I have spent several days off and on looking for a good introduction to blockchains and cryptocurrencies for someone with mathematical background but no specific computer science or cryptography background. I've had no real luck. All of the books I find are either targeting investors, who don't care about the mechanics and just want to make money, or experts, whose language I am unfamiliar with.

For example, I don't really know what a hash function is, but I am totally comfortable with number theory, combinatorics, probability, etc.

What is a good introduction to blockchain and cryptocurrencies for someone with a reasonably strong math background, but no domain specific knowledge?

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    $\begingroup$ A hash function is just a map that is computationally hard to invert. What else do you want to know? How is your background in computer science? $\endgroup$
    – Zhen Lin
    Jan 25, 2022 at 5:41
  • $\begingroup$ @ZhenLin Don't read too much into that one example--I only provided that as an example of the sort of language barrier that a mathematician (without a CS background) might have in approaching crypto. My CS background is a basic knowledge of coding (mostly for numerical PDE and ODE), but no knowledge of the theory, especially as it pertains to cryptography. $\endgroup$
    – Yly
    Jan 25, 2022 at 5:45
  • $\begingroup$ You might get better responses/advice posting this on a blockchain / crypto investing/ computer science/… Q&A site or forum because that’s where the experts are. $\endgroup$ Jan 25, 2022 at 5:57
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    $\begingroup$ Try 3Blue1Brown's "But how does bitcoin actually work", youtube.com/watch?v=bBC-nXj3Ng4 He gives you a mathematician's view of crytopgraphy, digital signatures, etc. $\endgroup$ Jan 26, 2022 at 17:23
  • $\begingroup$ Yan X. Zhang wrote a good overview article of the Mathematics related to blockchain. It is not exactly an introductory article, but some topics there that are related to cryptocurrency could appeal to you (e.g. to analyze CFMMs such as Uniswap you can use tools from convex optimization and avoid most of the CS part related to cryptography). $\endgroup$
    – shamisen
    Jan 27, 2022 at 4:25

2 Answers 2


I'd change your search to be on cryptography, rather than blockchain, as the hash function is where all the interesting maths is. There seem to be quite a few online lectures searching for "mathematics of cryptography". Just browsing books, Applied Cryptography by Bruce Schneier gets high reviews, and is apparently quite mathematical (including reviews telling you not to be afraid of the maths).

The rest of blockchain designs are the practical issues with having a distributed database. That could potentially be a very long rabbit hole. Outside of the obvious suggestions of books and tutorials on YouTube, the Morning Paper blog covered quite a few papers in this area, as one of his main interests. But this is aimed at computer scientists.


First, download the errata of any book that you are going to read and print it and place it inside the book. If possible, in one pass edit the book for the errata.

For block chain;

Of course, those books are not talking much into the mathematical side of the blockchain. One may need to look see Hash functions, Elliptic Curves, Digital signatures like ECDSA, and some introduction to Grover and Shor's quantum algorithms.

For the Cryptography/Mathematical side;


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