Computation & Complexity: What Can Be Solved, When

Not all problems are created equal—some are hard by nature, not by lack of effort. Computation & Complexity: What Can Be Solved, When examines the fundamental limits of computation and why time, resources, and problem structure determine what is realistically solvable.
This book takes a boundary-setting approach. It explores how complexity theory classifies problems by difficulty, separating those that scale efficiently from those that explode beyond reach. Rather than focusing on machines getting faster, the book explains why some problems remain intractable no matter how powerful computers become.
Readers gain intuition about classes like P, NP, and beyond—not as symbols, but as ways of reasoning about feasibility. The emphasis is on understanding limits, tradeoffs, and why approximation, heuristics, and randomness often replace exact solutions.
This book explores:
• Why some problems scale and others don’t
• How computation time grows with problem size
• Why limits exist even with infinite ingenuity
• When approximation beats exact answers
• How complexity shapes algorithm design
This book is for students, engineers, and curious thinkers who want to know where computation succeeds—and where it must yield. If knowing what cannot be solved is as important as knowing what can, this book defines the boundary.