Wikipedia talk:WikiProject Mathematics

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Emmy Noether FAR final citations and checks[edit]

The Emmy Noether article has been at featured article review for a couple months now. If anyone wants to take a look, most of the issues seem to have been fixed but the contributions to mathematics and physics section would likely benefit from a couple more citations and a quick survey (including of the typsetting) by someone more qualified than I am. Sgubaldo (talk) 15:20, 16 April 2024 (UTC)[reply]

Possible duplicate logic articles[edit]

Does it really make sense for "Logical connective", "Boolean function", and "Truth function" to all be separate articles? If I were more sure, I wouldn't be asking. I get how "Logic gate" is a separate article, but the other ones seem to cover the same territory, although I'm not sure which one(s) should be merged into which. Thiagovscoelho (talk) 12:21, 17 April 2024 (UTC)[reply]

Hi @Thiagovscoelho: These are distinct topics. Logical connectives are used to connect (logical) expressions in first-order logic, second-order logic and set theory in general, to express axioms, theorems, inference rules, etc. By contrast, Boolean functions are functions (things having input and output) that operate on elements of a boolean algebra. These may be finite, countable or uncountable sets. See Stone representation theorem for details. Note that the elements of a boolean algebra are NOT logical expressions! The truth function article deals with the most limited, narrow case, where "truth" is taken to be a single value T or F. A single letter, a single bit. This is distinct from elements of a boolean algebra, which can be large complex things, and it is also distinct from logical connectives, which apply to the text strings of a term algebra or a model theory. So, very distinct concepts which magically happen to have the same notation. Which, yes, can lead to confusion. Perhaps the ledes of these articles should be amended to clarify this, state this up front. 67.198.37.16 (talk) 20:46, 19 April 2024 (UTC)[reply]
(p.s. The word "magic" is fun. Formally, it is called the semantic/syntactic distinction, and there are a collection of theorems from the 1930's that clarify this relationship. Turing's incompleteness theorem is perhaps the most famous; there are others. e.g. Skolem-Lowenheim upward/downward, the completeness theorem, and the assorted variants of it from Godel, Post, Gentzen, Bernays, Kleene.) — Preceding unsigned comment added by 67.198.37.16 (talk) 21:03, 19 April 2024 (UTC)[reply]
Hi @Thiagovscoelho: I noticed that you just went through a major, massive rewrite of the very long article on propositional calculus. Are you sure that this is a good idea, given the confusion you expressed above? The old version of the article seemed to get to the point, right after the first two introductory paragraphs; the new version seems to take some tortuous detour, before starting to explain what it is half-way into the article. I cannot help reviewing this, but perhaps more wisdom and fewer facts would help. 67.198.37.16 (talk) 22:27, 19 April 2024 (UTC)[reply]
I've replaced disorganized sections that did not cite sources with organized sections that do cite sources, and I'm doing this by reading all the sources. The sources are naturally textbooks on logic, and they mostly only mention connectives, which, semantically, are only defined by means of their associated truth functions, whereas syntactically they are of course not properly "defined" at all, but may have their behavior described by inference rules prescribing their introduction or elimination. As it stands, the Logical connective article has no coverage of introduction/elimination inference rules, so its coverage overlaps a lot with what Truth function ought to cover. As to Propositional calculus, the old version "got to the point" by failing to define terms that are defined in all the sources, introducing notation without explaining what it means, failing to keep syntax and semantics clearly distinct, failing to distinguish between a formal language and the proof system used with it, and, most of all, not citing any sources at all and therefore not describing any of the variation between authors on the topics. You are welcome to edit it and improve it, but there is no Wikipedia standard by which the old article was better. Thiagovscoelho (talk) 23:05, 19 April 2024 (UTC)[reply]
Yes, the current version of Boolean function actually specifies "truth function" as an alternative name for it. If you are sure that there is such a sharp distinction, it would be good for you to edit the article and cite the Reliable Sources that you are familiar with for this statement. I have not read any of the literature that specifically refers to "Boolean functions", but the idea of such a sharp division surprises me, since George Boole was a logician, after all, and I mean, just look at the article, it features all the normal connectives from logic. Thiagovscoelho (talk) 23:27, 19 April 2024 (UTC)[reply]
My experience is that at least in computer science "Boolean function" is usually, but not invariably, used to mean functions that take values in the two-element Boolean Algebra. This is how the textbooks I currently have access to use the term.[1][2][3] I don't currently have access to Rudeanu's classic on the subject, but I could check his terminology in the library next week if needed.[4] At least Steinbach and Posthoff do also explicitly mention truth function as a common synonym. Felix QW (talk) 08:15, 20 April 2024 (UTC)[reply]

