Mathematical Explorer’s Serendipitous Creation – A Thousand Pages of Mathematical Beauty
posted: 03-Feb-2025 & updated: 04-Feb-2025
I aim to create a companion resource that illuminates connections between concepts and enriches their mathematical exploration journey.
Math Codex
- Math is Fun & Beautiful! - slides
- Math is Fun & Beautiful! - article version (converted from slides)
A Journey Through Mathematical Beauty
Mathematics has always been a profound passion of mine, rooted in both its pure beauty and the joy of exploration. This passion has guided me through increasingly intricate mathematical landscapes – from the elegance of number theory to the captivating world of inequalities, and onward into deeper territories of abstract algebra and analysis — few people could ever imagine how thrilled I was when learning about the moment when the French mathematician, Lebesgue, won the race of inventing (or finding) a new way to overcome the limits of Riemann integral in 1912, which let all human race witness the birth of measure theory! My journey expanded further into linear algebra and its numerical applications, statistics (with particular focus on its measure-theoretic foundations), and ultimately to convex optimization – an advanced field with powerful practical applications that became the focus of my thesis work at Stanford University under supervision of Prof. Stephen P. Boyd.
What began as a personal project — creating LaTeX slides to preserve these insights for my future self 😊 — evolved into something far more significant. As the collection grew, I recognized its potential to serve as a comprehensive resource for others who share this mathematical curiosity. The resulting work, particularly the article version available in the section, represents a synthesis of these extensive slides and research.
My goal throughout has been to create something that would resonate with advanced learners and professionals in the field. Through careful attention to clarity in explanations and rigor in proofs, I’ve aimed to make these complex concepts not just accessible, but genuinely engaging for those ready to explore them deeply.
A profound realization recently dawned on me: my lifelong urge to deeply understand mathematics wasn’t fundamentally about mathematics at all … It was an expression of something far more fundamental — my innate desire to glimpse universal truth. This connection between mathematical exploration and the search for universal truth isn’t just philosophical speculation; I explore it thoroughly with concrete examples in my related posts on From Prime Numbers to Physical Laws - Arbitrariness or Inevitability? and (WIP) Inevitabilities!.
Genesis - From Personal Notes to Mathematical Odyssey
My journey began with a deceptively simple goal: to create a structured approach for studying and retaining advanced mathematical concepts. I started documenting the concepts that most challenged and captivated me — from the elegant foundations of algebraic structures to the subtle depths of real analysis and measure theory. LaTeX emerged as the natural choice for this endeavor, offering the precision and beauty that mathematics demands. What started as personal study slides unexpectedly blossomed into an extensive collection, spanning across diverse mathematical territories I hadn’t initially planned to explore.
Though my initial intention was just to create simple notes, I found myself drawn to the rich feature set that LaTeX provides beyond its beautiful typography. The powerful indexing and citation systems became invaluable tools, allowing me to weave connections between related concepts throughout what eventually grew into close to 1,000 pages of slides — a scope that, as mentioned, I never anticipated!
Evolution - Beyond Personal Understanding
As my collection of slides approached the thousand-page mark, I began to see their potential beyond personal reference — they could serve as a valuable resource for others on similar mathematical journeys. This realization led to a meticulous process of organization and refinement, transforming dense technical content into clear, comprehensive explanations while preserving the mathematical rigor that advanced topics demand. The challenge of balancing accessibility with depth became a driving force, pushing me to develop presentations that would engage readers while maintaining the precision essential to mathematical understanding.
Bridging Minds - A Resource for Mathematical Explorers
This work is crafted specifically for advanced learners and professionals who are deeply immersed in mathematical studies. While the material’s complexity places it beyond general audience territory, it offers profound value for those venturing into the deeper waters of mathematics — from the abstract realms of algebra and real analysis to the practical domains of convex optimization, and numerical linear algebra. My vision is to provide these dedicated minds with more than just another reference; I aim to create a companion resource that illuminates connections between concepts and enriches their mathematical exploration journey.
Horizons Unfold - The Path Forward
While this work represents years of mathematical exploration and documentation, I see it as just the beginning of a greater journey. The mathematical landscape is vast, and there are still many territories to chart — from deeper investigations into linear algebra and its numerical foundations to the fascinating realm of combinatorial optimization. My vision extends beyond just adding content; I aim to forge a living mathematical library that grows and evolves, serving as a trusted companion for students, educators, and professionals who share this passion for mathematical discovery.
The Continuing Quest for Universal Truth
Mathematics stands as humanity’s most precise language for describing universal truths — a bridge between abstract thought and practical revelation. Through sharing this work, I hope to contribute not only to the mathematical community but to all fields where mathematical rigor illuminates the path to discovery. From theoretical breakthroughs to practical applications, this resource aims to serve as a catalyst for advancement across disciplines. I invite fellow travelers on this mathematical journey — whether you’re an advanced learner exploring these depths or a professional seeking precise understanding — to join in this ongoing exploration of mathematical beauty and truth.
Continue the Exploration Together!
I deeply value dialogue with fellow mathematical explorers. Your insights, questions, and perspectives can enrich this ongoing journey of discovery. I welcome all comments and discussions — please reach out to me at sunghee.yun@gmail.com with “universal truth” in the subject line.
This is just the beginning of our mathematical conversation! I'll be exploring each topic in depth through upcoming blog posts, starting with our first deep dive into inequalities! Stay connected for these mathematical adventures!