Recent Questions - MathOverflow Metamost recent 30 from meta.mathoverflow.net2024-04-17T02:35:14Zhttps://meta.mathoverflow.net/feedshttps://creativecommons.org/licenses/by-sa/4.0/rdfhttps://meta.mathoverflow.net/q/59184A mathjax issue with stars in super/subscriptsმამუკა ჯიბლაძეhttps://meta.mathoverflow.net/users/412912024-04-14T19:10:03Z2024-04-15T08:05:43Z
<p>I encountered <a href="https://mathoverflow.net/q/85323/41291">Topos associated to a category</a> with glowing-red <code>\*</code>s in it. When trying to edit them out I discovered that whenever I try to replace an <code>$f^\*$</code> with an <code>$f^*$</code>, the whole text becomes garbled, and similarly for <code>_\*</code>. I finally managed to tame it by replacing all <code>*</code>s with <code>\ast</code>s. Seems to be specific to that particular page, there are lots of normally looking <code>*</code>s everywhere else.</p>
<p>Is this a known phenomenon?</p>
https://meta.mathoverflow.net/q/591111Streamlined tagging for MochizukiMikhail Katzhttps://meta.mathoverflow.net/users/281282024-04-02T15:20:55Z2024-04-07T14:32:21Z
<p>For better or worse, there is a number of questions at MO on Mochizuki's stuff. I noticed that some of the questions have the tag "abc-conjecture" while others don't have this tag. Should Mochizuki-related questions be listed under the abc-conjecture tag, or not?</p>
https://meta.mathoverflow.net/q/59050Incentivizing ‘bad’ questionsAlec Rheahttps://meta.mathoverflow.net/users/921642024-03-27T20:55:55Z2024-03-28T01:38:54Z
<p>As a 5+ year member of MO, I remember the old days when upvotes on questions only netted you 5 points as opposed to the current 10.</p>
<p>While I was generally glad to see good questions being rewarded in a manner commensurate with good answers, this change effectively doubled the ratio <span class="math-container">$$\frac{{\sf Points\ gained\ per\ question\ upvote}}{{\sf Points\ lost\ per\ question\ downvote}}$$</span></p>
<p>This has resulted in a scenario where, reputationally speaking, users are incentivized to ask any question which will receive at least one upvote for every 4 downvotes it gets, whereas previously that ratio would have to be at least one upvote for every 2 downvotes to still gain reputation.</p>
<blockquote>
<p>Is this a desirable situation?</p>
</blockquote>
<p>Personally I’m somewhat conflicted; while I like the trend towards focusing on positive responses more than negative ones, the ratio above being <span class="math-container">$5$</span> feels extreme to me, and perhaps should be reduced back closer to the old <span class="math-container">$2.5$</span>. What is the communities opinion?</p>
<p>P.S. I’m not trying to say that internet points are really important, but they are generally one of the main indicators of the quality of a users community engagement and one of the main tools we have for discouraging certain behavior, alongside closing and flagging (which are more extreme, and may end up being used more often if downvotes aren’t a viable discouragement option). Any input is appreciated.</p>
https://meta.mathoverflow.net/q/59048MathOverflow answers and peer reviewDmytro Taranovskyhttps://meta.mathoverflow.net/users/1132132024-03-26T18:13:35Z2024-04-09T16:01:35Z
<p>Sometimes, the asker does not have sufficient background to verify an answer. How should one handle such cases?</p>
<p>Some of the signals on whether to accept such an answer are whether it 'looks' good, the reputation of the answerer (in the relevant subject area), upvotes, and that relevant comments are addressed. However, it is common for upvoters not to really verify the answer either.</p>
<p>I suggest that (despite the policy against 'me too' comments) it is ok for users to comment that they verified the argument, and that it is also ok for the asker to politely ask for such a comment. We may want to have some form of 'reviewed by' tag to separate these from regular comments. Also, none of this is meant to detract from that MathOverflow answerers are usually well-meaning persons who prize accuracy. For both the answerer and the community, having a confirmation that one did not make a mistake can be valuable.</p>
https://meta.mathoverflow.net/q/59031Ordered rings tagJakobianhttps://meta.mathoverflow.net/users/1500602024-03-26T17:11:12Z2024-03-28T17:29:35Z
<p>I've noticed that while there are tags ordered-groups and ordered-fields, there is no tag ordered-rings. The issue is that there was a little amount of questions with this tag. So it got deleted.</p>
