>The logical calculus is easier to execute than any of the techniques of mathematics itself, yet only in 1934 did Gerhard Gentzen set it out in a natural way. Even now, mathematics students are expected to learn complicated (epsilon, delta)-proois in analysis with no help in understanding the logical structure of the arguments. Examiners fully deserve the garbage that they get in return.

With an opening like that how can I not read the rest of the book?

This actually touches on some work I've been doing the past week - arbitrary term rewriting to test how reliable a given LLM is when it needs to reason about symbolic manipulation. Everything is dynamically generated to avoid the usual problem of memorising every validation set every llm seems to suffer from.

A someone interested in programming language theory, this book looks very interesting. Unfortunately the HTML is incomplete and very hard to read, and the book itself is quite expensive.

https://www.artima.com/shop/modern_mathematics may be of interest to people too.

This is up there with The Art of Computer Programming for me as a text that has clearly been painstakingly crafted by its author. It shares as well with TAOCP that it is simultaneously so many things: an introduction to programming language semantics, an introduction to category theory, (in later chapters) a reference on pretty sophisticated programming language semantics, and an exploration of the rich connections between all of these topics. I owe huge chunks of my bachelor's thesis [1] to Paul and I eagerly look forward to returning to his text after my retirement from software engineering :)

This book is for you if:

  - You have some exposure to PL semantics (lambda calculus, functional programming) in the operational tradition.
  - You have some background in abstract algebra and/or category theory.
  - You have neither but you're interested and willing to grind.

A word on the title: the contents are practical for doing mathematics; if you're interested in studying lambda calculi and want fancy techniques for writing light, elegant proofs about their properties, this is a great resource. If you're into building systems it may not be as useful to you.

[1] https://github.com/jaykru/thesis/blob/trunk/thesis.pdf

With llms and theorem provers doing the formalism, what is left is intuition - love the intuitionist focus in this book, also tying into what Bessis said in [1] I intend to read this book in depth.

Author: please fix the html rendering.

[1] https://www.amazon.com/Mathematica-Secret-World-Intuition-Cu...

For folks looking - The pdf you can find/buy has the math correctly rendered

https://www.amazon.com/Practical-Foundations-Mathematics-Cam...

Looking at the table of contents, this seems like a really odd title. In what sense is this practical and a foundation for mathematics?

I think the author assumes u know how to apply a practical foundation. We need another book here.

Practical in the same sense as André Weil's book on number theory is basic :)