The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools.
The goals of the program are to:
introduce mathematicians to new computational illustration tools to guide and inform their research;
spark collaborations among and between mathematicians, makers and artists;
find ways to communicate research mathematics to as wide an audience as possible.
The program includes week-long workshops in Geometry and Topology, Algebra and Number Theory, and Dynamics and Probability, as well as master courses, seminars, and an art exhibition.
Mathematical topics include: moduli spaces of geometric structures, hyperbolic geometry, configuration spaces, sphere eversions, apollonian packings, kleinian groups, sandpiles and tropical geometry, analytic number theory, supercharacters, complex dynamics, billiards, random walks, and Schramm–Loewner evolution.
Illustration media include: animation, interactive visualization, virtual and augmented reality, games, 3D printing, laser cutting, CNC routing, and textile arts. In addition, we welcome mathematical journalists, writers, and videographers interested in communicating and illustrating mathematics.
This semester program is partially funded by the Alfred P. Sloan Foundation award G-2019-11406 and supported by a Simons Foundation Targeted Grant to Institutes.
Objects created for mathematical visualization are beautiful and attractive in their own right. "Illustrating Mathematics" brings together artists, makers, and mathematicians seeking to harness the creativity of mathematical illustrations to further the public’s understanding of mathematical research. ICERM invites you to engage with these talented artists-in-residence and explore their work. Visualize mathematics through displays of art made using 3D printing, laser cutting, CNC routing, virtual reality, textiles, carving, painting, video, and more!
Illustrating Mathematics Art Exhibit Book Available for sale online:
Judy Holdener, Hilbert's Portrait via his Space-Filling Curve, Bridges Conference Proceedings (2020), 231-236.
Surbjit Tomka, The Fabric of Space Time and The Single Unified Field Theory by Dr SKK Tomka, 2022.
Katsumi Yamashita, Akemi Yasukawa, Hideo Sawada, Fabrication of Cotton Fabric with Superoleophilic/Superhydrophobic Characteristic on the Modified Surface by Using Fluoroalkylated Oligomeric Silica/Triazine Derivative Nanocomposites, Coatings 10 (2020), 174.
Martin Skrodzki, Science Communication and Outreach Events During the *Illustrating Mathematics* Semester Program at the Institute for Computational and Experimental Research in Mathematics (ICERM), Handbook of Mathematical Science Communication, vol. 3, World Scientific, 2021, pp. 165-181.
Gabriel Dorfsman-Hopkins, Deformation Spaces and Static Animations, dorfsmanhopkins2022deformationspacesstaticanimations:2211.08333, 2022.
Krishma Singal, Michael Dimitriyev, Elisabetta Matsumoto, Quantifying the Elastic Nature of Knitted Materials, APS March Meeting Abstracts, APS Meeting Abstracts, vol. 2021, 2021, pp. B17.003.
Krishma Singal, Michael S. Dimitriyev, Sarah E. Gonzalez, Alexander P. Cachine, Sam Quinn, Elisabetta A. Matsumoto, Programming Mechanics in Knitted Materials, Stitch by Stitch, singal2023programmingmechanicsknittedmaterials:2302.13467, 2023.
Wilder Boyden, Frank A. Farris, Polyhedral symmetry from ribbons and tubes, Journal of Mathematics and the Arts 15 (2020), 76 - 96.
Edmund Harriss, The Geometry of Curvahedra: Pairing Mathematics and Art, 2022.
Richard Evan Schwartz, Paper Moebius bands with T Patterns, schwartz2024papermoebiusbandst:2012.06953, 2024.
Richard Evan Schwartz, On The Optimal Paper Moebius Band, schwartz2023optimalpapermoebiusband:2012.07783, 2023.
evelyn Sander, Laura Taalman, Stephen Lucas, Modeling Dynamical Systems for 3D Printing, Notices of the American Mathematical Society 67 (2020), 1692.
Michael Dimitriyev, Krishma Singal, Elisabetta Matsumoto, Linked loops on a lattice: Formulating knitted fabric elasticity with coarse-grained curve mechanics, APS March Meeting Abstracts, APS Meeting Abstracts, vol. 2021, 2021, pp. B17.002.