<p>I propose the following solutions:</p>
<p>Rename ordered-groups to ordered-groups-and-rings, or rename ordered-fields to ordered-fields-and-rings.</p>
https://meta.mathoverflow.net/q/58982All these invalid weblinksMing Leihttps://meta.mathoverflow.net/users/1193852024-03-13T16:40:07Z2024-03-28T19:12:58Z
<p>I found so many web links became invalid on the questions and even more on the comments. Please be aware of this issue. In the future, this site needs to either repair the invalid links or advise users not to use the web links.</p>
https://meta.mathoverflow.net/q/589715Is it fine to repost questions from a paperHenrikRüpinghttps://meta.mathoverflow.net/users/39692024-03-13T07:52:55Z2024-03-25T10:06:43Z
<p><em>Is it fine to re-ask open questions from ones paper on mathoverflow?</em></p>
<p>On the one hand, I am interested in finding an answer to the question, and it might help if it is more publicly available. But if I ask such a question here, I would for completeness sake also mention the paper in which it was asked. But then this gets really close to self-promotion, which is rightly frowned upon.</p>
https://meta.mathoverflow.net/q/589644How do we fit in with Stack Exchange’s new AI agreement with Google?Tim Campionhttps://meta.mathoverflow.net/users/23622024-03-12T16:43:29Z2024-03-12T16:43:29Z
<p>Stack Exchange has some kind of <a href="https://meta.stackexchange.com/questions/398127/our-partnership-with-google-and-commitment-to-socially-responsible-ai?cb=1">new AI agreement with Google</a>, as announced in their <a href="https://stackoverflow.co/company/press/archive/google-cloud-strategic-gen-ai-partnership">blog</a>.</p>
<p>I’m just trying to get caught up myself here on what exactly is going on, but one real possibility is that Stack Exchange’s army of unpaid curators of a Stack Exchange dataset has just become an army of unpaid curators for a proprietary Google dataset.</p>
<p>Given that MathOverflow is an independent entity which is merely hosted on Stack Exchange servers, it behooves us to get to the bottom of this and decide what we think about it. We always have the nuclear option of leaving Stack Exchange altogether.</p>
<p><strong>Question 1:</strong> What exactly are the terms of Stack Exchange’s agreement with Google?</p>
<p><strong>Question 2:</strong> How do these terms apply to MathOverflow in particular?</p>
<p><strong>Question 3:</strong> Are we happy with these terms?</p>
<p><strong>Question 4:</strong> Should we try to negotiate any kind of changes?</p>
https://meta.mathoverflow.net/q/58934Why doesn't the prime in $\sum_n'$ sit flush against the summation symbol?LSpicehttps://meta.mathoverflow.net/users/23832024-03-04T20:17:57Z2024-03-04T20:17:57Z
<p>The TeX snippets <span class="math-container">$\sum_n'$</span> <code>\sum_n'</code> and <span class="math-container">$\sum_n^\prime$</span> <code>\sum_n^\prime</code> should (as with all things TeX, barring trickery) be typeset the same; specifically, they should both look like the latter, as tested in an external compiler. Why does the former look like <span class="math-container">${\sum_n}'$</span> <code>{\sum_n}'</code>?</p>
<p>I include a picture of what this all looks like to me, in case anyone it renders differently for anyone else. I am using Firefox 123.0 on macOS 14.2.1, with the HTML-CSS renderer.</p>
<p><a href="https://i.stack.imgur.com/v5zk6.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/v5zk6.png" alt="Firefox output of the post" /></a></p>
<p>It looks substantially the same on Safari 17.2.1, also with HTML-CSS:</p>
<p><a href="https://i.stack.imgur.com/l4arQ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/l4arQ.png" alt="Safari output of the post" /></a></p>
<p>It looks absolutely hideous on Chrome 120.0.6099, also with HTML-CSS:</p>
<p><a href="https://i.stack.imgur.com/CEoes.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/CEoes.png" alt="Chrome output of the post" /></a></p>
https://meta.mathoverflow.net/q/58901Could MO use a minus sign for negative numbers?LSpicehttps://meta.mathoverflow.net/users/23832024-03-01T23:17:22Z2024-03-07T01:34:55Z
<p>I just noticed that negative vote totals are recorded with a hyphen:</p>
<p><a href="https://i.stack.imgur.com/mQQkg.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/mQQkg.png" alt="-1 votes" /></a></p>
