Albert Hyunsung Shim to Publish New Mathematics Book Explaining Why dy/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 valuable resource in the field of mathematics education.
 
The book has already garnered early praise from academic circles. Professor Hemant K. Singh of the Department of Mathematics at the University of Delhi, a leading institution in India, shared his thoughts after reviewing the manuscript.
 
"This work is a game changer, particularly for the new learners of differential calculus. It makes the operation of calculus so mind-blowingly intuitive that the students do not have to remember all its nitty-gritties. The results are thoughtfully derived from the fundamental rules of calculus. This research is indeed made-easy for both the teachers and the students."
 
Albert Hyunsung Shim is a seasoned author of mathematics textbooks widely used in the U.S., particularly for AP Calculus and international math competitions. He currently heads the Institute for Mathematical Research and is slated to serve as a question setter for the Indian Mathematical Olympiad starting this fall.
 
“Mathematics derives its true value from uncovering and applying the logical structures that lie beneath its surface,” said Shim. “I hope this book inspires students to appreciate the inherent beauty of mathematics in a new way.”
  

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