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Title: Albert Hyunsung Shim to Publish New Mathematics Book Explaining Why dy over dx Behaves Like a Fraction

Albert Hyunsung Shim, founder of the Institute for Mathematical Research, which has offices in both Korea and the United States, is set to release a new mathematics book this August titled “Why dy/dx Acts Like a Fraction”, which offers a rigorous explanation of the true nature of the derivative notation dy/dx.[Albert Hyunsung Shim]In this upcoming work, Shim reveals that although dy/dx is not technically a fraction, its behavior can be mathematically justified as if it were one—based on the concept of limits, the foundational idea behind calculus. His research sheds new light on a symbol that has been used repeatedly in calculus education from high school to university, often explained only through intuition or memorized rules.For generations, students have accepted identities such as “dy/dx = (dy/du) × (du/dx)” and “dy/dx = 1 / (dx/dy)” as axiomatic or purely intuitive without seeing a formal justification. Even Gottfried Wilhelm Leibniz, credited with introducing the notation, is not known to have provided a rigorous rationale for its structure.Shim seeks to overturn this longstanding gap in mathematical pedagogy. His book reconstructs the internal logic behind dy/dx by employing the mathematical definition of limits. In doing so, he demonstrates the logical necessity for dy/dx to behave like a fraction, not just in appearance but in the underlying reasoning.The author anticipates that his findings will have practical implications in math education. By offering students a conceptual framework grounded in mathematical reasoning, rather than rote memorization, the book could foster deeper understanding of calculus and its foundational principles. The book will be published both in Korea and internationally. An accompanying academic paper is also expected to become a val...

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