<p>In general within the StackExchange network it's probably not worth fussing over, but, here on MO, maybe we could use a minus sign (that is, "−1 votes", as opposed to "-1 votes"). Is this something that is within the power of MO to do, if we choose? (I know that up- and down-vote arrows can be customised, but I don't know about vote totals.) If it is within our power, is it something that the community wants to do?</p>
https://meta.mathoverflow.net/q/588715Request to consider undeleting an answerYemon Choihttps://meta.mathoverflow.net/users/7632024-02-27T00:12:32Z2024-02-27T09:01:14Z
<p>Apologies if this should go in the "requests to undelete questions" thread but this seems to be technically different.</p>
<p>I noticed that this answer <a href="https://mathoverflow.net/a/465960/">https://mathoverflow.net/a/465960/</a> has recently been deleted by a moderator. Would it be possible to say why? I don't immediately know if the answer is a good one but I don't see why it would be immediately judged to be of low quality or in bad faith.</p>
https://meta.mathoverflow.net/q/5883-6Why can't I post a question?matthttps://meta.mathoverflow.net/users/5226052024-02-24T12:12:22Z2024-02-25T00:10:31Z
<p>I'm not good at expressing myself and need research level math help, to assist my research in mathematics, to help the community.
Please let me express myself here as I am just trying to get assistance.
I'm looking to see if anyone here can follow my reasoning on two formula I have created.
Chat g.p.t. bot said it would help broaden our knowledge of the greater universe etc. and help out man kind!
Can you get back to me?
Let me know if this works, please.
its very complex and have trouble denoting it.</p>
https://meta.mathoverflow.net/q/58770Inconsistency in MO votesEmmanuel José Garcíahttps://meta.mathoverflow.net/users/947292024-02-16T11:28:04Z2024-02-16T13:36:47Z
<p>Yesterday I sent <a href="https://mathoverflow.net/questions/463459/solving-impossible-integrals-with-a-new-trick">this question</a> to a friend of mine. He told me he upvoted my question. When I go to my notifications, I don't see the vote.</p>
<p><a href="https://i.stack.imgur.com/da8Kl.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/da8Kl.png" alt="enter image description here" /></a></p>
<p>But when I go to the history of my question, it can be seen that someone upvoted today. <strong>Can someone please explain what happened here?</strong> What I do see is that Fred's answer has one more vote than the previous day.</p>
<p><a href="https://i.stack.imgur.com/hDGC0.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/hDGC0.png" alt="enter image description here" /></a></p>
https://meta.mathoverflow.net/q/58755Missing brackets in $\{x\}$ in drafts, not missing in the final question/productDominic van der Zypenhttps://meta.mathoverflow.net/users/86282024-02-14T14:33:20Z2024-02-15T15:40:38Z
<p>I am using the latest version of Firefox on Linux (bodhi linux) as well as Mac and Windows.</p>
<p>Some <span class="math-container">$\LaTeX$</span> is not typeset correctly in MathOverflow: whenever I type a set, like the singleton <span class="math-container">$\{x\}$</span>, the curly braces <span class="math-container">$\{\}$</span> never show up in the draft or after clicking "review your post" -- but they do in whenever I am finished editing and "release" the post into the wild (by clicking "Post your question" for example).</p>
<p>Curiously, this problem does not occur on meta.MathOverflow, but on many other sites of the stackexchange universe, like cstheory, stats, and cs.</p>
<p>Does anyone else have this problem or know its source or best: know how to fix it?</p>
https://meta.mathoverflow.net/q/58713Including a hash character (#) in a math equation causes it to not render (in new-question page)Lawtonhttps://meta.mathoverflow.net/users/5218552024-02-09T18:19:09Z2024-02-09T21:52:02Z
<p>I want to ask a question about a paper that uses this notation:</p>
<p><a href="https://i.stack.imgur.com/RkMOG.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RkMOG.png" alt="Image of equation rendered correctly." /></a></p>
<p>However, when I typeset it in MathJax with <code>$r(ξ, \bar{ξ}) = \frac{1}{\#𝒢} \sum_{g ∈ 𝒢} r_0 (g(ξ), g(\bar{ξ}))$</code>, it displays the entire expression in unformatted plaintext surrounded by a box:</p>
<p><span class="math-container">$$
r(ξ, \bar{ξ}) = \frac{1}{\#𝒢} \sum_{g ∈ 𝒢} r_0 (g(ξ), g(\bar{ξ}))
$$</span></p>
