one’s five fingers, or (like Segner in his arithmetic) five points, and in that manner adding the units of the five given in intuition step by step to the concept of seven. One therefore truly amplifies one’s concept through this proposition 7 + 5 = 12 and adds to the first concept a new one that was not thought in it; that is, an arithmetical proposition is always synthetic, which can be seen all the more plainly in the case of somewhat larger numbers, for it is then clearly evident that, though we may turn and twist our concept as we like, we could never find the sum through the mere analysis of our concepts, without making use of intuition.
What exactly was Kant responding to – the idea that mathematical principles were analytic a priori judgments? Of course not, he was answering math atheism!