Wikipedia:Articles for deletion/Artificial intelligence in 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__EXPECTED_UNCONNECTED_PAGE__. Consensus is that the content fails WP:SYNTH. The arguments in favor of this view have been addressed by the "keep" side only to a limited extent. Instead, they mostly argue that the topic is notable, which is beside the point, because non-notability is not the reason for which deletion is sought. This means that the article can be recreated if this is possible with different, non-OR content.  Sandstein  07:23, 18 July 2023 (UTC)

Artificial intelligence in mathematics

 * – ( View AfD View log | edits since nomination)

This article consists only of WP:SYNTHESIS. This is clearly aknowleged by the unique content editor of the article, who wrote in Talk:Artificial intelligence in mathematics: "My intention is to provide a balanced, verifiable exploration of AI's role in mathematics".

The article cannot be rewritten into an article respecting WP policies, since there are very few, if any, successful applications of artificial intelligence to mathematics. On the opposite, there are many application of mathematics to artificial intelligence. So, the article title does not respect WP:NPOV, by suggesting that a minor aspect of the relationship between artificial intelligence and mathematics is the major one.

Before being a true article, the article was a redirect to computational mathematics, where artificial intelligence is not mentioned. As there is no other convenient target for transforming this article into a redirect, the only acceptable solution is to delete this article. D.Lazard (talk) 13:04, 3 July 2023 (UTC)
 * Note: This discussion has been included in the deletion sorting lists for the following topics: Mathematics and Computing. D.Lazard (talk) 13:04, 3 July 2023 (UTC)
 * Is automated theorem proving not a subfield of artificial intelligence, and does it not represent a successful application of artificial intelligence to mathematics? Jarble (talk) 18:17, 3 July 2023 (UTC)
 * "suggesting that a minor aspect of the relationship between artificial intelligence and mathematics is the major one".
 * The article's title simply reflects its focus -- the use and role of AI in mathematics -- and does not assert that this aspect is the most significant or the only one. Its existence doesn't diminish or overshadow the value of other perspectives, such as "Mathematics in Artificial Intelligence". Its presence doesn't negate the need or value of the other articles, which people are free to write. These articles exist to provide separate, focused information. Significance is not a zero-sum game. As a live example, consider Artificial intelligence in government. The title does not imply the application of AI to government is more important than of the government's role in regulating or promoting AI.
 * Only by deliberate policy distortion could you understand my statement "My intention is to provide a balanced, verifiable exploration of AI's role in mathematics" as an intention to provide WP:SYNTHESIS. If I were to be more careful with words I would have said something like "The intended purpose of the article is to provide a useful paraphrase from verified secondary sources."
 * The accusation of WP:SYNTHESIS is invalid, as the article can be written based on only review articles, examples of which are this from 2021: Towards the Automatic Mathematician.
 * Over the recent years deep learning has found successful applications in mathematical reasoning. Today, we can predict fine-grained proof steps, relevant premises, and even useful conjectures using neural networks.
 * Or a more recent, popular report from the New York Times: A.I. Is Coming for Mathematics, Too.
 * Concerning possible objection that contents of the article can be incorporated into other articles: Computational mathematics is a very poor fit for redirection, since it is almost entirely used in the sense of "numerical modeling and simulation". Nor is Automatic theorem proving appropriate as there is more to AI applications in mathematics than automatic deduction. There is also automated inductive reasoning/conjecturing, as one can see from the review articles, or the essay by Terence Tao given below. Note specifically that it is not limited to formal verification or automatic theorem proving ("The 2023-level AI can already generate suggestive hints and promising leads to a working mathematician and participate actively in the decision-making process.").
 * The article meets WP:SIGNIFICANCE, as application of AI to mathematics is long recognized by experts working in AI (Marvin Minsky, John McCarthy, etc), and there are conferences and journals (International Conference on Automated Deduction, Journal of Automated Reasoning, etc) dedicated to the field. They are being recognized by mathematicians, too, such as Terence Tao in Embracing change and resetting expectations, so it has WP:POTENTIAL to grow, as per eventualism. pony in a strange land (talk) 19:59, 3 July 2023 (UTC)

