Common Beginner Mistakes

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.

10–20 min focusProof-first mindset

Best flow: read → think on paper → write a short explanation → refine with feedback.

Reading

Core explanation

Beginners often make the same types of mistakes in proofs. Being aware of them helps you avoid them much faster.

Some frequent issues:

Proving examples instead of the general case.
Assuming what you are trying to prove ('circling logic').
Using unclear pronouns ('it', 'this', 'that') instead of precise objects.
Skipping key steps with 'clearly' or 'obviously' when they are not obvious.

None of these mean you're 'bad at proofs' — they are just habits you need to unlearn.

TL;DR — key idea

Beginner mistakes—like assuming the conclusion, only checking examples, or writing vaguely—are normal. Noticing them is the first step to fixing them.

Try these in your notebook

Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.

1
Which of these beginner mistakes do you think you are most likely to make, and why?
2
Take a statement like 'all prime numbers are odd except 2' and explain how someone might accidentally 'assume the conclusion' while trying to prove it.

Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.

Check your understanding

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.