November 21, 2019 Stops at the Granoff Center Math+Art Exhibit Watch for details for the special November Granoff Center stop.
B. Muetzel, Y. Mohanty
C. Sequin
G. McShane
C. G. Strauss
D. A. Brake
S. Schleimer, H. Segerman
B. Grossman
F. Farris
C. Nussear
R. Nelson
Petr Hruby, Timothy Duff, Anton Leykin, Tomas Pajdla, Learning to Solve Hard Minimal Problems, hruby2021learning:2112.03424, 2021.
Ricardo Fabbri, Timothy Duff, Hongyi Fan, Margaret Regan, David da Costa de Pinho, Elias Tsigaridas, Charles Wampler, Jonathan Hauenstein, Benjamin Kimia, Anton Leykin, Tomas Pajdla, Trifocal Relative Pose from Lines at Points and its Efficient Solution, fabbri2022trifocal:1903.09755, 2022.
Davi Geiger, Zvi M. Kedem, On Quantum Entropy, Entropy 24 (2022) no. 10, 1341.
William M Goldman, Geometric structures on manifolds, vol. 227, American Mathematical Society, 2022.
Diana Davis, Illustrating Mathematics, American Mathematical Society, Providence, RI, 2020.
Krishma Singal, Michael S. Dimitriyev, Elisabetta A. Matsumoto, Stress-Strain Studies of Knitted Swatches, Bulletin of the American Physical Society (2020).
Daniel Groves, Jason Fox Manning, Specializing cubulated relatively hyperbolic groups, arXiv 2008.13677 (2020).
Stepan Paul, The Flat Klein Bottle Rendered in Curved-Crease Origami, arXiv 2101.08865 (2021).
Glen Whitney, The Playground, Math Horizons 28 (2021) no. 1, 30-33.
Matei P. Coiculescu, Richard Evan Schwartz, The Spheres of Sol, arXiv 1911.04003 (2019).
Martin Skrodzki, H. Lipschutz, Vector Fields and Paul Klee -- A Summer School Course for gifted High-School Students, arXiv 2005.01983 (2020).
C. A. Yackel, Wallpaper patterns admissible in itajime shibori, Journal of Mathematics and the Arts 0 (2021) no. 0, 1-13.
Frank Farris, Wallpaper Patterns from Looping Strands: The Layer Groups, Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture, Tessellations Publishing, Phoenix, Arizona, 2021, pp. 71-78.
Frank Farris, Wallpaper Patterns from Nonplanar Chain Mail Links, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, Tessellations Publishing, Phoenix, Arizona, 2020, pp. 183-190.
Laura Taalman, Carolyn Yackel, Wallpaper Patterns for Lattice Designs, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, Tessellations Publishing, Phoenix, Arizona, 2020, pp. 223-230.
Gabriel Dorfsman-Hopkins, Candy Xu, Searching for Rigidity in Algebraic Starscapes, arXiv 2107.06328 (2021).
Martin Skrodzki, Illustrations of non-Euclidean geometry in virtual reality, arXiv 2008.01363 (2020).
Shashank Markande, Elisabetta A. Matsumoto, Knotty knits are tangles on tori, arXiv 2002.01497 (2020).
Frank A. Farris, Mathematical Art as a Discipline, Notices of the American Mathematical Society 68 (2021), 1.
Jeff Weeks, Non-Euclidean Billiards in VR, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, Tessellations Publishing, Phoenix, Arizona, 2020, pp. 1-8.
R{\'e}mi Coulon, Elisabetta A. Matsumoto, Henry Segerman, Steve J. Trettel, Non-Euclidean Virtual Reality III: Nil, arXiv 2002.00513 (2020).
R{\'e}mi Coulon, Elisabetta A. Matsumoto, Henry Segerman, Steve J. Trettel, Non-Euclidean Virtual Reality IV: Sol, arXiv 2002.00369 (2020).
Richard Evan Schwartz, On Area Growth in Sol, arXiv 2004.10622 (2020).
