Orange Window Publishing
What is the P vs. NP problem?
What is the P vs. NP problem? In simple words, it translates to the following question: Whether every problem whose solution can be quickly verified (NP) can also be solved quickly (P)? For instance, we can know at a glance if a Sudoku grid or a Rubik's cube is already solved. But does it mean we can solve it quickly too?
Apart from being one of the biggest mysteries in Computer Science, the P vs. NP Problem also has a deeper philosophical connection. The discovery of this problem is the culmination of an arduous journey that an entire tribe pursued in the twentieth century to arrive at a theory that would explain everything. The tribe included philosophers, mathematicians, logicians, and computer scientists. It was a journey filled with frustrations and triumphs. It was a journey that humbled some of the brightest minds on this planet. It was also a journey that was both an accomplishment and a failure. This book is not an attempt to offer a solution but to take you through the journey.
TESTIMONIALS
I bought this book because I was curious. I heard about the "P vs. NP problem" before but I didn't really know what it was about or why it was important. After reading it, I finally get it now, and it feels like someone showed me this really big secret that was there all along.
The author starts with very simple examples like checking if a word is a palindrome and gradually builds up to much harder ideas. At first it feels almost playful, but before you realize it, you’re grappling with the core concepts of computational complexity. I still remember the section where the number of state transitions jumps from 3 to 27 as input grows. It’s such a small detail, but it made the abstract idea of “complexity growth” suddenly click for me.
The storytelling is surprisingly engaging too. I never expected a discussion about the invention of chess to connect to why certain problems are considered hard, but it works. There are also plenty of real-world tie-ins like cryptography, optimization problems, AI, even quantum computing. The book constantly reminds you that this isn’t just theory locked away in academia. It has real consequences for how secure our data is, what kinds of problems AI might solve, and whether some challenges are simply unsolvable no matter how clever we are.
The book challenges you, and that’s where the magic is. The SAT proof had me pausing and rereading a few times, but the author always gives just enough guidance to help you get there on your own. And when the pieces finally clicked, it was one of the most rewarding “aha!” moments I have ever had from a book
By the end, I wasn’t just reading about a math problem anymore. I was thinking about the limits of computation, the fragility of assumptions we take for granted in technology, and even what it means for knowledge to have boundaries. It’s rare for a technical book to leave me feeling inspired and energized, but this one did exactly that.
I understand the content completely.
- Amazon Customer,
Japan