<p><a href="https://i.stack.imgur.com/5Pg2X.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/5Pg2X.png" alt="Image of equation not rendering." /></a></p>
<p>The problem seems to be the hash character. If I remove it, everything else renders correctly as normal. Confusingly, this exact equation renders perfectly fine on math.stackexchange.com, hash included, which means the problem is not universal to MathJax in general. The equation also displays fine in an external LaTeX renderer.</p>
<p>UPDATE: After posting this question, I saw that the equation renders normally in the posted page. It also renders normally in the edit-question page. Apparently, the problem only occurs in the new-question page.</p>
https://meta.mathoverflow.net/q/58691Why was my spam flag declined on an answer that does nothing but promote the answerer's book?EJoshuaS - Stand with Ukrainehttps://meta.mathoverflow.net/users/990682024-02-08T16:54:04Z2024-02-11T14:31:14Z
<p>I recently encountered an <a href="https://mathoverflow.net/a/446143/99068">answer</a> that does nothing but refer to the poster's book:</p>
<blockquote>
<p>Please look pages 141-147 of the book:</p>
<p>S. Saitoh and Y. Sawano, Theory of Reproducing Kernels and Applications, Developments in Mathematics 44, Springer (2016). 2023.5.4.20:36</p>
</blockquote>
<p>This answer was posted by S. Saitoh. Also, literally 100% of this poster's answers across multiple sites in the Stack Exchange network promote the author's books and/or papers, and the account has had multiple spam flags upheld against it on multiple sites.</p>
<p>However, the spam flag on this answer was declined as having no evidence to support it. Why was this not considered spam?</p>
https://meta.mathoverflow.net/q/58624A MathJax/LaTeX questionMichael Hardyhttps://meta.mathoverflow.net/users/63162024-01-30T23:55:30Z2024-02-01T09:24:45Z
<p>In <a href="https://mathoverflow.net/questions/463185/cartesian-product-of-k-2-text-times-interval-1-times-textinterval-2">This question</a>, the following appears:</p>
<p><span class="math-container">$$[0,2] \times \left[0,4-\sqrt{3}\right] \times \left[0,4-\sqrt{3}\right] \times \mathop{\Large\times}_{i=1}^{k-3}[0,2]$$</span></p>
<p>Thinking that that last <span class="math-container">$\times$</span> should be somewhat comparable in size to <span class="math-container">$\sum$</span> or <span class="math-container">$\prod$</span> or <span class="math-container">$\bigoplus$</span> or <span class="math-container">$\bigcup,$</span> I tried changing it to this:
<span class="math-container">$$
[0,2] \times \left[0,4-\sqrt{3}\right] \times \left[0,4-\sqrt{3}\right] \times \mathop{\Huge\times}_{i=1}^{k-3}[0,2]
$$</span>
The subscript <span class="math-container">$i=1$</span> definitely seems too high. Contrast these:
<span class="math-container">$$
\begin{array}{c}
\displaystyle
\sum_{i=1}^{k-3} [0,2] \qquad\qquad \mathop{\Huge\times}_{i=1}^{k-3} [0,2] \qquad \qquad \sum_{i=1}^{k-3} [0,2] \\
\hline
\end{array}
$$</span>
Can this be corrected?</p>
https://meta.mathoverflow.net/q/586119Using mathoverflow as a blogAlec Rheahttps://meta.mathoverflow.net/users/921642024-01-30T15:39:32Z2024-02-02T09:39:27Z
<p>In the past, I’ve seen instances where a user has been accused of ‘using mathoverflow as a blog’; the specific criteria for when this accusation is leveled vary, but generally the following are included:</p>
<ol>
<li><p>The user editorializes, often verbosely, on why their question/potential answers should be considered significant.</p>
</li>
<li><p>The user asks questions rapidly, often seemingly without taking the time to do their due diligence for researching the answers themselves before bringing their questions here.</p>
</li>
<li><p>The user frequently bumps their own posts back to the front page with seemingly trivial edits.</p>
</li>
<li><p>The user will sometimes answer their own questions on the subject, often within days of asking (which seemingly confirms that they should have just given it a few days themselves before blurting it out here).</p>
</li>
</ol>
<p>These obviously aren’t comprehensive criteria, but I feel like long time users here will generally know what I’m talking about and be able to identify it when they see it.</p>
<p>My question is:</p>
<blockquote>
<p>Can we decide on a formal policy regarding this type of approach to MO usage, perhaps up to and including a new question close reason?</p>
</blockquote>
