Most math apps ask you to pick an answer. Proofsmith asks you to argue for one.

Every level gives you a claim to prove and four labelled steps to fill in — not a blank page, and not multiple choice. You write the setup, the engine that does the work, the key insight specific to that problem, and the closing move that seals the argument. Real proof-writing, broken into a shape you can actually get a handle on.

WHY IT'S DIFFERENT

Proofsmith's grader doesn't just scan for the right words. Stuff every answer full of vocabulary with no real argument behind it, and it notices — that's a solved problem here, not a loophole. It checks whether your proof holds together: whether the ideas appear in an order that makes sense, whether you've actually made the argument or just gestured at it. Writing sloppy, jumbled, or keyword-stuffed answers costs you, exactly like it should.

Stuck? "What am I missing?" gives you a riddle for the idea you haven't landed yet — not the answer itself. You still have to work it out and write it in your own words.

SIX TECHNIQUES, EVERY MAJOR ONE

• Contradiction — assume the opposite, and break it • Induction — one case, then pass it down the line • Cases — split the problem, cover every branch • Symmetry — solve it once, get the rest for free • Pigeonhole — count two things and compare them • Invariant — find what never changes, and use it

103 hand-built problems across four difficulty tiers, from a gentle first proof to genuinely hard material — Ramsey's theorem, Bernoulli's inequality, the Frobenius coin problem, and more waiting in the hardest tier.

BUILT TO BE HONEST WITH YOU

Every proof is graded entirely on your device. Nothing you write is ever sent anywhere. No account, no sign-in, no ads, no tracking, no analytics. Play offline, forever, for as long as the app is on your phone.

Stars scale with difficulty, and a hint is always one tap away if you're stuck — it costs a star, so it's a real choice, not a freebie. Tap-to-insert phrase chips and a symbol row mean you're never typing math notation from scratch.

Free to start. Two optional one-time unlocks — every difficulty tier, or every hint — for anyone who wants to skip the grind. Nothing is required to keep playing.

You don't solve problems here. You build proofs.