What makes a great math explanation? | SoME2 results

A peer-review contest for math lessons has turned into a measurable engine for audience growth—and the winning entries point to a practical checklist for what makes math explanations worth watching. After the Summer of Math Exposition submission deadline, an algorithm paired videos for side-by-side comparisons, generating more than 10,000 judgments. That process didn’t just rank submissions; it also encouraged hundreds of creators to post around the same time and then watch each other’s work, helping young channels collectively rack up over 7 million views for this year’s video entries alone. Earlier submissions from last year’s contest added roughly another 2 million views in the same period, and at least one creator reported a dramatic jump in views during the peer-review window even without being directly reviewed.

Against that backdrop, the contest organizers selected five winners from more than 100 top-ranked entries, with additional community judges brought in to reduce bias. The selection criteria were four pillars: motivation, clarity, novelty, and memorability. Motivation operates on two levels. At the “macro” level, the best lessons hook learners by raising a compelling question—whether it’s a real-world puzzle like why a plane’s sound seems to drop in pitch, a hands-on challenge such as reverse-engineering the math behind smartphone panorama stitching, or a “nerd-sniping” problem like the prisoner hat riddle that asks for a strategy guaranteeing at least one correct guess. Motivation can also come from historical context, such as a calculus overview that makes students feel their confusions are part of a long tradition of grappling with infinity and infinitesimals, or from connecting seemingly unrelated paradoxes to a shared pattern that later supports category theory.

At the “micro” level, motivation means each new technical idea earns its place. Strong entries preview the intuition and visual scaffolding before introducing heavy machinery—like ray tracing concepts that arrive only after the rendering equation’s meaning is already grounded in examples. Others start from what students find unsatisfying (for instance, the “from on high” feel of the gamma function’s integral definition) and then build toward the final form by deriving it from desired properties. A recurring technique is to begin with a naive approach, show why it fails, and refine step by step—turning confusing concepts like dual numbers and automatic differentiation into logical upgrades rather than sudden leaps.

Clarity then determines how efficiently that attention is spent. The strongest explanations keep one or two concrete examples in view, let learners “play” with patterns through simulations or tweaks, and only generalize after intuition has formed. Even production choices matter: music can enrich storytelling, but it should not compete with technical focus.

Novelty splits into stylistic originality and substantive uniqueness. The contest’s entries use shared tools like Manum, but still aim for distinct voices. More importantly, novelty means presenting material that would be hard to find elsewhere—such as a percolation toy model that makes phase-change proofs more tractable.

Memorability is the final filter: lessons that land a satisfying “aha” or a question that stays with viewers. The five winners include a collaboration slot going to the percolation video, plus crystal structures via group theory, a history of calculus, ray tracing and speed-up algorithms, and the hat riddle problem-solving lesson. Each winner receives $1000 and a rare edition golden pie creature from Brilliant.