Digital Tools for the Working Mathematician
The craft of electronic computing machines
Preface
Modern mathematical work is increasingly linked to digital tools, from typesetting systems and computational libraries to proof assistants and AI search agents. Exposure to and experience with these technologies is often passed down informally, through office hours or lab groups, to those already well-supported by our institutions. The unwritten and rapidly growing body of fundamental skills needed to deploy these tools effectively is purportedly covered in some introductory (and probably optional) computer science course, or, worse yet, presumed to be self-evident from a lifetime of growing up in an online world.
We are currently experiencing a rapid transformation of our discipline—both its political economies and its epistemological foundations—through ongoing processes of automation, highlighted recently by the explosion of large language models and other generative AI tools. Accompanying this shift is that age-old optimism around transformative technologies: that AI (like the internet before it) is inherently equitable and democratizing. Of course, these technologies are built by powerful and complex entities that only incidentally (if at all) consult with the desires and needs of the communities from which they extract expertise (see, e.g., Avigad 2026, sec. 2). Left unexamined, digital tools do not automatically dismantle barriers; indeed, they are new avenues by which we reproduce and ramify existing inequalities.
As mathematical research is increasingly tied to enterprise-grade technologies accessible only to scholars in well-funded institutions, we must prepare our students to understand that these resources might not be available to them forever—and that they certainly are not available to all. By the same token, departments cannot assume that our students arrive understanding how to navigate a file system, or that they will “pick up” the fundamentals of \(\LaTeX\) before beginning their senior thesis projects. Our curriculum should make space for students to develop an understanding of these tools and their limitations, while also drawing attention to the ways in which the political realities of mathematical practice rely upon or uphold hierarchies.
Underlying this guide is the principle that systems built for accessibility inevitably become better for everyone. My goal with this resource is to make implicit knowledge explicit, preparing students to navigate the computational landscape of mathematical research while also confronting the much more important question of self-actualization in an inequitable world. As mathematics—a discipline which is unique in many ways, but especially for its reliance on funding graduate training through teaching appointments—faces a worsening crisis of reproduction, Digital Tools for the Working Mathematician is an invitation to reflect on the work necessary to defend, rethink, and build sustainable mathematical futures.