ITP Thesis Archive 2025

Project Description

"Not so Parallel" explores the discovery of non-Euclidean geometry through storytelling, focusing on the human experiences behind mathematical breakthroughs. Often, mathematics is seen as a rigid system of strict rules, making it feel distant and impersonal. However, history reveals that mathematics is shaped by human struggles, doubts, and perseverance. This project highlights the flaws within Euclidean geometry and what happens when those flaws are carefully examined. By showcasing the emotions of mathematicians—excitement, frustration, and hesitation—it seeks to honor their efforts and make their experiences more relatable.
To bring this story to life, I am creating two pop-up books centered on János Bolyai and his journey in geometry. The first is a black-and-white pop-up museum model, designed as an imagined immersive experience where the audience steps into Bolyai’s perspective. In this interactive space, they will feel the thrill of his discovery, followed by the disappointment and frustration upon receiving Gauss’s dismissive response. The second is a storybook, narrating Bolyai’s adventure from a third-person perspective, making his story accessible to a broader and possibly younger audience.
Through these works, this project serves multiple purposes: to organize and visually express my own understanding of the topic, to celebrate the mathematicians who contributed to non-Euclidean geometry, and to invite the audience to see scholars not as untouchable geniuses, but as passionate individuals who struggled, doubted, and ultimately changed the world.

Technical Details

Paper engineering.

Material and tool used:
Cardstock
Utility knives and scissors
Acrylic markers, pens, pencils
White glue, tape, ribbon
Rulers

Software used:
Illustrator (a few sketches for laser cutting)
Excel (measurements and calculations)

Research/Context

This project arises from a personal intersection of art, design, and mathematics. With a background in applied mathematics and a deep enthusiasm for geometric reasoning, I have long wanted to integrate mathematical ideas into my creative work. This thesis became an opportunity to reflect on a topic that I find both accessible and profound—non-Euclidean geometry—and to share it in a form that can engage those outside the mathematical world. My goal is not only to celebrate the elegance of mathematical thought, but also to soften the subject’s intimidating edges, making space for emotional connection and curiosity.
Geometry, more than other mathematical domains, lends itself to visual and spatial storytelling. Its foundational role in education and its visual clarity make it an ideal subject for reinterpretation through design. While Euclidean geometry is familiar to most, its structure is built on five postulates, the fifth of which—the so-called “parallel postulate”—is notably more complex than the others. For centuries, mathematicians tried and failed to derive it from the rest. This ultimately led to the discovery of non-Euclidean geometry, a groundbreaking shift that expanded the mathematical universe and challenged assumptions about space and logic.
As Marvin Jay Greenberg writes in Euclidean and Non-Euclidean Geometries: Development and History, the historical struggle to accept non-Euclidean geometry is “a valuable and accessible case study in the enormous difficulty we humans have in letting go of entrenched assumptions.” Inspired by this framing, my project focuses on János Bolyai, one of the central figures in this discovery. I aim to highlight his personal journey—not just the mathematical insights, but the emotional weight of working in this field.
To translate these ideas into a physical experience, I looked beyond textbooks to other fields. M.C. Escher’s art and the mobile game Monument Valley both explore geometric paradoxes and visual intuition in ways that resonate with broad audiences. At the same time, experiences like visiting MoMath, the National Museum of Mathematics, and doodle exercises I hosted for my peers have sharpened my awareness of how easily educational experiences can become light and playful.
By using storytelling and paper engineering, this project presents mathematical history as a personal, emotionally rich narrative. It aims to open the story up to new audiences—not as a lesson in formulas, but as a shared human experience of wonder and change.