[HN Gopher] ProofWiki is an online compendium of mathematical pr...
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ProofWiki is an online compendium of mathematical proofs
Author : Tomte
Score : 146 points
Date : 2022-05-07 08:50 UTC (14 hours ago)
(HTM) web link (proofwiki.org)
(TXT) w3m dump (proofwiki.org)
| HidyBush wrote:
| What's worse than mathematical proofs on Wikipedia? A whole
| Wikipedia of mathematical proofs!
| benrbray wrote:
| Wikipedia is can actually be a great source of high-quality
| mathematical exposition. It is often not the _best_ source, but
| I often use it as a jumping-off point for learning about
| advanced topics. It helps me turn "unknown-unknowns" into
| "known-unknowns".
| layer8 wrote:
| One problem with mathematical articles on Wikipedia is that
| there's no DAG structure to follow. You often end up running
| in circles trying to understand related concepts. For many
| mathematical definitions/objects/theorems there's also a lack
| of motivation or rationale given. Why do we have that
| concept/theorem? How/where is it being used in practice?
| jacobolus wrote:
| The key words here are _can be_. Some mathematics articles
| are high quality, but most are somewhere between completely
| inadequate and blandly mediocre. If you click through all of
| the math-related wiki-links in even the best mathematical
| articles, at least half of them are going to be a
| disappointment. Many articles are little more than a dry
| definition. In general articles are missing context, history,
| proofs, figures, references, .... Topics that dozens of top
| mathematicians focused decades-long careers on, for which
| there are multiple hundreds-of-pages-long excellent textbooks
| and dozens of papers describing the historical development,
| have a few measly paragraphs of text and no figures. Some
| high-level articles contain little more than a bullet list of
| wiki links. Biographies of mathematicians (except for a few
| exceptional famous people) generally have little to no
| mathematical content, and do not put work in context.
| Mathematicians writing in English (and _some_ older ones in
| German /French) get coverage but there are huge gaps in
| biographies of e.g. Soviet mathematicians.
|
| The best coverage is probably of the content of typical
| secondary school / undergraduate math curriculum. But even
| then articles are often full of lists of trivia while
| neglecting motivation and central ideas.
|
| The same is true for many other parts of Wikipedia though.
| Writing good Wikipedia articles takes a ton of work
| (research, organizing, writing, revising, drawing figures,
| building consensus with other editors, ...), and is a
| distributed volunteer effort, so the quality of material that
| does make it online is still surprisingly impressive.
| kragen wrote:
| If we can get those top mathematicians to license their
| textbooks and papers under CC0, CC-BY, or CC-BY-SA, we can
| incorporate their explanations and figures into Wikipedia.
| mateo1 wrote:
| Collaborative encyclopedia writing with anonymous people on
| the internet turned out a lot better than expected in most
| cases, but writing correct and coherent mathematical proofs
| is not one of it's areas of success.
| krastanov wrote:
| I have not explored the English Wikipedia math proofs, but
| the ones on the French Wikipedia are absolutely
| outstanding.
| mateo1 wrote:
| It could be because they are written by a single person
| and not edited often.
| SemanticStrengh wrote:
| Hi, sorry to hijack your comment but I saw in your
| description that you are a researcher in quantum
| computing. Slightly out of domain but I was wondering
| what you think about this cannonical quantization of
| gravity https://news.ycombinator.com/reply?id=31290590&go
| to=threads%... Feel free to ignore
| cpp_frog wrote:
| I remember that when I was a sophomore in high school I wanted to
| give a shot at higher maths and started reading some articles
| there. I found [0], which states that between any pair of
| distinct real numbers there exists a rational number. It was one
| of the first proofs I read, and found it so ingenious that I
| wrote it down and read it while commuting to school. Then I went
| on to study maths and found that the arguments and reasoning
| behind it were not that 'marvelous' [1], in fact, mathematics has
| several results/generalizations with the same underlying ideas
| (well-ordering principle, unboundedness of the naturals in this
| case) present as variations in any proof, not just this one. When
| mathematicians have a new tool we start applying it to everything
| we can.
|
| Another thing, there is [2] which has not the same purpose: it
| covers the majority of undergrad math with lots of examples and
| proofs, it's more like a textbook.
|
| [0]
| https://proofwiki.org/wiki/Between_two_Real_Numbers_exists_R...
|
| [1] There is some retrospective explaining, of course, the proof
| _was_ marvelous in ancient times, it 's just that in the modern
| formal abstract setting the ground was laid to characterize
| number fields with the properties the ancients used.
|
| [2] http://mathonline.wikidot.com/
|
| EDIT: there it says the proof was featured in 2013, the same year
| I was a sophomore.
| molly4mitchel wrote:
| namibj wrote:
| There's also the Archive of Formal Proofs: https://www.isa-
| afp.org/
|
| It has many (all?) publicly available Isabelle (proof assistant)
| proofs quite neatly organized.
| zaik wrote:
| Explaining proofs to computers is still a very different beast
| to explaining proofs to humans. Hopefully this gap will get
| narrower in the next 50 years or so.
| dwheeler wrote:
| Here is a larger compendium of mathematical proofs that are
| formally proved all the way back to ZFC axioms using classical
| logic, namely the Metamath Proof Explorer:
| http://us.metamath.org/mpeuni/mmset.html
|
| Metamath lets you state your axioms including your logic system,
| so there are other Metamath proof databases that make different
| assumptions.
| FabHK wrote:
| If you enjoy proofs, you'll enjoy _Proofs from THE BOOK_ , a
| collection of beautiful proofs. The title of the book is an
| allusion to the notion by Paul Erdos that God had a book with the
| most beautiful proofs.
|
| https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK
| siraben wrote:
| ProofWiki is an amazing resource for someone studying CS and math
| like myself. Definitions and lemmas are hyperlinked and the proof
| style is very clear. They even have multiple proofs for the same
| theorem. For instance[0], and they have a wide range of deeper
| topics such as measure theory[1].
|
| Good proof style is like good program style, if you use a big
| hammer of a theorem (cf. library function), you risk making the
| result more opaque to the reader than necessary. Proof 1 of [0]
| can be understood by essentially following the definitions
| whereas proof 2 uses Orbit-Stabilizer, but the argument is still
| quite slick.
|
| [0]
| https://proofwiki.org/wiki/Number_of_Distinct_Conjugate_Subs...
|
| [1]
| https://proofwiki.org/wiki/Pointwise_Convergence_Implies_Con...
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(page generated 2022-05-07 23:01 UTC)