TITLE: Papers on history and philosophy of mathematics suitable for master's students
QUESTION [6 upvotes]: In the fall, I will give a course called "Perspectives in Mathematics". This is a mandatory course at our master's program in mathematics (including applied mathematics and statistics). The course contents are rather vague, but we are supposed to cover historical and philosophical perspectives on mathematics, as well as the role of mathematics in society.
One thing I would like to do is to ask the students to read some short texts on topics such as history, philosophy and perhaps sociology of mathematics and discuss them in class. I would like these to be more than just popular science but still reasonably accessible. Also they should contain some interesting perspectives and perhaps challenge the beliefs of the students, so there is something to discuss. Finally, I want to cover not just the classical history of pure mathematics, but also applied mathematics and its role in society.
I would be really grateful for tips on research papers or other short texts that you think may be suitable.

REPLY [3 votes]: For the philosophy of mathematics, a standard reference is Benacerraf and Putnam's anthology Philosophy of Mathematics: Selected Readings.  This will provide a good introduction to some of the "traditional" topics in the subject such as logicism, intuitionism, formalism, and platonism.  There are of course many important topics not covered.  I'd recommend that you also consider something written by Imre Lakatos, such as Proofs and Refutations, as well as Humanizing Mathematics and its Philosophy: Essays Celebrating the 90th Birthday of Reuben Hersh.
For the history of mathematics, there is the encyclopedic book A History of Mathematics by Carl B. Boyer and Uta C. Merzbach.  In particular, this book has some good chapters on the early history of mathematics in non-Western civilizations, a topic that was largely neglected in the West until relatively recently.  Now, there's another take on the history of mathematics, which is to treat it not just as a subject in its own right but as something that can illuminate and inform the work of a research mathematician.  As mentioned by someone in a comment, the work of Harold Edwards is exemplary in this regard.  If your students have a strong enough mathematical background for it, I'd recommend the book Galois Theory.
A rather neglected topic is the relationship between mathematics and religion.  A good anthology is Mathematicians and their Gods:
Interactions between mathematics and religious beliefs, edited by Snezana Lawrence and Mark McCartney.  There are also the fascinating books Naming Infinity by Loren Graham and Jean-Michel Kantor and Equations from God by Daniel Cohen.
Many of your students may be interested in the topic of women in mathematics.  There are several books on this topic, such as Complexities: Women in Mathematics, edited by  Bettye Anne Case and Anne M. Leggett.
Finally, depending on how much you're willing to venture into controversial territory, you could consider devoting some time to the question of how to promote diversity, equity, and inclusion in mathematics.  Especially in the realm of mathematics education, DE&I is a very hot topic—possibly hotter than you want to touch.  I confess that I am not au courant with the literature, so I don't feel qualified to give recommendations, but one example I heard about recently (and which has generated heated debate) was A Pathway to Equitable Math Instruction. But perhaps others who are more knowledgeable than I am can provide better guidance in this area.