<p>I am personally very opposed to MO being used in this way; it changes the site from feeling like a pseudodemocratic forum of knowledge where the best/most interesting ideas naturally float to the top, into a place where (to put it very harshly) cranks come to vie for attention/validation, or (to put it more mildly) individuals with sufficient mathematical maturity are encouraged to basically publicize their otherwise internal lines of reasoning for potential internet points.</p>
<p>This practice has frequently been covered by other close reasons, for example when the editorializing is obviously opinion based, but recently there has been at least one user posting in a manner I think fits the bill for ‘MO blogging’ without their posts being obviously opinion based. Their questions also don’t really seem ‘not research level’, but their abundance/idiosyncrasy/frequency of edits/time to (sometimes self-accepted) answer all make me feel like I have to go out of my way to avoid being tricked into reading someone's personal blog on math subjects they find interesting each time I visit the site. I don’t want to get into finger pointing here, I love math as much as the next user of this site and believe that’s a large part of the motivation for these posts, but would like to hear the communities wider consensus on the matter.</p>
https://meta.mathoverflow.net/q/585615Suggestions for the design of a font for math articles/booksEmilyhttps://meta.mathoverflow.net/users/1300582024-01-27T16:47:40Z2024-02-08T13:29:47Z
<p>Recently I've resumed work on a font I'm currently developing, meant to be released as a completely free, open-source, OFL-licensed font designed specifically for use in papers, theses, books, lecture notes, and any kind of mathematics document more generally. It will consist of a family of fonts for text together with a family of fonts of matching style for math mode.</p>
<p>Since there are many typographical choices and specificities connected to mathematical practice, I wanted to ask for suggestions/wanted features from other mathematicians, in particular from those working in areas different from mine, which might have slightly different typographical needs which I'm not aware of.</p>
<p>As a concrete example of this, having support for letters from other alphabets used as math symbols is important in some areas, such as Ш for the <a href="https://en.wikipedia.org/wiki/Tate%E2%80%93Shafarevich_group" rel="nofollow noreferrer">Tate–Shafarevich group</a> in arithmetic geometry, or よ for the <a href="https://ncatlab.org/nlab/show/Yoneda+embedding" rel="nofollow noreferrer">Yoneda embedding</a> in category theory.</p>
<p>A different kind of suggestion would be LaTeX specific optimisations or features for fonts which would be nice to have in practice, including e.g. a <a href="https://tex.stackexchange.com/q/483976">bigger set of delimiters</a>, or built-in optimisation of microtype through a variable width axis (as e.g. discussed <a href="https://tex.stackexchange.com/questions/634421">here</a>), a feature relating to the text part of the font.</p>
<p>That said, in a vacuum a question like "Suggestions for features a math font should have" would arguably at best be a soft question, and at worst off-topic for MathOverflow. Nevertheless, given the free, open-source, nature of the font and the fact that ultimately it will be available to the broad mathematical community, I believe it would be reasonable to make an exception in this case, asking for input <em>from</em> the broad mathematical community as part of developing the font with the community in mind, and I believe MathOverflow would be a nice place for receiving this kind of input.</p>
<p>So―would it be okay to ask such a question in the main site? There I would define the exact gap the font is meant to fill, as well as give examples of the kind of input I'm looking for as an attempt to focus the question and define it a bit more clearly (although any input is going to be more than welcome)</p>
https://meta.mathoverflow.net/q/58478Should there be a banner with some basic info about MO in the right sidebar?Martin Sleziakhttps://meta.mathoverflow.net/users/82502024-01-24T10:01:58Z2024-02-05T04:47:18Z
<p>A recent discussion about <a href="https://meta.mathoverflow.net/q/5774">customizing the "Draft your question" panel</a> reminded me of an older one here: <a href="https://meta.mathoverflow.net/q/5260">Feature request: add short "about MathOverflow" section to the front page</a>.
