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Talk 01 — Mrinal Dhume (TU Delft) — [computing…]Local time: click here to view in your time zoneTitle: Difficulty-Based Generation of Paperfolding Puzzles
Abstract
Paperfolding puzzles are a unique type of puzzle: they may appear simple and accessible, yet they can be very challenging. Inspired by an existing puzzle, based on a square grid and containing slits, we developed a generalized model for such puzzles, with arbitrary shapes and slits. We present that model, for which we implemented a puzzle generator that models paperfolding using constraint solving, and derives the folded states for a given paper shape and size. We also discuss a difficulty metric for each puzzle layout generated, based on the various types of folds it requires. This allows for very customized puzzle generation, for both the target audience, paper shape and type of content per cell grid. Our generator found several new types of folds that are only possible because of the slits, which make the puzzles more varied, interesting and challenging. We conclude with a discussion on some features of the puzzle space for some simple formats.
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Talk 02 — Shanna Dobson (Harvey Mudd College ) — [computing…]Local time: click here to view in your time zoneTitle: Golden Architecture and Oneiric Diamonds: A Compendium of MathArt
Abstract
What does it mean to think in structures that cannot be seen? This presentation offers a compendium of MathArt through four mathematical poems—Diamond, Decembris, Golden Hyperphantasia, and ’Twas the Functorial Night—together with the film presentation Oneiric Architecture: The Sound of Resolution. Across these works, category theory, p-adic geometry, perfectoid spaces, Fibonacci structure, and mathematical memory become materials for poetic and cinematic composition. Diamond moves between a mineralogical diamond and Scholze’s categorical diamond, using total internal reflection, universal properties, and terminality to explore identity, confinement, and the haunting possibility of being unable to see beyond one’s own reflections. Decembris unfolds through Fibonacci line lengths, building a wintry imaginative world whose poetic architecture is itself mathematical. Composed as a golden fibble in a 13/8 structure, Golden Hyperphantasia imagines memory as an entangled, p-adic architecture in which moments are organized hierarchically rather than continuously. In ’Twas the Functorial Night, a luminous crescendo of mathematical, literary, and sensory allusion makes winter itself functorial, transfiguring the experience of studying for qualifying examinations into a radiant mathematical Christmas. Oneiric Architecture: The Sound of Resolution renders the experience of working in deep abstract mathematics as an interior glassy landscape shaped by music, movement, reflection, tension, and release. In concert, these works approach MathArt as a profound imaginative practice: a way of inhabiting unseen mathematical structures through poetry, pattern, fantasy, memory, and artistic form.
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Talk 03 — Mikael Vejdemo-JohanssonCancelled (CUNY College of Staten Island, CUNY Graduate Center) — [computing…]Local time: click here to view in your time zoneTitle: Incomplete Open Platonics
Abstract
Sol LeWitt famously enumerated all the incomplete open cubes, finding 122 of these connected, non-planar subsets of the edges of the cube. Since then, while several projects have revisited the cube enumeration, no such enumeration has been published for any other interesting solid. In this paper we present work on enumerating all the incomplete open platonic solids, finding 6 tetrahedra, 122 cubes (just like LeWitt), 185 octahedra, 2'423'206 dodecahedra and 16'096'166 icosahedra.
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Talk 04 — Christine Picot* (University of South Florida) and Josip Slisko* (Benemérita Universidad Autónoma de Puebla (BUAP), Mexico) — [computing…]*Presenting SpeakersLocal time: click here to view in your time zoneTitle: Old Puzzles, New Possibilities: Exploring the Pedagogy of Matchstick Puzzles
Abstract
Matchstick puzzles have challenged problem solvers for more than a century. What happens when we bring these historical puzzles into today’s classrooms? Using toothpicks in place of traditional matchsticks, we explored a sequence of historical puzzles with students in fourth- and fifth-grade classrooms. What began as a simple puzzle became an opportunity for students to search for multiple solutions, compare ideas, question assumptions, and explain their mathematical thinking. As students discovered that there could be more than one solution, confidence grew. Students who did not typically volunteer began sharing their solutions and ideas. The puzzles also created natural opportunities for mathematical vocabulary and conversations about squares, rectangles, equal sides, parallel and perpendicular relationships, and spatial reasoning. Students surprised us by finding multiple solutions where published versions showed only one and identifying possibilities not represented in the historical solutions we examined. We conclude with a six-matchstick challenge that pushed students beyond two-dimensional thinking and our use of “Sweet Help” to support exploration of a three-dimensional solution without giving away the answer. Together, these experiences show how historical matchstick puzzles can be reimagined as brief, low-preparation mathematical warm-ups with potential across K–12 classrooms to build confidence, encourage students to share their thinking, strengthen mathematical language, and create opportunities for reasoning and productive struggle.
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Talk 05 — Paul Hildebrandt (Zometool Inc.) — [computing…]Local time: click here to view in your time zoneTitle: The Zometool: math you can feel
Abstract
Fun ways to introduce relationships among numbers and space, using the Zometool. Learn how to make bubbles, shadows and projections from hyperspace. The Zometool is hands-on quantum math, mother of all maths and queen of the sciences. It's informed the work of numerous Nobel prizewinners and Fields medalists, but designed for kids, and kids of all ages love it. Find out why.
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Talk 06 — Shanthi Chandrasekar (Independent) — [computing…]Local time: click here to view in your time zoneTitle: Kolam- A Traditional Treasure Trove of Mathematical Concepts
Abstract
Kolam is a daily ritual among Tamil women, who create complex patterns with dots and lines using rice or rock powder on the floor in front of their houses. These aesthetically beautiful, mathematical patterns are philosophical, and signify the cosmos, symbolizing the concepts of impermanence, non-attachment and the cycles of creation and dissolution. Kolams are mathematical in their making involving geometry at its core. The patterns are composed of six key shapes formed by the six combinations of four quarters of a circle and a square. Concepts such as symmetries, fractals and graph theory are also involved in this creative art form though the practitioners perform it every day simply following an age-old tradition. In my Kolam-inspired artwork, I have tried to include the beauty of the art form along with its cultural, mathematical and philosophical significance.
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Talk 07 — Keynote Address — Nancy Blachman KEYNOTE SPEAKER (Julia Robinson Mathematics Festival) — [computing…]Local time: click here to view in your time zoneTitle: How can you spark interest & curiosity in mathematics? Try a Julia Robinson Mathematics Festival (JRMF.org)
Abstract
Martin Gardner suggested, “present an intriguing mathematical game, puzzle, magic trick, … [that some] tend to avoid because they seem frivolous.” That’s exactly what the St. Mary’s Math Competition qualifying problems did for me. Wanting others to have a similar sort of experience, I founded the Julia Robinson Mathematics Festival in 2007, with Google hosting the inaugural event. Since then, JRMF has hosted over 2000 events in over 30 states and on 6 continents, serving as a beacon for engaging underrepresented groups—including girls and minorities—in STEM. At each Festival, there are tables or (breakout rooms for online events) with different activities. JRMF’s low-floor, high-ceiling freely-available activities on JRMF.org use hands-on manipulatives and digital apps to invite participants to explore collaboratively or independently. The activities often captivate those who already enjoy math, as well as those who discover that math can be enjoyable. Designed for educators, parents, and students, JRMF offers activities for accessible open-ended engaging math explorations. Join this session to explore some of my favorite activities that spark interest and curiosity in mathematics.
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Talk 08 — Madonna Yoder (Gathering Folds) — [computing…]Local time: click here to view in your time zoneTitle: Origami Tessellation Design Possibilities from Two Simple Twists
Abstract
Origami tessellations are folded from a single sheet of paper using twisting shapes that are connected by pleats. If we restrict ourselves to using two particular twists (open hexagon and closed triangle twists), how many different patterns can be made? This search yields several infinite families of distinct designs using unexpected applications of symmetries on a variety of tilings.
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Talk 09 — Sy Chen (Origami Artist) — [computing…]Local time: click here to view in your time zoneTitle: Angles, Edges, and Epiphanies: Designing Puzzles Through Origami
Abstract
Geometric puzzles such as polyominoes and tangrams have long served as a meeting point for recreational mathematics and paper-based design. This presentation examines how to use origami techniques to generate playable geometric puzzles, emphasizing the mathematical and structural considerations involved in folding tiles from a single sheet. The talk begins discussion of an early design challenge: constructing a one-piece, two-color 5×5 checkerboard. Although attempts to complete the challenge were unsuccessful, they led to a systematic investigation of two-color double-sided checkered polyominoes, including trominoes, tetrominoes, and pentominoes. A major turning point occurred in March 2023 with the introduction of the “einstein” monotile. The development of foldable versions of the hat, turtle, and spectre shapes illustrates how origami can engage directly with contemporary discoveries in tiling theory. The presentation also addresses jigsaw-inspired constructions, notably a single square sheet that can be folded into 24 distinct fitting shapes. Collectively, these examples demonstrate the dual process inherent in origami puzzle design: the geometric precision required to engineer foldable tiles and the subsequent combinatorial richness of assembling them in tiling puzzles accessible to anyone regardless of their origami experience.
