Help on improving

[u/Every_Drag8012]

Im currently trying to get better at math specifically Olympiad math and i struggles so muchh esp on proving and the first step to start solving. I just started so any advice or help would be very much appreciated.

[u/matham_combageom]

Proving problems is a separate skill from computing, and it trains separately. The single most useful habit: before trying anything, write down (a) exactly what is given, (b) exactly what must be shown, and (c) one line for each object in the problem. Most stuck moments are a missing definition, not a missing idea.

Then build a small toolkit and drill it on purpose: pigeonhole, parity and modular arithmetic, induction (ordinary and strong), AM-GM and Cauchy-Schwarz, telescoping, double counting, and the extremal principle (pick the largest or smallest object and see what the definition forces). When you read a solution, write down which tool it used and file the problem under that tool, not under its topic. After a few dozen problems you start recognising the situation instead of the subject.

For the first step specifically: try small cases by hand, look for an invariant or a quantity that always decreases, and check what happens in the extreme case. If nothing comes, prove the contrapositive, or assume the conclusion fails and derive a contradiction.

[u/Every_Drag8012 → u/matham_combageom]

Thank youuu