In this imaginative, short book inspired by Alice in Wonderland, Aastha transports readers into “Calculand,” where Alice encounters the Mad Hatter, Cheshire Cat, and a delightfully silly caterpillar. Along the way, these whimsical characters introduce her to the core ideas of calculus: derivatives, limits, and the chain rule. With lively illustrations and playful storytelling, the project makes potentially intimidating concepts feel approachable. The judges admired the ingenuity of blending a beloved literary classic with mathematical ideas to create a welcoming doorway into calculus.
Click here to read Aastha’s book.
Purav’s “The Ballad of the Broken Sum” is a poetic yet comical tragedy told from the perspective of the harmonic series itself. Through verse, the series laments its fate: each term shrinking smaller and smaller, yet the sum forever refusing to settle. Along the way, Purav weaves in classical proofs—like Oresme’s grouping argument—while capturing the anxiety, persistence, and paradoxical “unharmonic” quality of this famous divergent series. The work is bold, poignant, and remarkably original, transforming a deep mathematical idea into a human drama. The judges were struck by its gutsiness, creativity, and emotional resonance, praising it as an unforgettable example of how poetry can illuminate mathematics.
Click here to read Purav’s poem.
Nickita and Philina bring high energy to this original musical performance about derivatives of trigonometric functions. Playing the keyboard and violin with jaunty flair, they perform a witty, memorable song that recites the often-confusing formulas in a way that’s hard to forget. The judges praised the musicianship, creativity, and humor of the performance, noting how the catchy tune will help students recall the formulas long after the performance is over. It’s a joyful example of how music can make learning math both fun and memorable
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Sujal’s essay brings a humanistic eye to the graphs of Algebra II and precalculus. The undulations of a sine wave become metaphors for life’s ups and downs; the shape of a circle mirrors the cyclical nature of life. By interpreting graphs as echoes of human experience, Sujal invites readers to see familiar xy-plane figures not as abstractions but as reflections of life itself. The judges admired this poetic interpretation, recognizing its potential to draw new audiences into mathematics by connecting it with emotion and meaning.
Click here to read Sujal’s essay.
Jason’s video turns a classic staircase problem into an explanatory tour de force. With humor, music, and great pacing, he introduces recursion formulas and dynamic programming through the question: how many ways can you climb an eleven-step staircase, if you can hop one, two, or three steps at a time? The ideas unfold in perfect order—skillful, but never pedantic—and culminate in real-world applications that show the broader reach of these techniques. The judges admired both the playfulness and the depth of this exceptionally well-crafted entry.
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In this innovative video, Neha and Sanvi translate the Collatz conjecture into music. Each number becomes a note on the piano, producing motifs that repeat when different starting numbers converge to the same sequence. By hearing the conjecture, rather than just reading about it, viewers gain an intuitive grasp of this famously unsolved problem. The judges praised the creativity, clarity, and interdisciplinary flair of this project, highlighting how human sensitivity to sound can reveal hidden patterns in mathematics.
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Inspired by the work of Vi Hart, Frida’s video explores why plants follow Fibonacci patterns. With a spirit of curiosity and wonder, she guides the viewer into the mathematics of phyllotaxis, the arrangement of leaves and seeds in plants. The explanations are pleasant and accessible, showing how the golden ratio and Fibonacci numbers appear in the natural world. The judges appreciated the enthusiasm and clarity of this project, as well as its ability to connect abstract mathematics to the beauty of everyday life.
Click here to watch Frida’s video.
Salma’s project uses a crisp, clever cartoon to illuminate one of the most famous problems in logic: the Wason Selection Task. By tying the puzzle to the idea of the contrapositive, she makes the underlying reasoning clear and accessible. The accompanying essay reinforced the lesson and framed the problem thoughtfully. While the cartoon’s style is simple, the communication is strong—conveying a subtle concept with admirable directness. The judges were impressed by this inventive approach to a classic puzzle in logic.
Click here to read Salma’s comic.
Grace’s video turns knot theory into a detective story, bringing abstract mathematics vividly to life. At the heart of the mystery lies the concept of tricolorability—an invariant that distinguishes different knots. With delightful clarity, Grace compares invariants to features of a person that remain unchanged despite changes in fashion or hairstyle, making a subtle concept instantly accessible. The judges loved the originality, charm, and concision of this entry, applauding its playful tone and lucid explanations as hallmarks of outstanding communication.
Click here to watch Grace’s video.
In this lively and inventive video, Chloe explains how mathematics transforms the apparent randomness of white noise into the more soothing pink noise. With clarity and humor, she ties the mathematics to real-world experiences teenagers care about—like how to get a better night’s sleep. The judges praised the strong explanatory thread, the use of props and scene changes, and the knack for making a non-standard topic both engaging and understandable. This was a polished, playful, and memorable exploration of math in everyday life.
Click here to watch Chloe’s video.
Samuel’s project combines poetry and visual design into a meditation on the experience of solving for x. The poem traces the arc of effort and understanding, from the blur of confusion to the moment when “the blur becomes a story.” The judges admired the integration of words, shape, and mathematical insight, all working together to convey what it feels like to wrestle with a problem until clarity dawns. Deeply original and beautifully expressed, this entry resonated as both art and math communication, earning its place as a standout winner.
Click here to read Samuel’s poem.
The judges are excited to recognize the video, “Skateboarding in 4 Dimensions,” by Thomas Li from Clarksville, MD, for its originality in making the connection between skateboarding and rotations in three dimensions. The video is passionate and fun, and the judges loved its playfulness. The skewering of the apple and Thomas’s genuine enthusiasm—conveying his belief that quaternion multiplication is cool—added to the video’s charm. This engaging and educational video stands out for its creativity and the enthusiasm it brings to learning and applying complex mathematical concepts.
Click here to watch Thomas’s video.
The judges are thrilled to recognize “PRIMES Card Game,” by Aria and Oma Makhija from Florham Park, NJ, for its elegant and original design, presenting a challenging yet accessible experience for players of all ages. The game involves using four given numbers and the basic operations of arithmetic (addition, subtraction, multiplication, division) to make a target prime number at the center of the card, encouraging players to find multiple solutions when possible. This engaging game can be played solo or with multiple players, providing excellent practice in mental arithmetic and fostering an appreciation for the properties of prime numbers. The card design is particularly commendable, offering clear instructions and examples that enhance gameplay. The accompanying video is both fun and informative, brimming with great energy. PRIMES Card Game stands out not only for its simplicity but also for its ability to engage and entertain children and adults alike.
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