structural:summarization, information:classification, information:filtering
Arguments for and against the Riemann hypothesis

Mathematical papers about the Riemann hypothesis tend to be cautiously noncommittal about its truth. Of authors who express an opinion, most of them, such as Riemann (1859) and Bombieri (2000), imply that they expect (or at least hope) that it is true. The few authors who express serious doubt about it include Ivić (2008), who lists some reasons for skepticism, and Littlewood (1962), who flatly states that he believes it false, that there is no evidence for it and no imaginable reason it would be true. The consensus of the survey articles (Bombieri 2000, Conrey 2003, and Sarnak 2005) is that the evidence for it is strong but not overwhelming, so that while it is probably true there is reasonable doubt.

Some of the arguments for and against the Riemann hypothesis are listed by Sarnak (2005), Conrey (2003), and Ivić (2008), and include the following: