A Brief History of Uniswap and Its Math

Timeline of Events

October 2016: Vitalik Buterin publishes a Reddit post introducing the general concept of an “on-chain automated market maker (AMM)”.

The Constant Product AMM

Note: the following assumes a basic knowledge of differential calculus.

  1. A trader wants to sell Δx units of α and the smart contract needs to compute Δy
  2. A trader wants to buy Δy units of β and the smart contract needs to compute Δx

Concentrated Liquidity

Uniswap v3’s primary innovation is concentrated liquidity. As stated in the whitepaper, Uniswap v1 and v2 “were designed to provide liquidity across the entire price range (0, ∞). This… means that much of the assets held in a pool are never touched. Having considered this, it seems reasonable to allow LPs to concentrate their liquidity to smaller price ranges than (0, ∞).”

References

Hayden Adams’ Summary of the Early History of Uniswap

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