Neither is really right or wrong, certainly neither is 'anachronistic'. There are two schools of thought: pronunciation as per the Catholic church, where the sound has evolved (to "ch") over hundreds of years of Latin being used as a working language, and pronunciation as per the Romans, for whom "c" was pronounced "k" (and "v" was pronounced "w"). Understanding the impact that PM had on mathematics is, to me, the important thing. That video focuses on MPE, but of course there are several efforts inspired by PM. Here's my video, I think you might like it: 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. 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. I argue in my video "Metamath Proof Explorer: A Modern Principia Mathematica" that the Metamath Proof Explorer (MPE) is a successor to PM. 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. 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. 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). This hierarchy of types was an early effort to avoid various paradoxes. From a deeper point-of-view, PM uses a set of axioms built on a hierarchy of types. Syntactically, PM uses a dotted notation instead of parentheses that most people find hard to read & generally undesirable. PM is NOT, however, important to read or understand itself in detail, as it's been superseded by later works. 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 shattered any argument that mathematics couldn't have rigorous foundations. In at least one list, it's one of the most important books in the 20th century. The presence of Whitehead & Russell's Principia Mathematica (PM) in history is a very important historical event. ![]() It's important to separate historical importance from importance to understanding by most people. > how would the Homo sapiens and the cosmos progress and advance if more people understood Principia Mathmatica? You can see more of its Metamath representation here: If you want to use a more Russell-type system, I think Quine's NF set theory is an elegant simplification of it. Most people have decided to not follow Russell's Typed Set Theory, as his hierarchy of types seems complex to many. There are other Metamath databases, as shown here at, such as the Intuitionistic Logic Explorer (it uses intuitionistic logic instead of classical logic) and the New Foundations Explorer (it constructs mathematics from scratch starting from Quine's NF set theory axioms). Metamath doesn't embed any particular logic or other axioms, so you can choose the axioms you wish. It is constantly updated as a collection, and every change is verified by multiple independently-implemented verifiers: In particular, the "Metamath Proof Explorer" (MPE) database uses conventional classical logic + ZFC and proves all sorts of things. You might find the Metamath databases to be very interesting (full disclosure: I participate). ![]() academic papers), and more long-term living documents (e.g. that we need fewer "write an move on" works (e.g. I am very excited to see this sort of "codification" work become a legitimate academic enterprise.
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