Mathematics is often one of these barriers that has to be removed in popular science; in , for example, remarks how he was told that every equation that he included in the book would halve its sales, and thus, he kept only a brief mention of E=mc2 in the introduction. On the other hand, mathematics can sometimes be simplified, or introduced slowly, as is the case in , where the maths are explained with almost patronising simplicity (although they repeatedly apologise for it). This simplification or cutting of finer details invariably leads to mixed results. Popular science can be the source of many misconceptions about scientific theories when done badly - often a theory can be misrepresented by a pop science writer wanting to over-emphasize the sensational aspects of it - but it can cement ideas and perceptions in the public mind when done well.
Much of the public experience with popular science comes through magazines, which range from the generally good ( until recently), to the unreadable (), to those with an unfortunate tendency to run far too many sensationalistic articles on pseudoscience (most of the rest).
Obviously, pop science requires that a lot of the complexity of scientific theories and understanding must be removed for a lay or non-expert audience to understand it. It takes months of lectures, revision and exercises for a dedicated science student to get to grips with the intricacies of their fields, and years for the consequences of the theories they study to become second nature. With popular science, the aim is to cut out what isn't necessary to understand a theory or to convey it in a way that leads to understanding far more quickly.
Television is another outlet for popular science, perhaps best typified by the 1980 TV series and the accompanying book by . has been one of the most enduring and influential introductions to popular science for billions and billions of people, which is probably a good thing because the science behind it is sound and well presented.