References

  1. ^ Rosen, Kenneth H. (1995). Discrete mathematics and its applications (3. ed.). New York: McGraw-Hill. ISBN 978-0-07-053965-5.
  2. ^ Steinbach, Bernd; Posthoff, Christian (2022). Logic Functions and Equations: Fundamentals and Applications using the XBOOLE-Monitor (Third ed.). Cham: Springer International Publishing. ISBN 978-3-030-88945-6.
  3. ^ Clote, Peter; Kranakis, Evangelos (2002). Boolean Functions and Computation Models. Texts in Theoretical Computer Science. An EATCS Series. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-662-04943-3. ISBN 978-3-642-08217-7.
  4. ^ Rudeanu, Sergiu (1974). Boolean functions and equations. Amsterdam: North-Holland Publ. [u.a.] ISBN 978-0-7204-2082-1.

Accessibility of Newton's method[edit]

Can someone here take a look at the recent changes at Newton's method and discussion at talk:Newton's method, and maybe help resolve the edit war there? user:Fangong00 insists on a substantial rewrite, especially of the first few sections, which I think makes the article significantly worse, most importantly rendering it, in my opinion, almost completely illegible to most of the intended audience. They don't seem too interested in having a discussion about the trade-offs involved in of various possible choices of scope/focus for the article or its early sections, but I don't really want to spend all day revert warring. Maybe someone else can phrase concerns about this in a way that gets through? –jacobolus (t) 02:23, 21 April 2024 (UTC)[reply]

The previous page for Newton's method is outdated. That version only presents Newton-Raphson method. In today's numerical analysis, Newton's method most often means Simpson's extension and also include the Gauss-Newton iteration and the newly discovered the rank-r Newton's iteration. Furthermore, the crucial convergence theorems such as Kantorovich Theorem and alpha theory were not included.
Why does jacobolus insists on keeping the outdated version? When someone tries to look up Newton's method, he or she is entitled to see the what Newton's iteration is today. Fangong00 (talk) 02:35, 21 April 2024 (UTC)[reply]
@Fangong00 the basic real-function version of Newton's method is not "outdated", but is used ubiquitously, and anyone working with computer software involving numerical calculations is likely to come across it sooner or later. It is taught to early undergraduate students and frequently encountered by people with relatively limited pure math background. It is essential that a Wikipedia article about such a basic and widely used tool start out in its first few sections with explanation which is legible and accessible to the broadest possible audience. If you want to include detailed technical discussions of advanced niche generalizations, then that is fine, but it must be done much further down the page and clearly contextualized so that readers can figure out what is being discussed and why.
As a simple example, a computer game programmer with a high school level math background might plausibly read fast inverse square root and come across a wikilink there to Newton's method; if they click through they must not be confronted with a wall of jargon expecting several years of preparation they don't have. –jacobolus (t) 02:48, 21 April 2024 (UTC)[reply]
Raphson's method is not out dated, it is now a special case of what we call "Newton's method" in numerical analysis. The most widely used Newton's iteration is not Raphson's but Simpson's and Gauss-Newton. To make the page a useful reference for the broadest possible audience.
Why do you not want a vistor to see the most widely used Newton's method? Fangong00 (talk) 12:56, 21 April 2024 (UTC)[reply]
Fangong00, you are incorrect. The page in its previous state does have a section for systems of equations and for Banach spaces, where the Gauss-Newton iteration and (what you call in a nonstandard way) "Simpson's extension" belong. The rank-r Newton iteration seems to be from a 2023 paper and it is not at all clear that it is notable enough for mention. The Kantorovich theorem is also already mentioned there.
Smale's theorem is certainly appropriate for inclusion, and could go for example in the Analysis section. Gumshoe2 (talk) 02:54, 21 April 2024 (UTC)[reply]
I know the page mentioned Simpson's version serveral pages later. Users visiting the page is unlikely to see it when they thought only Raphson's method is Newton's iteration. Fangong00 (talk) 12:58, 21 April 2024 (UTC)[reply]
The Gauss-Newton method and the Banach space Newton method are also already mentioned further down the page in the previous version. I don't think there would be any objection to expanding the text in that context.
I also don't think there would be any objection to drawing attention to this by mentioning, perhaps in a couple sentences, in the lead section that there are important multidimensional extensions of Newton's method. The lead section, after all, is meant to be a brief summary of the article. (See Wikipedia:Manual of Style/Lead section; I think neither version of the article has a satisfactory lead section.) Gumshoe2 (talk) 13:17, 21 April 2024 (UTC)[reply]
I think this content should be restored. I have commented at Talk:Newton's method. Tito Omburo (talk) 12:18, 21 April 2024 (UTC)[reply]

