Math: Scholarly, Popular, and Grey Literature

Popular writing does not necessarily imply a lack of credibility, but it may not be appropriate for your paper. Popular articles are written for a general audience, while scholarly or peer-reviewed articles are written for an expert audience. The process of peer review includes rigorous critique of an article's methods, analysis, and conclusions by other experts in the field who offer anonymous feedback. This feedback provides the means to vet an article by multiple other scholars before it is published. 

Popular articles: 

• Have been edited for clarity or style, but the science has not been rigorously vetted. 
• Should avoid or explain jargon or technical language.
• May be written in a more artfully descriptive style, using analogies or metaphors to explain complex topics.
• May describe the human interest story behind the research.
• Do not often include citations in the text or at the end of the article. 
• May include persuasive writing, or otherwise promote an agenda other than relaying information.

Scholarly articles: 

• Have been reviewed to examine the validity of the research methods and the credibility of the results. 
• Assume an expert audience and choose precise language.
• Use graphs, charts, or tables to explain results when appropriate. 
• Will always include citations in the text and at the end of the article. 
• Should report on shortcomings or limitations of the research. 
• Try to avoid bias and/or report any conflicts of interest.

Grey Literature: 

In a category by itself, grey literature consists of reports by government, non-profit, or for-profit organizations outside of the academic publishing industry. These can include government reports, white papers, and program evaluations. Grey literature can be a valuable and credible resource for your research, but has usually not undergone peer-review to scrutinize the science behind the report.