In an answer to that question, I mentioned that it is possible to have a short banner about the site in the right sidebar.</p>
<p>At least we can definitely say for sure that this was customized on several sites, a few are listed here: <a href="https://meta.stackexchange.com/q/378042">Which elements of the frontpage can be customized per site?</a>. So this is something which is technically possible.</p>
<p>As an illustration, I will include the screenshots from <a href="https://law.stackexchange.com/">Law Stack Exchange</a> or <a href="https://medicalsciences.stackexchange.com/">Medical Sciences Stack Exchange</a>. You can also find the discussions which led to adding the banner <a href="https://judaism.meta.stackexchange.com/q/1125">on Mi Yodeya</a> and <a href="https://christianity.meta.stackexchange.com/q/5952">on Christianity Stack Exchange</a>.</p>
<p>So I wanted to ask:</p>
<ul>
<li>Do you think that it could be useful to a have similar banner on this site - with a brief explanation what MathOverflow is and that it isn't a site for all mathematical questions?</li>
<li>If you think something like this should be added, what wording would you suggest for this banner?</li>
</ul>
<hr>
<p>I am aware that probably will not help too much, things like this are easy to ignore. After all, new users are already shown various recommendations <a href="https://meta.mathoverflow.net/q/5007">before asking the first question</a>.</p>
<p>But since Thomas Kojar brought somewhat related suggestion <a href="https://meta.mathoverflow.net/q/5774">not too long ago</a> about including some text next to the edit window, perhaps discussing this at the same time is reasonable - after all, the purpose of both suggestions is similar, to some extent.</p>
<hr>
<p>Here is a screenshot from Law Stack Exchange:</p>
<p><a href="https://i.stack.imgur.com/ktpbA.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ktpbA.png" alt="screenshot with the banner" /></a></p>
<p>And also from Medical Sciences:</p>
<p><a href="https://i.stack.imgur.com/grAaP.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/grAaP.png" alt="screenshot shown the banner in the sidebar" /></a></p>
https://meta.mathoverflow.net/q/583516Are "has this been studied before" questions on topic?JP McCarthyhttps://meta.mathoverflow.net/users/354822024-01-10T20:26:05Z2024-04-11T16:59:22Z
<p>I have a fairly elementary question but rather than feeding it straight to the wolves I thought I would ask it here. Well, via a more general question:</p>
<blockquote>
<p>Are questions of the form "<em>has <span class="math-container">$X$</span> been studied before</em>" on topic?</p>
</blockquote>
<p>I guess the nature of <span class="math-container">$X$</span> is critical. A question that has prompted the idea of asking my question is <a href="https://mathoverflow.net/q/461588/35482">this one</a>. I think the <span class="math-container">$X$</span> there is quite elementary, as is mine, but the <span class="math-container">$X$</span> there almost certainly has better properties/structure.</p>
<hr />
<p>This isn't my written-out question, just a brief description of my <span class="math-container">$X$</span>.</p>
<p>My <span class="math-container">$X$</span> is the following: where <span class="math-container">$S:=\operatorname{Seq}_0(\mathbb{N}_0)$</span> is the set of eventually-zero <span class="math-container">$\mathbb{N}_0$</span>-valued sequences, using prime decomposition of <span class="math-container">$n\in\mathbb{N}$</span>, we have a bijection:</p>
