@antoniolupetti: "The Mathematics of Bitcoin" is a short paper that examines Bitcoin from a mathematical perspective. It uses probabilit…
Summary
A tweet recommending 'The Mathematics of Bitcoin', a paper that mathematically analyzes Bitcoin protocol stability, double-spending probabilities, and mining profitability using stochastic processes and combinatorics.
View Cached Full Text
Cached at: 08/09/26, 09:21 PM
“The Mathematics of Bitcoin” is a short paper that examines Bitcoin from a mathematical perspective.
It uses probability, stochastic processes, martingales, combinatorics, and special functions to study some of the mechanisms behind the Bitcoin protocol. In particular, the paper discusses double-spending probabilities, mining profitability, block generation, mining strategies, and protocol stability.
If you want to go deeper, I also recommend “Bitcoin and Cryptocurrency Technologies” from Princeton University, which provides a much broader introduction to cryptographic hash functions, digital signatures, consensus, proof of work, mining, transactions, anonymity, security, and the incentive mechanisms behind cryptocurrencies.
Save both to your bookmarks. They are useful references if you are curious about the mathematical and technical mechanisms behind Bitcoin.
The Mathematics of Bitcoin: https://arxiv.org/pdf/2003.00001
Bitcoin and Cryptocurrency Technologies: https://d28rh4a8wq0iu5.cloudfront.net/bitcointech/readings/princeton_bitcoin_book.pdf…
The mathematics of Bitcoin
Source: https://arxiv.org/abs/2003.00001 View PDF
Abstract: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 ofarXiv:1601.05254(EMS Newsletter, 100, 2016 p.32).
Submission history
From: Ricardo Pérez-Marco [view email] **[v1]**Mon, 2 Mar 2020 07:57:44 UTC (205 KB)
Similar Articles
@antoniolupetti: "Mathematics for Computer Science" is one of the best freely available textbooks on the subject. In more than 1,000 pag…
A free textbook 'Mathematics for Computer Science' is available under CC BY-SA 3.0, covering key topics for computer science students.
@antoniolupetti: "Mathematics of Neural Networks" is an excellent set of lecture notes for anyone who wants to study modern neural netwo…
A set of lecture notes covering the mathematics of neural networks, from basic activation functions to geometric concepts like group convolutions and equivariance.
@antoniolupetti: "Matrix Calculus for Machine Learning and Beyond" is an interesting set of free lecture notes for understanding the mat…
A set of free MIT lecture notes on matrix calculus for machine learning, combining rigorous mathematics with visual explanations.
@Propriocetive: New preprint: Mathematics is All You Need 2 — Sign-Stabilized Behavioral Fibers in Transformer Residual Streams. Headli…
A new preprint titled 'Mathematics is All You Need 2' presents the 'Two-Channel theorem,' demonstrating that behavioral fibers in transformer residual streams are sign-stabilized and causally steerable across different architectures (Qwen to Llama). The study claims high reproducibility and shows that the behavioral substrate is near-one-dimensional, separating generation from latent structure.
@RohOnChain: This 1 hour Stanford lecture on Markov Decision Processes will teach you more about the math behind systematic trading …
The article promotes a Stanford lecture on Markov Decision Processes as a valuable resource for understanding the mathematical foundations of systematic trading, claiming it offers more insight than a short-term internship at major financial firms.