Axiom: The Proof Game

SocialSure Private Limited

About this game

Chess apps turned an intimidating discipline into a daily habit for a hundred million people. Axiom does
the same for mathematical proof.

Every puzzle here is a real theorem. The base angles of an isosceles triangle are equal. A number whose
square is even is itself even. There is a prime larger than any number you can name. You prove them by
growing a tree of reasoning, one move at a time, and a verification kernel running on your phone checks
every step as you make it.

REAL PROOFS, REALLY CHECKED
There is an actual proof kernel under the board: a small classical natural deduction engine with a first
order term language. It refuses any step that does not follow, and before a proof counts it walks the
finished tree again from the root and re-derives every branch. Nothing is taken on trust from the
interface. It also produced every par in the game by searching for the shortest proof itself, so a gold
crown means you matched the machine, not a number somebody typed in.

YOU WILL NEVER TYPE MATHEMATICS
Eight moves carry the whole game, and each one is a button with a plain English name. Suppose. Prove both
halves. Pick a side. Take cases. Use a tool. Suppose it is false. Induction. Name it. Axioms and the
lemmas you have earned sit in a satchel at the bottom of the screen; drag one onto a goal and it either
clicks home or bounces back. There is no red cross and no buzzer, because a wrong guess in mathematics is
just a guess.

FROM EUCLID TO THE PRIMES
Forty four theorems across three regions. The Riverlands of Geometry is Euclid: congruence, isosceles
triangles, parallels, and the bridge of asses that stopped students for eighteen centuries. The Numbered
Steppes is parity, divisibility, induction and Euclid's proof that the primes never run out. The Logic
Fens is the shape of argument itself, from double negation to Peirce's law. Four of them are keystones
with a short illustrated history you can read once you have earned it.

THE DAILY PROOF
One theorem a day, the same one for everybody, worked out from the date on your device rather than
downloaded. That is why it works with the phone in flight mode. When you finish it you get a spoiler free
grid of the shape of your proof tree, your move count and the par, ready to drop into a group chat without
giving a single step away. Thirty days of archive, and a streak that is quietly counted rather than waved
at you.

CROWNS FOR ELEGANCE
Finishing is not the whole game. Every theorem records your proof length against the shortest one the
kernel can find. Match it with no hints and you take a gold crown. Come within two moves and you take
silver. Some of the shortest proofs are famous historical gems, and finding one yourself is the best thing
in here.

HINTS THAT TEACH STRATEGY
Three tiers, and none of them hand you the answer. A nudge asks the question a mathematician would ask
next. A strategy card names the shape of the argument. A ghost step lets the kernel point at one legal
move without placing it. Hints cost nothing except your claim on the gold crown, because knowledge should
not be a consumable.

THE FORGE
Pick a move you want to drill and the forge grows a fresh theorem around it, checks that it can actually
be finished, and hands it over. Your grip on each move fades over a few weeks, which is spaced repetition
wearing a work apron.

WHAT IS NOT IN HERE
No account, no sign in, no cloud, no leaderboard, no subscription and no advertising. Axiom does not
request the internet permission, so Android will not let it open a connection at all. Everything you do
stays in this app's storage on this phone, and you can export the whole record as JSON whenever you like.
The game is free and complete: every region, every theorem, every day.

Bring a cup of tea. Some of these took people a thousand years.

What’s new

A new look. Charcoal and crimson throughout, the mark of the interlocking proof on the map, and a proof
tree that turns to cut glass when the last branch closes.

Fixes: a proof built out of order now replays correctly in the satchel, leaving a proof mid cascade no
longer misbehaves, Back works properly during onboarding, and the app stops its timers and sound when it
goes to the background.

New: restore a progress file you exported earlier.