The Duality Revolution

My research in TRIZ started in 1973 with the discovery of a duality relationship in the TRIZ 40 principles. In 1974 I came to a conclusion that the way to resolve physical contradictions is separate the conflicting requirements between the dual "sides" of an object. Specifically, separation between parts and the whole (later called the separation in structure) followed from this idea. Then space-time duality in TRIZ was discovered, etc. etc.

Over time my research on duality grew beyond TRIZ and articles were already not enough to present it. Therefore, I decided to write a book. It is now available at Here is its synopsis:

Duality is everywhere. It is one of the fundamental building blocks of the world. The book examines inventive problem solving from the perspective of duality and provides a list of duality methods for solving inventive problems.

These methods often involve replacing a direct physical effect or chemical reaction with a dual one. The book presents, for the first time, a catalog of such dual effects and reactions, which makes it an indispensable handbook for inventors.

Not all problems can be solved in the form in which they are formulated. This requires transformation of the given problem into a dual problem. The book provides methods for such problem transformations.

Very often at the heart of a problem lies a contradiction. It has been found that contradictions can be resolved by separating contradictory requirements between the "dual sides" of an object. The book provides an exhaustive list of methods to accomplish such separation. Each method is illustrated with several examples of inventions in which it has been used.

The book also introduces the theory of dual technological systems and shows how to use it when solving inventive problems.

Surprising as it may seem, developing the theory of creative thinking and attempts to formalize it, led to an insight into what mathematics is. It is the science about equal dualities. This means that axioms of any mathematical theory can be replaced by other axioms asserting the equivalence of certain dual expressions. This is demonstrated in the book on the example of the axioms of the Euclidean geometry. It is also shown on several examples that theorems can be reformulated to reveal the equality of dualities hidden behind them.

The book is regularly updated and new stuff is added. Check out the latest and greatest version on Amazon.