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Talk 10 — Dan Bach (dansmathshop) — [computing…]Local time: click here to view in your time zoneTitle: Four, Fourier, Fouriest - See It, Hear It, Draw It with Sine and Square Waves
Abstract
Sine wave based Fourier series are well-suited to art, animation, and sound. In this talk we will see various methods of drawing and using Fourier series, including Form Your Face, Discrete Cosine Transforms, and Stacking Up the Circles. Other mathematical art examples that use Fourier approximations of the square wave are: Fourier Mountains, Sloppy Cube, the Banded Glass. Fourier series are quite good at approximating periodic functions, but have you heard, you can also listen to them! The Music of the Primes involves the Riemann Hypothesis, and ’in addition,’ Sounds Like Trig Spirit explores waveforms of compound trig functions. The components of a random compound wave are also fun to guess at, while seeing the closeness score in real time. Audience members will be encouraged to pretend to be students. Take these images and ideas back to your classes, or make your own art!
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Talk 11 — Caleb Madrigal (https://gods.art) — [computing…]Local time: click here to view in your time zoneTitle: Painting with Equations
Abstract
Graphing equations is typically done for the purpose of problem solving. But visualizing equations can also be done for the purpose of beauty. But typically, equations are visualized in binary logic (black lines on a white background). But when we take off the binary lens and put on a non-binary visualization algorithm, we get gradients of color. We refer to this as "fuzzy graphing". Mathematically we can think about this as graphing approximate equations (≈). Beyond making more interesting visuals, fuzzy graphs sometimes reveal details which are completely invisible in conventional (binary) graphs. In this talk, we'll also introduce a free new tool for fuzzy graphing.
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Talk 12 — Jacob Heidenreich (Loras College) — [computing…]Local time: click here to view in your time zoneTitle: Uses of Games and Game Design in the Classroom
Abstract
In this talk Dr. Heidenreich will outline several ways one can use games and game design in the classroom, and share his experiences doing each. This can vary from using a game as an object of study (e.g. doing statistical analysis on a game like Catan), designing games to teach mathematical concepts (like Function Battleship), modifying existing games to accomplish the two above things, designing one's whole class as a gamified experience, or using game design principles to structure your class in a way that isn't obviously gamified.
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Talk 13 — Lidia GonzalezCancelled (York College of the City University of New York) — [computing…]Local time: click here to view in your time zoneTitle: The License Plate Challenge
Abstract
The most recently issued New York State (NYS) automobile license plates consist of three letters followed by four digits (ie. ABC1234). I am unaware of any restrictions, so for the purposes of this work, assume that any four digits may appear in a plate and that each digit may be repeated one or more times. The License Plate Challenge is a sort of solitaire that involves using the digits on a plate to construct a valid number sentence. For example, the digits in the plate ABC1234 can be used to create 1+4 = 2+3. In this talk I explore the question of whether, given certain conditions, it is possible to construct such a sentence for all possible plates.
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Talk 14 — Söhnke Vetter (Universität Bremen) — [computing…]Local time: click here to view in your time zoneTitle: Tensegrity as a Geometric Design Principle for Lighting Objects - The Development of the Pendant light Teru
Abstract
Tensegrity describes a structural principle in which elements under compression are held in position by elements under tension, creating stable spatial configurations through the interaction of opposing forces. This presentation explores how this principle can be used not only as a structural system, but as a generative geometric principle in product and lighting design. The project investigates how variations in the arrangement, rotation and transformation of compression members can produce different spatial configurations and surface patterns. Starting from elementary tensegrity structures and polygonal geometries, a series of physical models and digital constructions was developed to explore relationships between geometry, symmetry, modularity and form. The investigation culminates in the development of Teru, a lighting object in which a textile membrane is tensioned by the compression members. The resulting form emerges from the interaction between component arrangement, prestress and material behaviour. The design process therefore combines geometric exploration with physical prototyping and considerations of light, material, fabrication and functional use. By moving between mathematical experimentation and design practice, the work examines how relatively simple structural rules can generate complex and unexpected spatial forms. Tensegrity is thus approached as an interdisciplinary field connecting pattern exploration, material experimentation and artistic design.
