Papers on history and philosophy of mathematics suitable for master's students 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.
 A: In hopes that some commenters will post their suggestions as answers, let me post this recommendation here.
An increasingly important aspect of contemporary mathematics is the role of computers and experimental mathematics.  One article addressing this is Marjin Heule and Oliver Kullmann's 2017 The Science of Brute Force in Communications of the ACM (and included in the next year's Best Writing on Mathematics).
The motivating example for the article is the authors' resolution of the boolean Pythagorean triples problem: Starting from 1, how far can the integers be colored red or blue with no monochromatic solutions to $x^2 + y^2 = z^2$?  Their 200 terabyte proof based on SAT solvers shows that $\{1, \ldots, 7824\}$ can be 2-colored to avoid monochromatic Pythagorean triples, but $\{1, \ldots, 7825\}$ cannot---previously, it was not known whether there was a finite limit.
The larger discussion brings in Appel and Haken's proof of the four color theorem, Lam's proof that there is no projective plane of order 10, the interplay between computation and theoretical results to resolve the Erdős discrepancy problem, and the notion of "alien" mathematical statements.  The article is a well written mix of mathematical detail and philosophical considerations with quotations from David Hilbert and Oscar Wilde.
A: 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.
A: An interesting (and topical!) topic would be the commentary on the status and philosophy of mathematics by Nikolai V. Ivanov a.k.a. Owl, as expounded in his blog Stop Timothy Gowers. While it was active only for a couple of year or so (the last post seems to be dated February 2017), the posts are extremely interesting and thought provoking. It is clear that Owl thought deeply about the topics, and I learned a lot from his posts. In any event, this will certainly fulfil your requirement that

Also they should contain some interesting perspectives and perhaps challenge the beliefs of the students, so there is something to discuss.

