Math — Common Mistakes

A collection of the most common errors students make in math, with explanations of why these intuitions fail.

Most math mistakes are not random. They come from understandable shortcuts: overgeneralizing a rule, ignoring a condition, or treating a symbol pattern as if it always means the same thing. These pages unpack the tempting wrong idea, show where it breaks, and replace it with a more reliable way to think about the concept.

Use this section when a topic keeps producing the same kind of error even after more practice. The right fix is usually not more repetition, but a clearer mental model of what the concept is doing and why the shortcut feels convincing in the first place.

Use these pages to diagnose:

which shortcut or false pattern keeps showing up in your work,
what idea you should check before redoing the problem,
and how to replace a fragile rule with a more reliable explanation.

Each linked guide below isolates a mistake pattern and gives you a better interpretation to reuse on new problems. That makes the fix more durable than simply correcting one answer and moving on.