Honouring an academic who juggles computer graphics, mathematics and art seamlessly
The Association for Computing Machinery has named Professor Craig S. Kaplan a 2025 Distinguished Member in recognition of his pioneering contributions to the design and modelling of computational geometric patterns and non-photorealistic rendering. He is among 61 individuals worldwide honoured this year for outstanding scientific achievements in computing.
“Congratulations to Craig on this much-deserved recognition from ACM,” said Raouf Boutaba, University Professor and Director of the Cheriton School of Computer Science. “This honour is his fourth major accolade in 2025, recognizing his teaching and research excellence. Earlier this year, he received the Faculty of Mathematics Award for Distinction in Teaching, was named a Fellow of the Fields Institute, and his co-discovery and proof of the first aperiodic monotile was cited by Sir David Spiegelhalter in BBC Science Focus magazine as the most important mathematical breakthrough of this century.”
Professor Craig S. Kaplan juggles a range of interdisciplinary topics with ease, working at the intersection of mathematics, computer graphics and art. He develops mathematical tools and algorithms that generate ornamental patterns and support artists and designers.
His work frequently incorporates knowledge from computer graphics, classical and computational geometry, human–computer interaction, graph theory, symmetry and tiling theory, and perceptual psychology. He holds the Marsland Fellowship in Information Technology, a prestigious award that supports his research program.
Professor Kaplan’s research, teaching and service excellence
Solving the long-standing einstein problem
Professor Kaplan’s most celebrated accomplishment is his 2023 co-discovery and proof of the first aperiodic monotile. Known as the hat, the 13-sided polygon fills the infinite plane without gaps or overlaps in a pattern that cannot repeat. Its discovery resolved the famous einstein or “one stone” problem in tiling theory, an open question for more than six decades.
Professor Kaplan’s involvement began when David Smith, a mathematical hobbyist, contacted him about a promising shape with seemingly aperiodic properties. Together with collaborators Joseph Samuel Myers and Chaim Goodman-Strauss, the team solved the einstein problem and published their proofs in a paper titled “An aperiodic monotile” in Combinatorial Theory. Shortly thereafter, the research team published “A chiral aperiodic monotile,” a paper in which they proved that a related family of shapes, called spectres, tile the plane aperiodically using only translations and rotations, satisfying an even stricter definition of aperiodicity.
The discovery captured global attention. Media outlets including The New York Times, The Guardian, CNN, New Scientist, Smithsonian Magazine, Quanta Magazine and Scientific American covered the breakthrough extensively. TIME magazine later named the hat as one of the best inventions of 2023, highlighting it alongside advancements in supercomputing, entertainment technology and materials science.
The public celebrated the discovery through online discussions, creative experimentation, and events such as Hatfest, a conference held at the University of Oxford’s Mathematical Institute. As co-discoverer Chaim Goodman-Strauss reflected, “People made this their own… It’s absolutely unique, in my experience, for a mathematical result to have a cultural life like that.”
In the January 2025 issue of BBC Science Focus magazine spotlighting the game-changing breakthroughs shaping the world since the year 2000, Sir David Spiegelhalter described the solution to the einstein problem as “the most important mathematical breakthrough of this century.” Aperiodic monotile enthusiasts continue to explore the shape as 3D-printed objects, quilting and textile designs, ravioli, and as stained glass art created by Sir David Spiegelhalter himself.
Impossible solids: Insights that helped elucidate molecular structure
The five Platonic solids and 92 Johnson polyhedra have long fascinated mathematicians. While exploring them, Professor Kaplan became intrigued by what he called “near misses,” geometric oddballs tantalizingly close to being a mathematically perfect solid. He documented many of these polyhedra on his website, including a structure built from 11-sided polygons, equilateral triangles and squares.
Years later, a Japanese biologist studying a manufactured protein structure known as a TRAP-cage discovered Professor Kaplan’s work. The molecular cage, formed from TRAP rings and bonded together with gold atoms, mirrored the structure of a near-miss solid Professor Kaplan had documented on his site and built using paper shapes and tape. Through a computational analysis of the stability of the TRAP-cage, Professor Kaplan helped the research team confirm that the protein’s molecular structure was physio-chemically possible. The resulting interdisciplinary study was published in Nature as “An ultra-stable gold-coordinated protein cage displaying reversible assembly.”
Geometric patterns in art and design
Professor Kaplan has long held an interest in computer-generated Islamic geometric patterns, a field that he leads. His paper with David Salesin, “Islamic star patterns in absolute geometry,” is the definitive work on the topic and has influenced both academic understanding and practical implementation of these patterns.
He has also made fundamental contributions to non-photorealistic rendering and geometric pattern generation. In particular, his paper with David Salesin titled “Escherization,” presented at SIGGRAPH 2000, helped draw the two fields closer together. He remains a sought-after reviewer in this research area and continues to explore the artistic and mathematical potential of decorative tilings, particularly in the style of M.C. Escher.
Professor Kaplan has developed a wide range of computational techniques to create, manipulate and analyze decorative patterns in computer graphics. His research with his students on image-guided maze construction, presented at SIGGRAPH 2007, introduced innovative graphical and combinatorial algorithms to design mazes based on images. And his work on optical art rendering with lines and curves introduced an algorithm that takes an arbitrary image and automatically generates the corresponding optical art composition.
More recently, he and his students have expanded digital tools for artistic abstractions with new techniques to pixelate vector line art, synthesize geometric patterns and draw hatching strokes, a traditional artistic method to produce tonal and shading effects. These contributions have expanded the techniques available for artistic rendering in computer graphics.
Professor Kaplan has been commissioned to create designs for various contexts including book covers, furniture, theatre productions, and architectural elements. His 3D-printed geometric kippahs were featured in an exhibition at the Museum of Modern Art in New York, and his parquet deformations have been incorporated into architectural installations at the National Museum of Mathematics.
Teaching excellence and service
In 2025, Professor Kaplan received the Faculty of Mathematics Award for Distinction in Teaching, recognizing educators who demonstrate exceptional pedagogical skill and a deep commitment to student learning. Known for lectures that are memorable, engaging and highly effective, he brings clarity and enthusiasm to complex mathematical and computational topics.
Since 2005, Professor Kaplan has served on the board of the Bridges Organization, which oversees the annual Bridges conference on mathematics and art. He contributes to executive decision-making and helps manage operations that make the conferences a success. In 2017, during the 50th anniversary of the Faculty of Mathematics, he hosted Bridges Waterloo 2017, a week-long event that brought together experts and enthusiasts in mathematics, art, music, architecture, education and culture.
ACM Distinguished Members at the Cheriton School of Computer Science
Professor Kaplan is the 13th faculty member at the Cheriton School of Computer Science to be named an ACM Distinguished Member. Previous recipients are Professors Daniel Vogel (2023), Khuzaima Daudjee (2022), Florian Kerschbaum (2019), Ian Goldberg (2017), Kenneth Salem (2017), Jo Atlee (2016), Charles Clarke (2015), Ihab Ilyas (2014), Mark Giesbrecht (2013), Don Cowan (2010), Anna Lubiw (2009), and Jeffrey Shallit (2008).
The Association for Computing Machinery is the world’s largest educational and scientific computing society, uniting computing educators, researchers, and professionals to inspire dialogue, share resources and address the field’s challenges. ACM strengthens the computing profession’s collective voice through strong leadership, promotion of the highest standards, and recognition of technical excellence. ACM supports the professional growth of its members by providing opportunities for life-long learning, career development, and professional networking.