Talk:How to Solve It

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Is this page still a stub? How much do we need on what is really only ever going tobe a brief review of book to call it no longer a stub.

--Daniel.allen 20:32, 25 September 2005 (UTC)[reply]

I agree. Removing stub template now. -MatrixFrog 05:01, 13 March 2006 (UTC)[reply]

"Here is a problem related to yours." -- This was Polya's phrase; I reverted to it because the connotation is that you are reading a resource, not just searching for it. --Ancheta Wis 23:04, 4 June 2006 (UTC)[reply]

I tried searching for "traditional mathematics professor" in the external link that was added 28 Jan 2010 but it only returned the entry in the TOC which is frustrating because this professor has a useful message. --Ancheta Wis (talk) 13:42, 6 February 2010 (UTC)[reply]

PDF (External links) illegal

That doesn't look very legal to me, what is the copyright status? I think it should be removed. --217.83.168.16 (talk) 17:45, 13 May 2014 (UTC)[reply]

I have removed the link in question just in case. If it does not indeed violate Wikipedia's copyright policy, and it fits Wikipedia's content guidelines, feel free to include it.Rcrptmncr (talk) 21:42, 28 March 2015 (UTC)[reply]

"Formal Analogue" => massive [citation needed]

The right-most column of the table in this section https://en.wikipedia.org/wiki/How_to_Solve_It#Heuristics is interesting but looks like original research of some sort, at least the source is not cited.

The third column was introduced quite a while ago (2006) by User:SheldonN: https://en.wikipedia.org/w/index.php?title=How_to_Solve_It&oldid=40826817

Any idea where this came from? As far as I can tell it's not the Pólya book... Arided (talk) 23:17, 30 January 2017 (UTC)[reply]

Back in the 1980s, this kind of AI terminology was "in the air" in Silicon Valley, at least, so the 3rd column seemed like a small addition at least to me, when editor SheldonN added it. The terminology was very common then. I remember seeing many of the items in Nils Nilsson (1980), Principles of Artificial Intelligence from the 80s. Other well-known authors who I learned these things from, include Richard Duda and Peter Hart. --Ancheta Wis (talk | contribs) 01:18, 31 January 2017 (UTC)[reply]

It goes without saying that Polya came first. The application to AI was meant to make machines more intelligent (as I learned from Peter Hart). --Ancheta Wis (talk | contribs) 02:23, 31 January 2017 (UTC)[reply]

@Arided I agree. It's commentary, sometimes using language very different from the book itself that's very obviously from a much later decade. In fact I'd say Pólya goes to some lengths to avoid that kind of language. Musiconeologist (talk) 22:12, 15 March 2024 (UTC)[reply]

I've tagged the column as potential OR. Maybe a compromise would be to delete that, but put the linked articles in a See also: section? Musiconeologist (talk) 22:51, 15 March 2024 (UTC)[reply]

About references for a single word ("Polya")

Hi, Ancheta Wis. You reverted a reference that I removed (diff). No problem with that, at all, I was considering auto-reverting and instead asking here, so here goes. The problem I see is that the reference is "referencing" a single word, and the word is the book author's name, so I do not see what reference does that need at that point of the article. The text goes: "Pólya^[9] mentions that there are many reasonable ways to solve problems.^[3]". Looks like the whole sentence is referenced by [3], so... What is reference [9] about? The same goes later on with "Pólya^[25] mentions that much can be gained by [...]", and that was the one that really got me thinking that there is some referencing style here that I do not understand. And maybe it will be hard for others, too. So, in short, what is intention of those references? - Nabla (talk) 13:12, 9 April 2017 (UTC)[reply]

Hi @Nabla, As you know, the book is a classic. The 'how' consists of 4 pithy steps which reduce to 4 words which are frequently passed over. It is important to cite the important steps, in this case the 'little words'. Because in mathematics as H. S. Wall has said: "In mathematics, the little words are important". -- HS Wall, Creative Mathematics. --Ancheta Wis (talk | contribs) 14:46, 9 April 2017 (UTC)[reply]

Ancheta Wis, if you are replying, I am not understanding... Why does the word "Polya" needs a reference? Sure, we should reference stuff, but "Polya"?... I don't get it. - Nabla (talk) 18:27, 9 April 2017 (UTC)[reply]

When I have the time to get back to this, perhaps each of the refs could be recast as Notes (meaning the amplification of a level of understanding), since our understanding of mathematics occurs gradually, in layers, for each person. Alternatively, on a mechanical-editorial level, for example, we could simply replace one of the questioned page citations with an {{rp|p.8}}. But briefly, the book notes and Polya's directions for mathematical thinking could be revisited by a reformatting. --Ancheta Wis (talk | contribs) 19:13, 9 April 2017 (UTC)[reply]

The issue here is a question of style, and the answer may be found at WP:CITEFOOT: "add the citation to the end of the clause, sentence, or paragraph, so long as it's clear which source supports which part of the text" unless it is necessary to defend use of a particular word or phrase.

In the present article:

Note [25] may be moved to the end of the clause or sentence.
Note [9] is redundant with note [3] at the end of the sentence, so it may be omitted.

Would this resolve Nabla's concerns without sacrificing information Ancheta Wis wants to preserve? ~ Ningauble (talk) 14:06, 10 April 2017 (UTC)[reply]

Yes. Removing [9] is what I did (and was reverted) precisely because it felt redundant (it points to the same page). I would have moved [25] but I paused to think :-) - Nabla (talk) 20:47, 10 April 2017 (UTC)[reply]

Yes. I plan to amplify on Polya's 4 steps with reformatting. --Ancheta Wis (talk | contribs) 22:09, 10 April 2017 (UTC)[reply]

Okay, for the time being I have moved/removed the citations as discussed. Amplification on the substance of this important work will be very welcome. (I would also like to see some more information about its influence on mathematical education.) ~ Ningauble (talk) 15:46, 11 April 2017 (UTC)[reply]

Details about the four principles

Details about the four principles first appeared on October 21, 2009 and citations appeared later. However, in Wikipedia's article the restatement of the problem is mentioned with regard to the 1st principle, whereas in Polya's book (1957) it is mentioned with regard to the 2nd principle. The main questions, "What is the unknown? What are the data? What is the condition?" (1st principle) are not mentioned in the article neither is the strategy of thinking of a similar problem that has been solved in the past (2nd principle). --Matr700 (talk) 00:56, 13 April 2018 (UTC)[reply]

removing testimonial from Influence section

I removed this from the Influence section:

"* Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book."

When a math book sells a million copies, it is self evident that many people are pleased with it. Influence would be something more specific, such as Polya's ideas being widely used in the teaching of physics. 73.89.25.252 (talk) 09:57, 24 January 2021 (UTC)[reply]