Wikipedia:Articles for deletion/Classical mathematics

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was delete‎. The proposed redirect has been rejected as inappropriate, but may be pursued separately at RfD. Owen× ☎ 12:56, 25 July 2024 (UTC)[reply]

Classical mathematics

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This is not a thing. It claims to be about "classical mathematics", in distinction to constructivist approaches, but this distinction is actually entirely about classical logic, a topic for which we already have an article and do not need a second one. My WP:BLAR (a redirect to classical logic) was reverted by an anonymous user, un-reverted by CFA, reverted again by the anon, and supported by Викидим, so rather than continuing to edit-war over the redirect we should discuss it. Here is the discussion. —David Eppstein (talk) 22:08, 17 July 2024 (UTC)[reply]

Redirect to Classical logic: as a WP:REDUNDANTFORK. An article already exists on classical logic. C F A 💬 22:12, 17 July 2024 (UTC)[reply]
Comment. As I have requested, please give me a day. The topic seems to be wider than constructivist / nonconstructivist disagreements over logic foundations. That said, I did not support the anon, and explicitly commented that "I am not sure this topic deserves an article, but I will try". --Викидим (talk) 22:23, 17 July 2024 (UTC)[reply]
Note: This discussion has been included in the list of Mathematics-related deletion discussions. —David Eppstein (talk) 22:45, 17 July 2024 (UTC)[reply]
Keep. Now that I did some reading (and a little bit of writing), here are the arguments:

The term is much broader than just foundations of mathematics
There are plenty of sources discussing the classical mathematics in a broad and narrow sense
It ~~has little to do~~ is not directly ~~with~~ equivalent to the Classical logic

A merge into the Foundations of mathematics can be considered. --Викидим (talk) 03:21, 18 July 2024 (UTC)[reply]

What are some of these sources? Gumshoe2 (talk) 05:30, 18 July 2024 (UTC)[reply]

Many works on constructive math provide large discussion on its counterparts and summarize the differences. For an extreme example, an entire volume dedicated to this topic:

Sommaruga, G. (2011). Foundational Theories of Classical and Constructive Mathematics. The Western Ontario Series in Philosophy of Science. Springer Netherlands. ISBN 978-94-007-0431-2. Retrieved 2024-07-18.

Large amount of works discuss the classical math in the more broad sense: as a list of results (mostly of the 19th century) underlying the modern mathematical research, a vocabulary that a mathematician has to know in order to understand the colleagues, for example:

Koch, H. (2012). Introduction to Classical Mathematics I: From the Quadratic Reciprocity Law to the Uniformization Theorem. Mathematics and Its Applications. Springer Netherlands. ISBN 978-94-011-3218-3. Retrieved 2024-07-18.

Викидим (talk) 06:53, 18 July 2024 (UTC)[reply]

I don't have any clear view on the issue of classical logic vs classical mathematical logic vs classical mathematics vs constructionist logic, or anything else along these lines.

However your second reference seems to use "classical mathematics" in the most informal way, the way one might equally say "the Pythagorean theorem is classical" or "the Atiyah-Singer theorem is, by now, classical." Although it's a word commonly used and understood by mathematicians in such ways, I don't think it has any particular meaning (in this context) which is systematic enough for a wiki article. That's not to say it doesn't have other meaning which might warrant it, I'm not taking a position on that. Gumshoe2 (talk) 19:02, 18 July 2024 (UTC)[reply]

I have no background in logic, so if a professional will state here that my #3 is incorrect, I will accept it, there is no need to argue the opposite at length. My observation that researchers treat the classical mathematics as a broader subject than the classical logic is based on phrases like "those who take the semantic paradoxes to motivate a retreat from classical logic to a non-classical logic usually assume that their logical reform leaves classical mathematics itself intact" (from Williamson, Timothy (2024). "Can Non-classical Logic Treat Mathematics as Exceptional?". Themes from Weir: A Celebration of the Philosophy of Alan Weir. Vol. 484. Cham: Springer International Publishing. doi:10.1007/978-3-031-54557-3_2. ISBN 978-3-031-54556-6., many similar ones are easy to find). Again, if this is some philosophical nonsense that I am taking at the face value, just let me know. Викидим (talk) 08:05, 18 July 2024 (UTC)[reply]

Comment. In the math world, the word "classical" is most often used to contrast older results or theory with more modern theory. This usage is both related to "classical mathematics" in distinction to constructive mathematics as well as "classical logic" in distinction to other logic. Mathwriter2718 (talk) 13:29, 18 July 2024 (UTC)[reply]

Keep. This page improves wikipedia by aiding understanding of the topic (philosophy of mathematics) including Constructivism (philosophy of mathematics). Rockycape (talk) 03:09, 19 July 2024 (UTC)[reply]
Delete the article in its current form is WP:SYNTH. Various people over the past 150 years have used the term to refer to various "older" mathematical approaches. I'm not sure the definition as an antonym of constructive mathematics is the primary definition; I think the term is too vague for a redirect to Constructivism (philosophy of mathematics) Walsh90210 (talk) 02:32, 19 July 2024 (UTC)[reply]
To add more evidence for your point: in glossary of classical algebraic geometry the word "classical" has nothing to do with opposition to constructivism as a foundation; it is about an unrelated shift in terminology for an area of mathematics that happened in the 20th century. —David Eppstein (talk) 07:40, 20 July 2024 (UTC)[reply]
Attaching an adjective "classical" to different mathematics-related nouns will definitely alter the interpretation of adjective, this particular mismatch is to be expected. Therefore your comment looks like more of an argument against a redirect from Classical mathematics to Classical logic. Викидим (talk) 08:32, 20 July 2024 (UTC)[reply]
It is an argument that the word "classical" is not used with a single coherent meaning in mathematics and is not a fit topic for an encyclopedia article (see also WP:NOTDICT). —David Eppstein (talk) 18:44, 20 July 2024 (UTC)[reply]
I did not notice any large difference in fuzziness between the broad sense of classical math and that of Classical physics. In the latter case, the exact choice of meaning also depends on the context. In both cases the "classical" part stopped early in the 20th century. That said, I do see the differences in popularity of terms "classical physics" (definitions abound in any encyclopedia) and "classical mathematics" (the definitions are fewer and farther in between and are mostly defined as an opposition to something: "not modern math", "not constructive math", "not intuitionist math"), adding up to about 10x ratio on Google. Викидим (talk) 05:30, 21 July 2024 (UTC)[reply]
Delete as synthesis and an attempt to write a dictionary definition, neither of which is what we are here to do. XOR'easter (talk) 17:29, 22 July 2024 (UTC)[reply]
delete, per XOR and David. Artem.G (talk) 15:46, 23 July 2024 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.