  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).

History and Overview;Cryptography and Security