By Tom Edgar

What is your favorite mathematical topic to introduce to people? For me, it's visual (or visually-inspired) proofs of well-known and not-so-well-known mathematical facts. In my experience, every mathematician (where that term should be broadly interpreted to mean people who enjoy math) has some topic they love sharing. The MAA publications are great for finding these gems and learning from the people who enjoy sharing expository ideas. You should always consider writing for the MAA publications when you have such an idea to share with others.

But, often those publications don't reach as far as they could. Modern media outlets drive people to alternate sources. Enter the pandemic and remote interactions. Many math educators and math enthusiasts learned a variety of new skills to bring mathematics to their classrooms and communities. Why not use those skills to expand your reach? Write your ideas AND create related digital content.

During the summer of 2021, Grant Sanderson, known for beautiful videos providing mathematical explanations as 3Blue1Brown, and James Schloss designed a contest to inspire people to create mathematical exposition that is accessible and broadly available. Astonishingly, this contest, formally known as the Summer of Math Exposition 1 (or SoME 1), received over 1200 submissions! Clearly people are hungry for interesting and engaging mathematical content, and MAA members are precisely some of the people who should be creating that content.

The skills you have developed during the pandemic may provide you with the opportunity to share your favorite ideas with more people than you could have ever imagined. Some of our colleagues are already doing just that. For instance, Mohamed Omar has a fantastic channel exploring nonstandard tools and techniques that can be helpful in undergraduate studies and beyond. I recently learned from his channel that every positive integer can be written as

for some integer k. Or check out Katherine Stange's channel containing great number theoretic exposition including her wonderful video describing the mathematics behind sieves and factor stencils—she was inspired to create this particular video about factoring large numbers by the contest, but now we can all benefit from the explanation into eternity. Or consider Michael Weselcouch's channel; he recently began sharing mathematical ideas using Minecraft. I particularly enjoy his use of Minecraft to approximate mathematical constants (even when the approximation isn't as great as he had hoped). This clever idea makes mathematics more exciting and accessible to the population of Minecraft lovers, which I am told is quite massive.

I submitted a piece to the SoME 1 contest and as part of that I participated in peer review. I came across many excellent videos that I now have ready to share with my students. For instance, Carl Turner's video shows why quintic polynomials are generally unsolvable without requiring (explicitly) a lot of the details from Galois theory. And here is one from Eric Severson visualizing Fibonacci identities using tilings (a great way to drive students to the MAA Beckenbach prize-winning book Proofs that Really Count: the Art of Combinatorial Proof by Jenny Quinn and Art Benjamin). I also enjoyed Noah Miller's exposition about the Dirac belt trick, topology, and spin-1/2 particles. I have only cracked the surface of the 1200 submissions to the contest. When you watch these videos, you begin to brainstorm ways that you can share your favorite ideas in a similar fashion.

Of course, some people might be intimidated by the numerous fantastic resources already out there—Mathologer, Numberphile, 3b1b, Tibees, etc.—and think they can't produce the same quality of videos or don't have as interesting ideas about which to present. Don't let others discourage you from using your newfound digital skills to share your mathematical insights.

Communication is a core value of the MAA. If we all write, and we all create related media, we encourage more and wider participation in mathematics. You can even use newer media outlets to drive traffic to your exposition in the MAA publications. As a personal anecdote, my SoME1 submission animates a proof of the two-variable mean inequalities from an upcoming article that I wrote for Mathematics Magazine. Whenever you turn out a new mathematical result, think of a way to write a related expository piece and to create videos, blog posts, or other media to promote the amazing work you do.

*Endnote: After writing this post, Grant Sanderson posted a video of the winners of the competition. None of my favorites listed above were winners; however, nearly all of them were specifically mentioned in his video round up.

Tom Edgar is a professor at Pacific Lutheran University and the current editor of Math Horizons. He has recently been animating classic and newer proofs without words on his YouTube channel Micro Visual Proofs.