Why teach math history?

I would like to incorporate math history into my own teaching because I believe it would emphasize the importance of a concept and provide more context. Moreover, it would make the overall subject seem more ‘human’ and not so technical and mechanical. Also, there are some really cool stories associated with certain mathematicians and concepts. Off the top of my head, the easiest way I can incorporate math history into my teaching is by presenting a short paragraph about the concept, such as who created it and how it came to be, before starting the lesson. Another method I can think of is creating a project where students research the history of specific topics or mathematicians and present their findings to the class. This helps students develop important skills and adds a nice change of events in the class.

What first made me 'stop' was realizing how long incorporating history into math education has been advocated, along with the many objections to it. Most objections seemed logical, and I could see myself agreeing as a student. Though this makes me wonder if those objections explain why I had so little exposure to math history in high school. I can only recall one instance of learning it before the concept itself. This lack made university harder when classes focused more on history (problem, necessity, context) rather than what I used to call the ‘meat,’ the solution. One line I loved from the article was “No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down." The objection I disagreed with was (O10) lack of assessment. I don’t think math history should be graded. Its purpose is to create motivation and engagement, and testing it might cause students to memorize facts. I remember in Grade 12 when my teacher told the story of Gauss and the sum of numbers. I was able to relax and listen closely because I knew it would not be tested. One part I still question is the reconstruction step, where history enters implicitly or explicitly. I understand the explicit part, but not the implicit part, and I would like an example. If we are looking at ‘the historical development from the current stage,’ how do we introduce past history?