How Not to Be Wrong: The Power of Mathematical Thinking

How Not to Be Wrong teaches that mathematics is not primarily about calculation but about disciplined reasoning. Most major conceptual errors—political misjudgments, medical mistakes, financial delusions, superstitions—arise from predictable misunderstandings of probability, correlation, randomness, regression, and nonlinear effects. Mathematics protects us from confident ignorance by demanding clarity in assumptions, skepticism toward easy explanations, and humility about the unknown.

Ellenberg argues that we cannot eliminate uncertainty, but we can dramatically reduce avoidable mistakes. When we recognize survivorship bias, regression to the mean, the difference between correlation and causation, the danger of straight-line thinking, and the meaning of probability, we stop being fooled by compelling but flawed stories. Mathematical thinking strengthens judgment, allowing logic and intuition to work together. We may still be wrong occasionally, but we will be wrong for better reasons—and right more often when it matters.

Jordan Ellenberg is a mathematician and professor at the University of Wisconsin–Madison, specializing in number theory. He earned his PhD from Harvard University and has written extensively for publications such as The New York Times, Wired, and The Wall Street Journal. Ellenberg is recognized for making sophisticated mathematical ideas accessible and engaging for general audiences through real-world examples, humor, and storytelling. His work emphasizes the everyday relevance of mathematics and the importance of using it to think clearly in a world filled with misleading statistical claims and complex decisions.