Please add new comments below this notice. Thanks, ✗  plicit  14:13, 10 July 2023 (UTC)
 * Keep. I added the following references to the article. Notability was already demonstrated; it is now even more clearly demonstrated.
 * Eastmain (talk • contribs) 23:17, 3 July 2023 (UTC)
 * Comment The first article ("Advancing mathematics by guiding human intuition with AI") is certainly an interesting case study. I am not sure we can infer much from this about AI in mathematics in general though.  In case people did not notice, of the list of authors three seems to be academic mathematicians (who presumably provided the required mathematical background for posing the problems examined).  All the other 11 authors were employees of DeepMind.  So this really reads as an advertisement for the company's capabilities more than anything else, more than an analysis of AI in mathematics in general.  As for the NY Times article, I can't comment as it is behind a paywall.
 * PatrickR2 (talk) 05:28, 18 July 2023 (UTC)
 * comment (somewhere between "delete" and "needs a major cleanup and focusing"). The first section, and the above comments, about AI aiding in generating new conjectures, or suggesting proof strategies fits with the title. Is it significant and written about enough for its own article? Maybe... The second section I do not understand the relevance. As I read it, it says that a mathematical technique TTT is used to solve mathematical problem PPP. The link is that technique TTT is also used in AI? But that just means that some mathematical theorems are useful in many areas of mathematics, which is no news, that's just normal in mathematics. In short: the first section may have potential, the second section seems irrelevant, it is mathematics beeing mathematics (not AI involved). One problem (on the article, or on my reasoning) may be a lack of clear definition of what AI is, beyond the enthusiasm of the day. - Nabla (talk) 23:43, 8 July 2023 (UTC)
 * Delete This article definitely reads like WP:Synth trying to merge two fields of sciences. Hence, instead of dedicating a full article add this as a subsection in to Mathematics or as a write up in tools subsection of Artificial intelligence. Nanosci (talk) 13:43, 9 July 2023 (UTC)
 *  Relisted to generate a more thorough discussion and clearer consensus.
 * Delete This article definitely reads like WP:Synth trying to merge two fields of sciences. Hence, instead of dedicating a full article add this as a subsection in to Mathematics or as a write up in tools subsection of Artificial intelligence. Nanosci (talk) 13:43, 9 July 2023 (UTC)
 *  Relisted to generate a more thorough discussion and clearer consensus.
 * Based on WP:SYNTH, delete. Nanosci (talk) 14:39, 10 July 2023 (UTC)


 * Keep per WP:PRESERVE. Note that deleting this may itself be a form of recency bias. Buzz around (a few specific use cases of) AI does not change the fact that historically, AI has been heavily involved in math. This is not WP:SYNTH, and probably just needs a bit of care. I don't prefer it but a possible alternative merge to automated reasoning but if done with care it might suffice. &mdash;siro&chi;o 20:33, 10 July 2023 (UTC)
 * "the fact that historically, AI has been heavily involved in math"
 * This "fact" is rather disputable! To say the least, the article's current phrasing "Its use has transformed the way mathematicians approach problems, understand abstract concepts, and conduct computational mathematics" is an extreme overstatement which is not borne out by the article's content. Gumshoe2 (talk) 18:59, 11 July 2023 (UTC)
 * Keep, topic is notable as the subject of several articles, has decades of history, and does not require synthesis. Enervation (talk) 04:19, 11 July 2023 (UTC)
 * Comment Most of the contents could be merged into Computer-assisted proof, an article about automated theorem provers used by mathematicians. As far as I checked, all text of Artificial intelligence in mathematics actually deals with automated theorem proving, except for Risch algorithm, which seems to belong to computer algebra. - Jochen Burghardt (talk) 18:27, 11 July 2023 (UTC)


 * Delete as all content in the Applications section belongs in computer-assisted proof and all content in the Logical AI section seems to be irrelevant to the topic. Gumshoe2 (talk) 18:54, 11 July 2023 (UTC)


