The AMM

Draw every mix of the two pans that keeps the product whole, and you get this curve. The pool is always exactly one point on it. A trade does one thing only: it slides the point along the curve. Nothing else can move it.

Now the names. A pot that always quotes both sides is doing a market maker's job with no human inside: an automated market maker, an AMM. The rule, two amounts whose product holds, is the constant product formula. Uniswap runs on exactly this.

Buy a little ETH and the point slides a little: the pan lightens slightly, the price barely moves. Buy a lot and the point travels into the bend, where every extra ETH costs more USDC than the one before. The curve steepens against you.

This is price impact, and it is geometry, not punishment. In checkpoint one a big order ate through a thin queue; here it climbs a steepening curve. Same lesson, new machine: size moves price, and this machine never pretended otherwise.

So where exactly does the number come from? Divide the pans. Thirty thousand USDC over ten ETH reads three thousand per ETH. Nobody typed that in. The tilt of the scale is the price, and every trade that retilts the pans rewrites it.

Notice what is missing: no price feed, no announcement, no human judgment. The pool does not know what ETH is worth. It only knows what it holds. Hold that thought, because it is about to become a problem.

Your big buy just tilted the scale: this pool now prices ETH above what Binance says. The pool cannot notice. But a trader watching both screens can, and the gap is free money: buy where it is cheap, sell where it is dear.

Function first: traders paid by the gap itself to push the pool back in line. The name: arbitrageurs. Nobody hires them, nobody thanks them, and they are the only reason a blind machine quotes sane prices. Tap the three stops on the curve.

So far you moved the pool and the world corrected it. Now flip it: the world moves while the pool stands still. First, notice who funded that last correction: the arbitrageur's profit came out of the pot itself. Whoever filled that pot quietly pays, every time the world moves.

That quiet cost gets a name in the next lesson. For now, the flipped case. ETH doubles on Binance within an hour. This pool holds ETH, and nobody trades against it. What is it quoting?

Now you can see why this machine won the ground it won. It is always on. It needs no listings desk: anyone can fill a pot for any pair of tokens, and a market exists by dinner. And because it is a contract, other machines can plug straight into it.

That last property made permissionless markets real, and this whole act is a tour of the machines that plugged in. But before we crown it, find the edge of the lens.

The half second, mapped again: your swap met a pot, slid a point along a curve, retilted a scale, and left a price that traders paid by the gap will keep honest. If you did our Web3 course, this is the machinery under the Uniswap swap you met there.

One thread is left hanging. Somebody filled that pot, and they are paid from every swap. Next: the business of being the house, and the cost nobody mentions at the door.