There And Back Again – Mathematical Association of America

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The utility of pure research into esoteric topics can facilitate societal revolutions.

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social Though my mathematical research since the mid-1980s has focused almost exclusively on the application of mathematical thinking to real-world problems, my PhD and almost all my research in the decade or more that followed it were in the decidedly pure areas of axiomatic set theory, in particular a study of the axioms...

The Hyperdoors Theory

By Pup Horst A magician searches for community Joe Ledoux is “not” a “mathematician” – he is an artist and a magician. However, he joins the likes of Marjorie Rice and an anonymous internet forum user in crafting new mathematics as inspired by his main interests. He made a new visualization of the hypercube that does...

An Unexpected Research Journey

By Lew Ludwig Ten years is a long time to be away from the research table. In that time, I've gained a few gray hairs, lost a few LaTeX shortcuts, and watched the world of generative AI grow from curious whisper to research partner. Lately, I’ve been imagining what it might look like to jump...

Still Needed In the Picture

By Lew Ludwig I'm starting to see real progress. At workshops and webinars, more colleagues are reaching out with, "Hey, I gave AI a try!" That's the point—whether you end up using AI or not, you've got to try it in your own teaching arena to understand what it's really capable of and where it...

AI in Action: Charting New Paths through Enhancement, Creation, and Integration

By Lew Ludwig Author’s Note: Throughout this article, 'AI' refers specifically to generative AI unless stated otherwise. I will primarily discuss ChatGPT 4o, the free model, due to its widespread use with our students. In my last three posts, I've encouraged you to engage with AI to better grasp its capabilities and limitations, helping you...

From Monologue to Dialogue: Engaging the MAA Community in AI Discussions

By Lew Ludwig When I first started this column over a year ago, I naively named it "There and Back Again: A Mathematician’s Tale of AI Exploration," a nod to Tolkien that I thought was a clever pun. I expected to explore generative AI and report back, complete with generating fun, Hobbit-esque images in a Shire-like...

Opening the Gate Without Losing the Flock

By Lew Ludwig As we navigate through our third year of integrating generative AI into higher education, it’s becoming increasingly clear that this technology will not quietly fade away like MOOCs (remember those?). Not only are students already using a variety of AI technologies, but employers also expect graduates to possess AI skills. Consequently, students...

A Baker, a Decorator, and a Wedding Planner Walk into a Classroom

By Lew Ludwig Baking, Decorating, or Planning: What Role Are Your Students Playing? Are your students learning to bake the cake? Are they learning to decorate the cake? Or are they acting as wedding planners so they can outsource the cake so they can focus on the other stuff? This analogy, shared by Maha Bali...

The Higher Ground

By Lew Ludwig One of the more memorable scenes from the Star Wars prequel trilogy features a pivotal standoff between Jedi master Obi-Wan Kenobi and his apprentice, Anakin Skywalker, on the fiery volcanic planet of Mustafar. As their duel reaches a climactic end, Obi-Wan secures a tactical advantage by positioning himself on a higher embankment....

There and Back Again: Of Tails and Tubes

By Lew Ludwig Recently, I was pleased to run into two former students collaborating at a whiteboard table in our library. They were deep in thought—or perhaps confusion (are these really so different?)—over something written on the table. After our initial pleasantries, I asked what they were working on: sequences. They were puzzling over the...

The Temperature of the Room

By Lew Ludwig So, have you had that conversation with your students yet? You know, the one where you discuss your AI policy and explain the reasons behind it? It's a chat more and more educators are having. Gone are the days when banning AI outright seemed feasible; crafting "AI-proof" assignments now feels like a...

Preparing Our Classrooms for AI This Fall

By Lew Ludwig As we approach August, my thoughts inevitably turn to classes and syllabi. However, this year feels different. I'm determined to be more intentional about incorporating generative AI into my teaching. I'm guided by two key principles: first, more students are likely to use generative AI, and second, graduates who cannot think, write,...

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