> how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? It's important to separate historical importan

> how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? It's important to separate historical importance from importance to understanding by most people. The presence of Whitehead & Russell's Principia Mathematica (PM) in history is a very important historical event. In at least one list, it's one of the most important books in the 20th century. PM shattered any argument that mathematics couldn't have rigorous foundations. PM instead showed that it was possible to start from relatively simple axioms and really prove all the way up to a higher level. PM is NOT, however, important to read or understand itself in detail, as it's been superseded by later works. Syntactically, PM uses a dotted notation instead of parentheses that most people find hard to read & generally undesirable. From a deeper point-of-view, PM uses a set of axioms built on a hierarchy of types. This hierarchy of types was an early effort to avoid various paradoxes. Almost no one uses a hierarchy of types like this today; it's far more common to use Zermelo-Fraenkel set theory with the axiom of choice (ZFC). Even if you wanted to use a hierarchy of types, which is rare, you're probably more likely to use Quine's "New Foundations" which provides a much simpler foundation for mathematics. It's not important to understand PM in detail, but knowing that it's possible has inspired many more recent efforts, and that is more important. I argue in my video "Metamath Proof Explorer: A Modern Principia Mathematica" that the Metamath Proof Explorer (MPE) is a successor to PM. MPE uses modern notation (e.g., parentheses) and ZFC set theory combined with classical logic, so it uses modern conventions, but it also tries to prove "everything" from a very few axioms. Thankfully, we can now use computers to verify every last step (with multiple independent implementations), so we can have much more confidence in the proofs. Here's my video, I think you might like it: https://www.youtube.com/watch?v=8WH4Rd4UKGE https://www.youtube.com/watch?v=8WH4Rd4UKGE That video focuses on MPE, but of course there are several efforts inspired by PM. Understanding the impact that PM had on mathematics is, to me, the important thing.