Just got this from the library, it's a real page turner. Heard about it in this excellent interview: https://www.typetheoryforall.com/episodes/goedel-s-incomplet...

Logicomix is novel, and done well, but flawed … it's deficiencies lie in what it leaves out which may come across as an unfair charge but in this case the charge is warranted. There is a more historically correct and less orthodox work waiting in the wings for whosoever should attempt it.

This is commonly believed, but Gödel didn't identify a logical error at the heart of the whole enterprise, he proved astonishing theorems revealing limitations of any sufficiently powerful formal system. One can kind of think of the Principia as a science experiment to find the extent to which known mathematics could be proven from foundational axioms that could be thought of as "laws of logic". To make their system work, Russell and Whitehead themselves had to add extralogical axioms, such as their Axiom of Reducibility [0] and the Axiom of Infinity, giving empirical evidence (but not a proof) that "laws of logic" alone were not enough. They were also aware of limitations in their own system, such as the inability to define the cardinal $\aleph_\omega$ [1].

Like the article says, what they did was ahead-of-its-time, and a monumental influence on all subsequent work on formal systems, including Gödel's work, regardless of whether Russell and Whitehead achieved their initial aims.

[0] https://en.wikipedia.org/wiki/Axiom_of_reducibility [1] https://www.gutenberg.org/files/78255/78255-h/78255-h.htm#Pa...

That's not how to spell Ludwig Wittgenstein!

>there is indeed a huge logical error at the heart of the whole enterprise but it was not discovered until much later by Kurt Gödel.

Which leads us to our next borderline impenetrable book, Gödel, Escher, Bach by Douglas Hofstadter.

Utter nonsense ... there is no known logical error in PM. Gödel proved that Russell and Whitehead's goal was unachievable but that's a totally different matter.

OTOH, Russell found a logical error at the heart of Frege's work, and PM fixed it by introducing the theory of types.

There's a reason mathematics was known as "penalty copy" and was notoriously difficult to typeset and even more difficult to turn a profit on.

For a deep dive into both ends of that, see the history of publication of Knuth's TAoCP where the text was originally published traditionally by setting metal type on a composition machine (to the extent possible), then compositors would add the additional characters and spacing material necessary to compose the equations and so forth so as to lay out a galley (which would then be proofed/corrected) --- a successive edition was then typeset using an early imagesetter, which looked so ghastly that DEK considered giving up, but when informed that the imagesetter was controlled by a computer declared, "I am a computer scientist, I can fix that." and expected to knock out a typesetting system over his next sabbatical....

Roughly a decade later, TeX 1.0 was released.... the current version is 3.141592653 (with new versions adding another decimal place as the version tends towards \pi) --- while we're still waiting on the full publication of Vol. 4, it is widely considered that TeX was worth the delay.

apocryphally a typesetter saw "make x as small as possible" at the end of a math problem to be typeset, and did exactly that

No it's not.

No it wasn't.

And you did not read it.

EDIT: source: took logic as undergrad + wrote on the tractatus which required a lot of pre-reqs to understand. 0 chance a course at undergrad level ever assigns principia mathematica. I don't care if you went to yale or oxford or ecole normale ... 0 chance. Most charitable interepretation: some pages of it + was on a bibliography. not required reading.

if feel embarrassed, that is the consequence for lieing. There is such a thing as intellectual honesty.

link the syllabi for the classes

It is not. The foundation of math is contested -- but afaik it is widely held that HoTT is the, erm, hottest contender to the throne https://en.wikipedia.org/wiki/Homotopy_type_theory

I would highly recommend "PROGRAM = PROOF" by Samuel Mimram.

It covers everything from pure lambda calculus through dependent type theory up to homotopy type theory. In comparison to the HoTT book, the book "PROGRAM = PROOF" is oriented less towards mathematicians more towards programmers. It contains also a short introduction to OCaml and Agda.

The book can downloaded from the authors web page:

https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching...

https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/publicat...

I think your latter comment is kind of analogous to people writing python (or any high-level language) without understanding assembly. I think maybe that reduces the mystery a bit?