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Talk 15 — Duston Wetzel (independent) — [computing…]Local time: click here to view in your time zoneTitle: Wetzel's Weaves: An Exploration of Periodic Helices
Abstract
Almost a decade ago, I was asked a deceptively simple question: How would you build a large gyroid? I never answered this question, but my attempts led me down a rabbit hole of discovery-beginning with the gyroid's geodesics. In this talk, I will tell the story of my ongoing project to discover, classify, and physically build periodic arrangements of woven helices-modular structures that combine screw symmetry and friction to stay together without glue, welding, or joints of any kind. Using a combination of mathematical modeling and physical experimentation, I have discovered dozens of such structures, including doubly periodic, triply periodic, and polyhedral variations. These structures demonstrate how local geometric constraints can produce global periodicity, symmetry, and connectivity. What began as an attempt to understand a famous geometric surface eventually became a playful exploration of a family of geometric objects. The project sits at the intersection of science, technology, engineering, art, and mathematics.
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Talk 16 — William Holt (IU Bloomington Alumnus) — [computing…]Local time: click here to view in your time zoneTitle: Solving Cubics in Origami, and one Practical Application
Abstract
The combination of a ruler and compass on a piece of paper can construct several complicated designs and geometric wonders. Famously, there is a limit to the types of constructions possible with these tools. In particular, it can be proven that it is impossible to trisect an arbitrary constructed angle, and that it is impossible to construct a cube of double the volume of a given cube using just a ruler and compass. However, these tasks are possible with origami methods due to paper's inherent structure. As a mathematician and origami artist, I use several geometric origami techniques in my designs and artwork, most of which have strong ties to the underlying mathematics of paper folding. In particular, precise constructions are especially important to my current origami design series on "skeletal polyhedra". This talk will showcase several interesting geometric constructions involved in my origami design process, including some constructions outside the scope of ruler and compass, and will demonstrate the necessity of such constructions and the consequences of poorly placed approximations.
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Talk 17 — Alex Feingold (Binghamton University (State University of New York)) — [computing…]Local time: click here to view in your time zoneTitle: Tessellations from hyperplane families: Weyl and kagome cases
Abstract
For a research project with colleagues, I have been studying tessellations of Euclidean spaces which arise from families of hyperplanes. Many examples come from a finite type root system and associated finite Weyl group, W, whose affine extension acts on the tessellation. Other examples do not come from a root system and Weyl group. In this talk I will discuss the details of some Weyl and some non-Weyl kagome tessellations, including 3D printed models which help to visualize the geometry.
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Talk 18 — Taiki Aiba (Georgia Institute of Technology) — [computing…]Local time: click here to view in your time zoneTitle: Quad-Packing in the Game EvenQuads
Abstract
EvenQuads is a SET-like card game in which the goal is to find quads, sets of four cards satisfying a prescribed pattern. The cards in a Quad-2N deck naturally correspond to the points of the finite affine geometry AG(N, 2), where quads correspond to affine 2-flats. In this paper, we investigate the extremal problem of determining which collections of k cards contain the maximum possible number of quads. Using the affine geometry underlying the game, we develop a structural theory of flat-packed sets and prove that every maximally quad-packed set is flat-packed. As a consequence, we show that the maximum number of quads among k cards depends only on k and not on the ambient deck size, and that, up to affine equivalence, there is a unique maximally quad-packed set of k cards. To derive this key result, we show that if a set of size k spans a dimension larger than ⌈log2(k)⌉, then it is not maximally quad-packed.
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Talk 19 — Son Tu (Baylor University) — [computing…]Local time: click here to view in your time zoneTitle: Irrational Motion, Uniform Distribution, and Homogenization
Abstract
A particle moving in a straight line on a torus can trace a surprisingly intricate pattern. For irrational directions, the trajectory becomes uniformly distributed, but a subtler question is: how fast does this happen? We will explore this question through geometric examples and simple Fourier ideas, showing how the rate depends on both the arithmetic properties of the direction of motion and the regularity of the quantity being averaged. This naturally leads to Hölder and Besov spaces, which measure oscillations across different scales. We will conclude by explaining how the same quantitative averaging problem appears in homogenization, where microscopic oscillations are replaced by effective large-scale behavior.