According to Kant’s Critique of the Power of Judgement, in the end all estimation of magnitude is sensible, or ‘aesthetic’, and the absolutely great in aesthetic estimation is called ‘the mathematical sublime’. This article identifies the relevant sensible element with an inner sensation of a temporal tension: in aesthetic comprehension, the imagination encounters an inevitable tension between the successive reproduction of a magnitude’s individual parts and the simultaneous unification of these parts. The sensation of this tension varies in degree and (...) facilitates aesthetic estimation in general. But in the special case where it comes to involve a sense of exceeding our imagination’s limit, we judge a magnitude to be mathematically sublime. Pace Kant, I argue that this limit is private and contingent rather than transcendental, such that the judgement of the mathematical sublime is neither universal a priori nor necessary. (shrink)