The focus of this article is a question that has been neglected in debates about digitalization: Could machines replace human scientists? To provide an intelligible answer to it, we need to answer a further question: What is it that makes (or constitutes) a scientist? I offer an answer to this question by proposing a new demarcation criterion for science which I call “the discoverability criterion”. I proceed as follows: (1) I explain why the target question of this article is important, and (2) show that it leads to a variant of the demarcation problem of science. (3) By arguing that it is probably an essential feature of science that we can make scientific discoveries, I suggest a novel way of dealing with this problem by proposing a new demarcation criterion. Before introducing it, (4) I analyze an exemplary case of a real scientific discovery, and (5) argue that scientific discovery processes have a general underlying structure. (6) I introduce my discoverability criterion for science and present my master argument that helps us understand which criteria have to be fulfilled in order to decide whether machines can replace human scientists or not. (7) I conclude by answering the article’s target question and bringing forward a take-home message.