Online platforms have become the primary source of information about scientific advances for the wider public. As online dissemination of scientific findings increasingly influences personal decision-making and government action, there is a growing necessity and interest in studying how people disseminate research findings online beyond one individual platform. In this paper, we study the simultaneous diffusion of scientific articles across major online platforms based on 63 million mentions of about 7.2 million articles spanning a 7-year period. First, we find commonalities between people sharing science and other content such as news articles and memes. Specifically, we find recurring bursts in the coverage of individual articles with initial bursts co-occurring in time across platforms. This allows for a ranking of individual platforms based on the speed at which they pick up scientific information. Second, we explore specifics of sharing science. We reconstruct the likely underlying structure of information diffusion and investigate the transfer of information about scientific articles within and across different platforms. In particular, we (i) study the role of different users in the dissemination of information to better understand who are the prime sharers of knowledge, (ii) explore the propagation of articles between platforms, and (iii) analyze the structural virality of individual information cascades to place science sharing on the spectrum between pure broadcasting and peer-to-peer diffusion. Our work provides the broadest study to date about the sharing of science online and builds the basis for an informed model of the dynamics of research coverage across platforms.