David Cutler is in the spotlight for his work on a tasty-sounding mathematics problem. In January, the New York Times featured a research paper authored by Cutler and Neil Sloane, the founder of The On-line Encyclopedia of Integer Sequences. Titled "Cutting a Pancake with an Exotic Knife," the paper explores the "lazy caterer problem," or how to cut a pancake or other circular object into the most pieces with the fewest cuts.
Cutler said he was pleasantly surprised by the attention the paper has received.
"I think especially in math, you always think the things that you're doing are not of general interest to the public," Cutler said. "A lot of math is pretty arcane to some extent. It's always nice to see that people are interested in it."
The problem is more complicated than it might sound. The pancake is infinitely spreading in every direction, and you've got just one knife to cut it.
Cutler said it's often an introductory problem for undergraduates studying the math of counting, called combinatorics.
Sloane, whom Cutler dubs a "pretty big deal" in the combinatorics side of the world, gave a seminar mentioning the pancake problem at a program Cutler was attending over the summer. The program was part of the U.S. National Science Foundation Research Experiences for Undergraduates and held at Rutgers University Center for Discrete Mathematics & Theoretical Computer Science.
"He's a very eclectic guy who sort of allows his mathematics to be guided by capricious whims," Cutler said of Sloane. "He's very fun to talk to."
Sloane posed the question of how you might deal with the same problem with a less optimal tool—like if you fell and bent the knife.
Their paper explores how to best place weirdly shaped knives on the pancake.
Looking for respite from the complicated research on complex geometry he was doing in the program, Cutler took a crack at maneuvering these theoretical knives to make the maximum number of pieces.
"I stayed up probably until 2 a.m. one night," Cutler said. "I sent [Sloane] a result that I thought I had. And from then it just went, yeah, we could probably write something out of this."
Cutler said his initial contribution focused on proving rigorous bounds for the problem and utilizing experimental mathematics, which is using computation to investigate mathematical objects and identify properties and patterns, to guess at a possible correct statement for the problem. He then used traditional mathematics to prove the statement to be true.
By trying different ways of jiggling the knives, he gathered more evidence of the maximum number of cuts you could get from different knife shapes.
Yet all this data was no more than a good guess at a solution. That's where the collaboration with Sloane came in.
Data from Sloane's On-Line Encyclopedia of Integer Sequence, paired with Cutler's experimental evidence, helped them come to their novel findings in the paper.
Working on the pancake problem was a fun project for Cutler, who saw it as "too simple to leave untouched."
"I'm generally frustrated by not knowing things," he said. "I really don't like when I have a problem and I've put some mind toward it and I can't answer it. It's fun to work on math. There's always a little dopamine rush of doing something for the first time."
David O. H. Cutler et al, Cutting a Pancake with an Exotic Knife, arXiv (2025). DOI: 10.48550/arxiv.2511.15864
Citation: Student serves up fresh solutions to the pancake problem (2026, March 10) retrieved 11 March 2026 from https://phys.org/news/2026-03-student-fresh-solutions-pancake-problem.html
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