SoME4 Prizes
Winners of the supplementary "helpful for teachers" prize we set up for the 2025 Summer of Math Exposition
For the 2025 Summer of Math Exposition, I promised a set of supplementary prizes for entries that were helpful to teachers. Although long overdue now, I’m happy to announce the final selection.
Reminder of how prizes work this year
In past years, I chose a set of five “general” winners. These were entries I felt enthusiastic about recommending to this audience, as judged by novelty, clarity, and memorability.
For 2025, I decided to do it differently. We already have a peer review system that I think does a wonderful job of surfacing the generally great content that this audience will enjoy. Indeed, we announced its results for SoME4 a few months ago, and if you explore the top entries, I’m confident you’ll find lessons you enjoy.
This year, I wanted to use prizes to reward something not necessarily already rewarded by the peer review and the social internet, which is the content that shows strong promise to be helpful to teachers. Sometimes this aligns with what peer reviewers will enjoy, but not always.
We solicited teacher feedback on all the results and compiled them. My job was then to review that feedback, and to watch/read many of the most promising entries myself, and select five of them to receive a prize of $1,000 each.
Part of why I’m so egregiously late in giving a final selection here is that there is no perfect and objective way to do this. I say this every year, but for those who were not selected, please take the word “winner” with a heavy grain of salt. I spent countless hours watching and reading many, many pieces that I thoroughly enjoyed, and which I see as positive contributions to the internet, constituting a significant superset of the ones featured here.
Final selection
As I reviewed each entry, I asked, “If I were teaching a course on this subject, how eager would I be to share with my students?”
It was very rare that I’d imagine simply assigning a video or article wholesale to be consumed by a student on their own time. Teaching is best when it’s dynamic and personal, so instead I’d feel drawn towards picking out bits and pieces, perhaps borrowing examples or pulling out interactive elements that could be used in the classroom. I’d then weigh this together with the teacher feedback that we had gathered.
In no particular order, these were the five final selections:
The fight over fairness that revolutionized math. This offers a nice motivation for expected value and adjacent topics in probability. I think it’s easiest to remember a piece of math if you feel like you invented it yourself, and the examples laid out by the creator here offer a nice scaffold that any probability teacher could use in a class of their own to guide students to reinvent core concepts in probability for themselves.
Relativity in Desmos. For students in any physics class introducing special relativity, this would be most relevant after having built up some of the fundamentals. The creator has offered an easily shareable set of demos to highlight some key properties of Lorenz transforms. Engaging with these stands to sharpen a student’s intuition for thinking about spacetime diagrams, and I can easily envision a teacher picking and choosing ones to fit their particular lesson’s needs.
A trick for analyzing cubics, by Dr PK Math. This highlights a nice property of cubic functions useful for problem-solving. I appreciate the spirit represented by the video, which is that of a teacher sharing something obscure-but-fun with their fellow educators. Tricks like this are often very specific, but the acts of both using and proving it offer students a great chance to practice fundamental ideas for working with polynomials.
The world’s oldest algorithm. As the creator points out, Euclid’s Algorithm is shown in essentially all elementary number theory textbooks when they talk about unique factorization. I appreciated the framing of the lesson here, and the underlying motivation, and think anyone teaching an introductory number theory class would find it a useful structure to draw from.
The science of complexity. This is a beautiful article featuring a few examples of studying interesting macroscopic behavior from simple microscopic rules. This would be a nice warmup into any stat mech class, and many of the demos could be pulled out by teachers to fit their specific lessons.
A few other personal favorites I’d like to share
As I said, the peer ranking gives a great starting place for anyone looking to discover new creators/explainers, with or without added commentary from me. Nevertheless, since I looked through quite a few entries, I can’t help but highlight a few I particularly enjoyed.
This is a very small subset of those I could have brought up. Please do explore the others if you find yourself hungry for more.
+1
Great ideas well explained!