June 6, 2026
Glazed and confused
Mathematician solves origami donut efficiency challenge with fewest folds
Math genius cracks the paper donut mystery, but commenters are furious about the missing payoff
TLDR: Richard Evan Schwartz proved the most efficient known way to fold a paper donut shape, solving a long-running math puzzle. Commenters immediately stole the spotlight by demanding a photo of the finished donut and arguing that if glue is involved, it doesn’t count as real origami.
A mathematician just did something that sounds absurdly specific and somehow very impressive: he proved the most efficient way to make a paper donut shape—known in math as a torus—using the fewest possible folds. The new PNAS paper by Richard Evan Schwartz tackles a long-running puzzle about how little paper-folding complexity you can get away with. In plain English: if you want to turn flat paper into a donut, how minimalist can you be?
But the real action is in the reactions, where readers instantly turned this from a neat math story into a mini-comment-section brawl. The loudest complaint? "Show us the actual donut!" One reader flat-out declared that not showing the finished folded shape was "criminal," which honestly captures the mood perfectly. People were less interested in the proof than in the visual payoff, and they were not shy about saying so.
Then came the authenticity fight. Another commenter threw down the classic purist challenge: if it uses glue tabs, is it even origami? Suddenly the story wasn't just about math—it was about standards, gatekeeping, and whether paper engineering is cheating if adhesive sneaks in. That turned the whole thing into a wonderfully nerdy scandal: part geometry triumph, part craft-community side-eye. The vibe is half "wow, brilliant" and half "excuse me, this donut is fake news unless I see it folded with no glue."
Key Points
- •Richard Evan Schwartz published a PNAS paper giving a proof related to the minimum-fold efficiency of constructing an origami torus.
- •The article defines efficiency using the minimum number of vertices, which is equivalent to minimizing triangles in the triangulation or folded edges.
- •An origami torus is described as a finite arrangement of triangles whose angles around each vertex sum to 2π.
- •Earlier paper torus examples used thousands of vertices, while later constructions reduced that number to ten and then nine.
- •The article says a torus cannot be triangulated with fewer than seven vertices, which narrowed the unresolved range before Schwartz's result.