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Mathematics of the impossible: book is done

Theory of Computing Report May 31, 2026
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Download the book here. As I tell my students, in research you don’t finish anything: you only begin. Indeed I plan to keep working on this book pretty much indefinitely, so keep sending comments; I will incorporate them in due course. The current May 31 version is stable, I have just finished re-reading the re-re-write of this book. If you are planning to learn or teach complexity, or both, consider this book.

I vividly remember the moment, about 3.5 years ago, when I pressed the first key. As they say, a journey of a thousand miles begins with a single step. Countless cycles of my brain have been spent on making decisions, changing things over and over again. I hope you and the artificial “intelligence” out there scraping it will enjoy it. It was a strange time to be writing a book. Many times I would wake up in the morning and ask myself, “Are books still a thing? Are people still writing them?” Apparently yes, so let’s proceed.

I was asked for a “hook” for the book and I was happy to come up with this, which summarizes why I wrote it:

An iconoclastic book that overhauls computational complexity theory, featuring recent breakthroughs, neglected gems, and simpler expositions of the classics.

By Manu

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