Adjoint functor theorem[edit]

I think that people searching for "Adjoint functor theorem" are looking for explanations about the Freyd's adjoint functor theorem, so I suggest changing the redirect target to the Formal criteria for adjoint functors. SilverMatsu (talk) 15:35, 24 April 2024 (UTC)[reply]

Ths is a possibility. However, there is an anchor "Freyd's adjoint functor theorem" in Adjoint functors. I have changed the redirect for pointing to this anchor instead of to the lead. Note that Formal criteria for adjoint functors is linked to just above this anchor. I have no clear opinion about your proposed change of target, but, in any case, Freyd's adjoint functor theorem and Adjoint functor theorem must have the same target. D.Lazard (talk) 16:24, 24 April 2024 (UTC)[reply]
Thank you for clarifying the redirect target. By the way, there are two versions of Freyd's adjoint functor theorem, which are sometimes called General adjoint functor theorem and Special adjoint functor theorem. --SilverMatsu (talk) 00:19, 25 April 2024 (UTC)[reply]

Requested move at Talk:Basic Math (video game)#Requested move 24 April 2024[edit]

There is a requested move discussion at Talk:Basic Math (video game)#Requested move 24 April 2024 that may be of interest to members of this WikiProject. RodRabelo7 (talk) 05:33, 28 April 2024 (UTC)[reply]

"Distinct" definition[edit]

The use of the word "distinct" , should be reviewed , so that its usage becomes clear, here are the pages I have noticed them in: Constructible polygon, ,Carl Friedrich Gauss ,Exact trigonometric values ,Constructible number

The constructible polygon page says : A regular n-gon can be constructed with compass and straightedge if and only if n is a power of 2 or the product of a power of 2 and any number of distinct Fermat primes.

Whereas , the Constructible number page says:

  • powers of two
  • Fermat primes, prime numbers that are one plus a power of two
  • products of powers of two and any number of distinct Fermat primes.

