The paper focuses on the lectures on the philosophy of mathematics delivered by Wittgenstein in Cambridge in 1939. Only a relatively small number of lectures are discussed, the emphasis falling on understanding Wittgenstein's views on the most important element of the logicist legacy of Frege and Russell, the definition of number in terms of classes—and, more specifically, by employing the notion of one-to-one correspondence. Since it is clear that Wittgenstein was not satisfied with this definition (and with the overall logically-oriented approach), the aim of the essay is to propose a reading of the lectures able to clarify why that was the case. This reading shows (unsurprisingly) that his better known views on language and mind expressed in Philosophical Investigations illuminate his conception of mathematics.