Lesson subsection
Read the explanation, try the on-paper prompts, then explain the idea in your own words. Use AI feedback as a mentor, not a shortcut.
Best flow: read → think on paper → write a short explanation → refine with feedback.
A mathematical proof is a logically complete argument that shows why some statement must always be true. Seeing five or ten examples is evidence, but a proof explains the underlying structure that makes the statement inevitable in all valid cases.
When mathematicians say "prove it," they are not asking you to convince them with intuition or pictures alone. They want a chain of statements where each step either uses a definition, a previously proved fact, or a clearly valid logical rule.
TL;DR — key idea
A proof is not just convincing; it is a logically complete argument that works in every valid case, not just in examples.
Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.
In your own words, explain the difference between being 'convinced' something is true and having a proof.
Give an example of a statement that seems obviously true and explain why a mathematician would still want a proof.
Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.
In 3–6 sentences, explain the core idea of this subsection as if you were teaching a friend who hasn’t seen it. Focus on the logic, not just the final statements.
AI is optional. Use it to spot gaps and sharpen your wording, not to replace your own thinking.