2026 Joint Mathematics Meetings
Benjamin David Grimmer
Artists
Benjamin David Grimmer
Assistant Professor of Applied Mathematics and Statistics
Applied Mathematics and Statistics, Johns Hopkins University
Baltimore, MD, USA
Statement
Mathematical research is often far from approachable; I aim to shorten this distance. Much of my work takes open and active research questions, finding ways to fix them in our local three-dimensions for us all to then explore together. Generally, I find that three-dimensional objects are much more compelling to engage with and start thinking about than drawings and figures on a chalkboard can be. Please touch and engage with these objects :)
Artworks
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Figure 2: Best-Known Rupert's Passages
74.0 x 71.0 x 13.0 cm
Wooden Shelf (Oak and Maple) and PLA plastic
2025
This work takes Rupert's problem, which has been studied for more than 300 years, and makes it concrete.
Wonderfully, a cube can have a carefully cut hole in it, allowing another equal-sized cube to pass through.
Recently and equally wonderfully, Steininger and Yurkevich constructed a polyhedron that does not have this property.
For all the classic shapes on this shelf (Platonic Solids, Archimedean, Catalan, Johnson), the best known passage is shown.
For the ones in gold, it's open whether a passage exists! You are invited to try to prove none exist or be the first to discover one.
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The 4/3-Norm Ball has a Circular Shadow
28.0 x 8.0 x 6.0 cm
Ceramic, Glass and PLA plastic
2025
The p=4/3-norm ball (made in ceramic) has the nearly unique property that one of its shadows is a perfect circle.
This property is only shared with the p=2-norm ball, which has the property from every angle.
The piece showcases this wonderful fact by placing three colored copies of the p=4/3 norm ball, 3D printed, in a glass cylinder.
When viewed from above, one can see that the top ball (purple) fully eclipses the lower ball (green), which in turn fully eclipses the lowest ball (blue).
This property is dual to the equally wonderful fact that a slice of the p=4-norm ball is a perfect circle. This is left as an exercise to the reader.