Principia mathematica
by Alfred North Whitehead, Bertrand Russell · first published 1910
6% recommend89% neutral6% critical
Why HN recommends it
Dense but rewarding foundational text on logic and mathematics. Its rigor, historical importance, and careful construction stand out. Best suited to those studying the foundations of mathematics in depth.
Common criticism: Its proofs are famously long and hard to follow, with 1+1=2 taking hundreds of pages.
Summarised by Claude from recommending comments
Principia Mathematica has been described as one of the greatest intellectual achievements of human history. It attempts to rigorously reduce mathematics to logic. Among other things, it defines the concept of number. It is obviously a very dense and abstract work which has been made all the more difficult to read in light of more recent developments in the symbolic representation of logical concepts. It would be helpful in any new edition of the book to provide a summary of the reactions to and developments of the ideas in the work, a list of corrections, a bibliography, and a table of eq
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Here is a classic which is lacking: The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. https://en.wikipedia.org/wiki/Principia_Mathematica
on “Basic Library List: Math Assn of America Recommendations for Undergrad Libraries” ↗…some particular game of chess, the bishop won't suddenly be allowed to move sideways? Anyway: if you are really interested in the reduction of arithmetic to pure logic, check out Russell and Whitehead's Principia Mathematica-- or better yet, read the graphic novel "Logicomix" which does a wonderful job of covering the domain for non-specialists.
on “It’s science if it bites back” ↗…worth reading about too, to summarise the Greeks. And Zeno's paradoxes. * meaningness.com as an entry-point to Buddhist philosophy in general. * Logicomix as an introduction to Russell & his project in Principia Mathematica. * Mill's Utilitarianism, Hannah Arendt 'The Human Condition', and Henry George 'Progress & Poverty' for politics, history and economy, throw in a bit of Rawls. Schiller's 'The Robbers' is also very…
on “What, exactly, do philosophers do?” ↗…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…
on “Whitehead and Russell’s Principia rewritten in Coq” ↗…TED's glossy sheen, and that world is found by looking up original sources. Don't read the Wikipedia article on Gödel's incompleteness theorem and stop there. Read On Formally Undecidable Propositions in Principia Mathematica and Related Systems I. It will be hard, but it will be awesome. Don't watch a cool TED talk and immediately show it to all your friends: look up the journal paper the presenter was referencing and actually…
on “What are the most intellectually stimulating websites you know of?” ↗…existing mathematical techniques so people would believe him, so people would accept it right away. "Subrahmanyan Chandrasekhar, who is a great 20th century astrophysicist, actually wrote a version of the Principia Mathematica for the common reader. If you ever want to know what Newton was actually up to in the in his great masterwork the Principia I would advise not buying either the original Latin or English but buying Chandrasekhar's…
on “Who Said Nobody Read Isaac Newton?” ↗…proofs either. It is a couple thousand pages, so there is a large grey area between perfect understanding and having skimmed. 'Modern' books on logic or set theory are not nearly as well constructed as Principia Mathematica. (And the interesting part for me is the way that it is constructed). I don't think Russel and Whitehead wrote it as a textbook...
on “Great Reading in Computer Science” ↗If one is into this kind of thing, one should really read these books: [1] [1] https://en.wikipedia.org/wiki/Principia_Mathematica
on “Mathematics Made Difficult – A Handbook for the Perplexed (1971) [pdf]” ↗…quality or relevance of the writing is going to change much on the scale of decades. Maybe it starts to get archaic at some point, but people still get a lot out of reading Homer. If it's something like Principia Mathematica, that might honestly be timeless as long as human-like creatures exist who can read and understand math and physics.
on “Amazon's overcomplicated new product star ratings are no bright idea” ↗Dear xyzzy, Unfortunately, you missed that the author's proof does not actually prove inferential undecidability (sometimes called "inferential incompleteness") of Russell's Principia Mathematica for the following reason: The [Gödel 1931] proposition *I'mUnprovable* does **not** exist in Principia Mathematica because it violates restrictions on orders of propositions that are necessary to…
on “What Gödel Discovered” ↗…Frege's Begriffschrift for a long while (first seen in the late 1870s[1]). Either way, this was literally Gödel's first paper (published in 1944: "Russell’s Mathematical Logic") and he never mentioned Principia Mathematica again. [1] https://www.math.uwaterloo.ca/~snburris/htdocs/scav/frege/fr...
on “Whitehead and Russell’s Principia rewritten in Coq” ↗On a related note, I read somewhere that Godel was the only person Russell believed had read and understood "Principia Mathematica" besides the author themselves.
on “Donald Knuth never told Steve Jobs that he was full of shit” ↗…They prevent a solution to the Turing Halting problem, and they placed a firm limit on projects such as Russell and Whitehead's tendentiously named "Principia Marthematica" (http://en.wikipedia.org/wiki/Principia_Mathematica), a very ambitious project that was fatally undermined by Gödel's work. The incompleteness theorems need to be considered in the present question -- we're inside the "system" we're trying to analyze,…
on “Is the Universe a Simulation?” ↗> Mathematics textbooks would be intractably longer if they spelled out every step in explicit, formal detail. Just as an example, Russell & Whitehead's Principia Mathematica famously requires some 400+ pages to prove that 1+1=2 (well, they prove some other stuff, too, I suppose.) See the image and caption here to get a flavour: https://en.wikipedia.org/wiki/Principia_Mathematica
on “Titans of Mathematics Clash Over Epic Proof of ABC Conjecture” ↗…Dijkstra’s wonderfully succinct observation: “…the intellectual effort needed to conceive or to understand a program need not grow more than proportional to program length.” [3]: See Whitehead and Russell, Principia Mathematica [4]: http://www.jsoftware.com/papers/tot.htm Lazy is also bad. Computers aren't lazy. Starting off by thinking about them as lazy puts programmers on that path for total abstraction. So much energy…
on “Why calculating is better than scheming (1987) [pdf]” ↗