14

Is proofwiki.org a reliable source of math proofs?

I'm inspired by this question about wikipedia. This site has much less traffic and not very known, but it appears in some google search about math, and I wonder your "subjective opinion", experience, if you found errors, if the proofs are satisfactory. I made a similar one about mathworld.

Community
  • 1
Santropedro
  • 690
  • There are some occasional errors (I think there was a question about asking about how the "wrong" proof (on proofwiki) works on this site, and that's how I remember one), but generally it's a good source to get an idea how the proof goes, if nothing else. But I haven't used the site enough to make unbiased judgement, so bear that in mind. – user160738 Mar 12 '17 at 20:31
  • Sometimes you need to read/loose into 5 lemmas for completing a single proof. Usually the proofs aren't "invented" and it is a good source if you are sure of what you are searching for. – reuns Mar 12 '17 at 20:51
  • 6
    What I like a lot about ProofWiki is that its definitions and theorem statements are very precise yet concise (as opposed to other sites such as Wikipedia and Mathworld), that its omnipresent links come in very handy when you want to quickly check something while reading (while PlanetMath and Wikibooks lack links) and that it does not restrict to a specific topic (Wikibooks, $\pi$-base, Groupprops, Similar Wikis and more) – Bart Michels Mar 13 '17 at 20:05
  • Yes, but there are some occasional typos. – ahron Sep 12 '22 at 03:06

2 Answers2

21

I find proof wiki to be reasonably reliable. The worry with the site is that it is very incomplete - often times proofs will cite theorems that don't have proofs on proof wiki. As a result, sometimes you have to go hunting for lemmata.

All websites have occasional errors, but proof wiki seems to me to be as reliable as a random survey paper.

Stella Biderman
  • 31,475
  • 1
    Well, if with your reputation you find it reliable, It will probably be enough for me. – Santropedro Mar 12 '17 at 20:44
  • 6
    I agree on ProofWiki being incomplete. This is mainly due to a low number of contributors. We need to somehow make it more known, and attract contributors. – Bart Michels Mar 13 '17 at 20:28
  • I have used lately proof wiki, I can attest it is a somewhat reliable source for basic math facts at least. – Santropedro Apr 14 '17 at 16:10
8

For me, the main advantage of ProofWiki is how it is structured: as a web of axioms, definitions, and theorems that are interlinked through hyperlinks. Articles aim to be modular in that they contain only what's strictly necessary, referring to previous results and definitions where possible. Also, every major step is justified with a link to a previous result. ProofWiki gives me the confidence that, if I really really wanted to, I could trace any result back to the most fundamental of axioms.

When I first found the website (through searching for some proof or definition on Google), I had a bit of difficulty trying to grok the proofs, with their dry, precise, one-sentence-per-line style. But over time, this became a part of the value.

I'd say ProofWiki is most helpful as a reference, rather than for learning new material. For example, I find it very useful when I need a reminder of a proof or a definition. The conciseness of the presentation means that I can very quickly get an overview of the structure and flow of a proof, and identify each step very clearly. The text contains precisely what it needs to contain; I don't need to read explanatory sentences or passages about definitions/results that I already know. If I'm unsure about any particular step, I can just click on the link that takes me to the theorem/definition that is being used.

I also use it as a learning aid. I am a student, and sometimes the definitions and theorems in lectures are presented somewhat vaguely or I am left unsure about certain details. While the "textbook style" of writing is useful when you're being introduced to a new concept or result, the dry, precise style of ProofWiki is best when you're trying to get a rigorous mathematical "file" of the definition or result at hand.

Sure, ProofWiki sometimes contains errors, but at least in my experience, most of the time it's reliable. (Although admittedly what I'm looking up is mostly undergrad material, since that's what I'm studying.) Since I don't use it to learn new material but rather as a reference, I always read articles having had some exposure to the subject, so I read them critically, and it's easy enough to detect a mistake (and as far as I've seen, in the majority of cases they are just typos or other editorial errors).

Disclaimer: I am currently a (sporadic) contributor of ProofWiki

Anakhand
  • 3,075
  • Agreed that proofwiki would be terribly dry and difficult to understand for learning a topic the first time. – qwr Oct 06 '21 at 01:21