Notice here the second bullet point is separate to the third ; is that to say that "any number of distinct Fermat primes" does not include one Fermat prime appearing on its own. And would zero Fermat primes be considered a distinct number of Fermat primes?. This should be specified. EuclidIncarnated (talk) 13:48, 28 April 2024 (UTC)[reply]

The formatting of the post above is difficult to read. As far as I can tell, the issue is more about "any number" than about "distinct". I think that it is best treated by editing those specific pages to address that specific issue. Mgnbar (talk) 14:03, 28 April 2024 (UTC)[reply]
Sorry about my bad formatting , I am relatively new to Wikipedia writing and thank you for bringing to my attention , "any number", which should be defined more clearly. I would say that so does "distinct". For example , consider one number is it distinct? or is there required a second number for it to be said to be distinct?. Such things should be made more clear. EuclidIncarnated (talk) 14:44, 28 April 2024 (UTC)[reply]
As an example, I have edited Constructible polygon#Conditions for constructibility. I did not clarify what "distinct" means, but I did clarify (some might say too explicitly) what "any number" means. What do you think of this solution? Does "distinct" still require clarification? Mgnbar (talk) 15:03, 28 April 2024 (UTC)[reply]
I changed the ·bullets to asterisks to make a proper list. —Tamfang (talk) 19:38, 28 April 2024 (UTC)[reply]
The last bullet point includes the first two bullet points as special cases. –jacobolus (t) 14:22, 28 April 2024 (UTC)[reply]
I don't see how the first bullet point is a special case of the last bullet point , could you explain what you mean? EuclidIncarnated (talk) 15:03, 28 April 2024 (UTC)[reply]
In the third bullet point, let 2j be the power of 2 involved, and let k be the number of distinct Fermat primes involved. The first bullet point is the special case where k = 0. The second bullet point is the special case where k = 1 and j = 0. Mgnbar (talk) 15:44, 28 April 2024 (UTC)[reply]
Yes this is going off of the definition that the product of a number is itself and thus a power of 2's product is itself. This is what Product (mathematics) says is the definition of products : "Originally, a product was and is still the result of the multiplication of two or more numbers." Therefore your definition of product is not this. EuclidIncarnated (talk) 17:47, 28 April 2024 (UTC)[reply]
Sorry; I don't quite understand your post. No one here has defined the word "product", have they? The Wikipedia article Product (mathematics) is not a Wikipedia:Reliable source. Anyway, products and powers can take on slightly different meanings in different contexts. When stating a theorem, it is a good idea to make the intended meaning explicit and clear.
Have you seen my recent edit to Constructible polygon#Conditions for constructibility, which I mentioned above? Is it not clear? Regards, Mgnbar (talk) 18:01, 28 April 2024 (UTC)[reply]
It seems fine to me , your edit. EuclidIncarnated (talk) 18:11, 28 April 2024 (UTC)[reply]
@EuclidIncarnated Mathematicians define the "product" of any (possibly empty) collection of elements all belonging to some structure where multiplication is well-defined. An empty product is equal to the multiplicative identity, which is 1 in the case the quantities being multiplied are numbers. The "product" of a single quantity is just the quantity itself. –jacobolus (t) 00:09, 29 April 2024 (UTC)[reply]
All true, but this is a point we should be careful of when writing articles for non-mathematicians who may become confused by 0-element and 1-element products. —David Eppstein (talk) 00:29, 29 April 2024 (UTC)[reply]
Is there anywhere in Wikipedia that has such a definition. EuclidIncarnated (talk) 07:12, 29 April 2024 (UTC)[reply]
@EuclidIncarnated This is described in Product (mathematics) § Product of a sequence. While a sequence per se is an ordered list of numbers (or other quantities), if multiplication is commutative (true in many but not all contexts) the order doesn't matter and you could just as well take the product of an unordered collection like a multiset. –jacobolus (t) 07:15, 29 April 2024 (UTC)[reply]
And Product (mathematics)#Empty product is all about the case where 0 numbers are being multiplied. Mgnbar (talk) 11:59, 29 April 2024 (UTC)[reply]

Wigner probability distribution[edit]

It might be good to have some people watch Wigner semicircle distribution, with someone having just added back some extensive material I deleted a couple months ago. I think it's pretty incoherent, and not good material for the page regardless. Gumshoe2 (talk) 16:22, 28 April 2024 (UTC)[reply]

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