The Delicate Art of Brute Force

How to Compute It When You Can't Solve It

Paul J. Nahin

• Publisher: Princeton University Press
• Year: 2026
• Print ISBN:
  9780691267470
  9780691267463
• eBook ISBN:
  9780691289625
• Topic: Mathematics
• Subtopic: Programming
• Index: Mathematics

Using everyday computational power to tackle complex—and seemingly unsolvable—math problems

Confronted by a math problem of seemingly impenetrable difficulty, what can you do? In The Delicate Art of Brute Force, Paul Nahin shows how even if you can’t solve such a problem, you can still get an answer. The computational power of your own computer—the desktop in your home office, the laptop on your coffee table—can be deployed to overwhelm a problem’s complexity through a massive number-crunching assault. Nahin presents a series of apparently intractable math problems and shows the thought process that allows computational solution. Most of the problems are not abstract constructions but originate in the real world—one chapter is titled “How Wi-Fi Coverage and Anti-Submarine Warfare Are the Same.” For each one, Nahin compares computational and analytical approaches, demonstrating how well the computer solutions agree with theory. As a bonus, sometimes the computational solution is better, giving more insight or greater flexibility.

Along the way, Nahin traces the evolution of high-speed electronic computation, explaining that it upended the way analysts approach complex math problems. After the postwar debut of ENIAC (Electronic Numerical Integrator and Computer) and the ever more powerful electronic computers that came afterward, problems that were simply too difficult or messy for analytical treatment could be defeated by the application of pure brute force—the ability of computers to perform an enormous number of simple operations in just minutes. Today, we can harness that computational power from our couches. Accessible to anyone who’s mastered high school calculus, this engaging book gives both mathematicians and nonmathematicians plenty to think about.

Table of contents

• Cover Page
• Also by Paul J. Nahin
• Title Page
• Copyright Page
• Dedication
• Contents
• Prelude: The Birth of Electronic Computation
• 1. Computers That Play Games
• 2. A Gambling Problem (the Monte Carlo Concept)
• 3. The Carpenter’s Problem
• 4. Wi-Fi Coverage and Antisubmarine Warfare Are the Same Math Problem
• 5. A Problem in Electric Circuit Theory
• 6. Simulation of a Purely Deterministic Problem
• 7. Schwartz’s Question: The Toughest Problem in This Book
• 8. A Counterexample Concerning Computer Simulations
• 9. Monte Carlo Integration
• 10. Gamma-Ray Paths across a Semicircle
• Appendix. Got a Math Question? Try Looking Here
• Acknowledgments
• Notes
• Index