Gabriel Dorfsman-Hopkins, Anwesh Ray, Peter Wear, On Picard Groups of Perfectoid Covers of Toric Varieties, arXiv 2011.03613 (2020).
G. McShane, Rank two free groups and integer points on real cubic surfaces, arXiv 2003.05967 (2020).
R{\'e}mi Coulon, Elisabetta A. Matsumoto, Henry Segerman, Steve J. Trettel, Ray-marching Thurston geometries, arXiv 2010.15801 (2020).
Mikael Vejdemo-Johansson, 3d-printing Identification Spaces of the Square., arXiv 1909.05893 (2019).
David L. Bachman, Matthias G{\"o}rner, Saul Schleimer, Henry Segerman, Cohomology fractals, Cannon-Thurston maps, and the geodesic flow, arXiv 2010.05840 (2020).
David L. Bachman, Saul Schleimer, Henry Segerman, Cohomology fractals, arXiv 2002.00239 (2020).
Jeff Weeks, Body coherence in curved-space virtual reality games, Computers & Graphics 97 (2021), 28–41.
Kelly Delp Lewis Campbell, Elisabetta Matsumoto, Bending Seams - How to Create Couture Curves, Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture, Tessellations Publishing, Phoenix, Arizona, 2021, pp. 249-252.
Yongju Bae, J. Scott Carter, Byeorhi Kim, Amusing Permutation Representations of Group Extensions, arXiv 1812.08475 (2018).
Edmund Harriss, Katherine E. Stange, Steve J. Trettel, Algebraic Number Starscapes, arXiv 2008.07655 (2020).
Martin Skrodzki, AI and Arts - A Workshop to Unify Arts and Science, w/k - Between Science and Art (2019).
Judy Holdener, Marie Snipes, A Trio of Beaded Surfaces, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, Tessellations Publishing, Phoenix, Arizona, 2020, pp. 417-418.
Arthur Baragar, Daniel Lautzenheiser, A game of packings, arXiv 2006.00619 (2020).
Ellen Eischen, Stephan Ramon Garcia, A Gallery of Gaussian Periods, arXiv 2012.10015 (2020).
K. Lindsey, C. Wu, A characterization of Thurston's Master Teapot, arXiv 1909.10675 (2019).
Greg McShane, Convexity and Aigner's Conjectures, arXiv 2101.03316 (2021).
J. Carter, Seiichi Kamada, Diagrammatic Algebra, 2021.
Rebecca E. Field, Ilarion V. Melnikov, Bryce A. Weaver, Dynamics on asymptotically conical geometries, arXiv 1710.00404 (2017).
A. Baragar, Enriques surfaces and an Apollonian packing in eight dimensions, arXiv 2003.09112 (2020).
Saul Schleimer, Henry Segerman, Essential loops in taut ideal triangulations, Algebraic & Geometric Topology 20 (2020) no. 1, 487–501.
Martin Skrodzki, U. Reitebuch, Eric Zimmermann, Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns, arXiv 2006.16676 (2020).
Saul Schleimer, Henry Segerman, From loom spaces to veering triangulations, arXiv 2108.10264 (2021).
Saul Schleimer, Henry Segerman, From veering triangulations to link spaces and back again, arXiv: Geometric Topology (2019).
Edmund Harriss, Gauss-Bonnet Sculpting, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, Tessellations Publishing, Phoenix, Arizona, 2020, pp. 137-144.
Judy Holdener, Hilbert's Portrait via his Space-Filling Curve, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, Tessellations Publishing, Phoenix, Arizona, 2020, pp. 231-236.
Roger Antonsen, Laura Taalman, Categorizing Celtic Knot Designs, Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture, Tessellations Publishing, Phoenix, Arizona, 2021, pp. 87-94.
Martin Skrodzki, Eric Zimmermann, Konrad Polthier, Variational shape approximation of point set surfaces, Computer Aided Geometric Design 80 (2020), 101875.
Martin Skrodzki, Eric Zimmermann, A Large-Scale Evaluation Of Shape-Aware Neighborhood Weights And Neighborhood Sizes, Computer-Aided Design 141 (2021), 103107.
