The article aims to create a concise document that illustrates the debate between mathematics and mathematics education and clears the muddle by synthesizing the literature on the subject. A desk review guided by an iterative literature search procedure and thematic analysis was conducted. "Mathematics and mathematics education" was the initial search key term. Numerous mathematicians and mathematics educators are paying attention to the discussion. The development of mathematics education as a subject of study or a teaching profession has been aided by numerous academic disciplines, including mathematics, philosophy, psychology, sociology, and anthropology. Both communities are interested in advancing mathematics's cultural transformation for the greater good of society, which reflects their shared concerns and areas of common interest. Conversely, there have been a great deal of discussions between various groups within the two communities; some of these discussions have been beneficial, but some have been harmful. Thus, a subsequent discussion focuses on evidence and reasoning, respectful exchange of ideas, willingness to modify views based on new arguments, and one aimed at clarity and improvement rather than victory will have added value to best benefit from the development. The pull-apart observed in Ethiopia is not unique or out of the ordinary. The study suggested a three-circle structure for collaborative work that covers several topics, including mathematical modeling, discoveries in mathematics, and the history of mathematics.