The mathematics of Bitcoin
This is an incremental survey that provides mathematical proofs for the stability of Bitcoin, relevant for researchers and practitioners in cryptocurrency and mathematical finance.
The paper tackles the mathematical stability of the Bitcoin protocol by estimating profitability and double-spend probability in closed form and proving stability theorems using martingale and combinatorics techniques, confirming empirical observations of the protocol's stability.
We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and several theorems are proved using martingale and combinatorics techniques. In particular, the empirical observation of the stability of the Bitcoin protocol is proved. This survey article on the mathematics of Bitcoin is published by the Newsletter of the European Mathematical Society, vol.115, 2020, p.31-37. Continuation of arXiv:1601.05254 (EMS Newsletter, 100, 2016 p.32).