 * Delete The boundaries of what counts as "artificial intelligence" are both vague and time-dependent (and lately it has become little more than branding), so the scope of any article with this title is unclear. Computer algebra is an encyclopedic topic, as is computer-assisted proof, but "artificial intelligence in mathematics"? Not so much. We should aspire to be something better than a junk drawer of stuff mentioned at HackerNews. XOR&#39;easter (talk) 20:10, 11 July 2023 (UTC)
 * Merge/redirect to computer-assisted proof (not sure how much there is to merge that isn't already covered in that article). I think the nom's interpretation of the article creator's intent is rather uncharitable, but the definitional problems pointed out by various contributors above are real and likely fatal at this stage. It seems noteworthy that most of the sources that purport to be about AI and mathematics actually end up talking about fairly narrow and specific applications. Perhaps in the future there will be enough scholarly debate around what "AI" actually means in the context of mathematics to support an article on that topic. -- Visviva (talk) 02:42, 12 July 2023 (UTC)
 * Hi @Visviva. I'm not completely comfortable with this merge for a few related reasons. First, automated reasoning seems like a more general possible target. Relatedly, historically, the meaning of AI was a bit different. Formal logic led pretty directly to the field of AI and the line between automated reasoning and AI was almost nonexistent. We now think of AI as something that gets close to passing a Turing test or even AGI. But for decades that was not what the field of AI was really focused on. This leads to my last point. I worry that we may be seeing a recency bias towards "new" AI rather than covering the entire field of AI. What do you think? &mdash;siro&chi;o 03:09, 12 July 2023 (UTC)
 * I think those are good points, and it's definitely not my field, but I am struck that the three mentions of "mathematics" in automated reasoning are either about computer-assisted proofs or old-fashioned proofs with no connection to computers. That still leaves me thinking that computer-assisted proof is the more precise target here. That said, I came into this discussion expecting to support a WP:TNT deletion to allow for the creation of a broad-concept article (BCA) here, since articles on these large, slippery topics are hard to write from scratch -- and represent something of an exception to WP:PRESERVE since IMX they are even harder to rewrite from a bad start. I still don't think that such a deletion would be a bad outcome here. But unless someone is volunteering to take a crack at a BCA right now (which is definitely not supported by the sources currently on hand), to my inexpert mind, it seems the referenced content we actually have here is substantially about computer-assisted proof, so my inclination is to merge whatever's mergeable to that article, and hope that something fresh might eventually sprout from the redirect. -- Visviva (talk) 04:14, 12 July 2023 (UTC)
 * Thank you for going in-depth on your opinion! I think these are fair points about a BCA, though I'm a bit more optimistic that what we have being able to evolve into one. I don't think I have it in me to start a BCA right now, but I am also less uncomfortable with the idea of the suggested merge. I'll think on whether I want to change my !vote, but at the very least it's a bit softer now. &mdash;siro&chi;o 04:49, 12 July 2023 (UTC)
 * Delete: based on WP:SYNTH. — Preceding unsigned comment added by PatrickR2 (talk • contribs)
 * Delete: None of the second half of the article is at all relevant to AI. Two of them are just algorithms in the same way that Gaussian elimination or the Euclidean algorithm are algorithms, just step by step processes. The third is just a kind of mathematical object like a group or a field is a kind of object. There are no sources indicating their special connection with artificial intelligence. And the first half is mostly related to automated theorem proving. I think an article by this name could be interesting and could use some of the material cited above in this discussion. But the article as is does not have notable material.Brirush (talk) 00:38, 16 July 2023 (UTC)
 * delete. Not every algorithm is AI, and not every news piece that has an AI in its title is about AI. Besides, current AI is just a neural net, do we want an article about "neural nets in mathematics"? Artem.G (talk) 12:25, 17 July 2023 (UTC)
 * Keep since reliable sources have been found above talking exactly about "artificial intelligence in mathematics."


 * Kate the mochii (talk) 04:35, 18 July 2023 (UTC)

Please add new comments below this notice. Thanks, NYC Guru (talk) 06:19, 18 July 2023 (UTC)
 * Redirect to computer-assisted proof - I'm persuaded by Visviva's arguments regarding the centrality of CAP to our coverage of AI in mathematics on Wikipedia. This is without prejudice to recreation if academic coverage of AI in mathematics that treats it as a subject cohesively, not just addressing the application of individual AI technologies in math. signed,Rosguill talk 04:53, 18 July 2023 (UTC)
 *  Relisted to generate a more thorough discussion and clearer consensus.


 * 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.