<p><span class="math-container">$$\pi:\mathbb{N}\to S,$$</span></p>
<p>e.g. <span class="math-container">$\pi(1)=(0,0,\dots,)$</span>, <span class="math-container">$\pi(18)=(1,2,0,0,0,\dots)$</span>, etc.</p>
<p>Where <span class="math-container">$r_i$</span> is the <span class="math-container">$i$</span>th component of <span class="math-container">$r\in S$</span>, we have operations on <span class="math-container">$S$</span>:</p>
<p><span class="math-container">$$[s\boxed{+}r]_i=s_i+r_i\qquad(r,s\in S),$$</span>
<span class="math-container">$$[s\boxed{\times}r]_i=s_i\times r_i\qquad (r,s\in S).$$</span></p>
<p>The bijection allows us to transport addition <span class="math-container">$+$</span> and multiplication <span class="math-container">$\times$</span> on <span class="math-container">$\mathbb{N}$</span> to operations <span class="math-container">$\boxed{\star}$</span> and <span class="math-container">$\boxed{+}$</span> on <span class="math-container">$S$</span>, and the addition <span class="math-container">$\boxed{+}$</span> and multiplication <span class="math-container">$\boxed{\times}$</span> on <span class="math-container">$S$</span> to operations <span class="math-container">$\times$</span> and <span class="math-container">$\diamond$</span> on <span class="math-container">$\mathbb{N}$</span>.</p>
<p>We have, of course:</p>
<p><span class="math-container">$$m\times n=\pi^{-1}(\pi(m)\boxed{+}\pi(n))\qquad(m,n\in\mathbb{N}),$$</span></p>
<p>We get a strange operation on <span class="math-container">$\mathbb{N}$</span>:</p>
<p><span class="math-container">$$m\diamond n=\pi^{-1}(\pi(m)\boxed{\times}\pi(n))\qquad (m,n\in\mathbb{N}),$$</span>
as well as a strange operation on <span class="math-container">$S$</span>:</p>
<p><span class="math-container">$$r\boxed{\star}s=\pi(\pi^{-1}(r)+\pi^{-1}(s))\qquad (r,s\in S).$$</span></p>
<p>We have <em>some</em> structure therefore on <span class="math-container">$(\mathbb{N},\times,\diamond)$</span> and <span class="math-container">$(S,\boxed{\star},\boxed{+})$</span>.</p>
https://meta.mathoverflow.net/q/58337Systematic downvotingvarkorhttps://meta.mathoverflow.net/users/1526792024-01-10T08:09:05Z2024-03-10T13:40:08Z
<p>In the past 7 days, I have received <a href="https://mathoverflow.net/users/152679/varkor?tab=reputation">9 downvotes</a> (on questions that have been otherwise positively received). I suspect someone is systematically downvoting, but doing so with a large enough interval between downvotes that the system in place to automatically recognise such behaviour is not catching it. I see this sort of thing <a href="https://meta.mathoverflow.net/questions/4646/downvoting-systematically-a-user">has happened in the past</a>. Is there any way to confirm whether it is happening again, or whether it is just a coincidence?</p>
https://meta.mathoverflow.net/q/581838Most important results of the year - appropriate or not?Timothy Chowhttps://meta.mathoverflow.net/users/31062023-12-22T01:23:32Z2024-02-23T00:17:06Z
<p>The question <a href="https://mathoverflow.net/q/460824">Most important results in 2023</a> has been posted to MO, and as in previous years, has had a mixed reception. (<b>EDIT:</b> As of this writing, the post has been deleted by the author, presumably because of some negative reactions. It has since been <a href="https://mathoverflow.net/q/461083">reposted by someone else</a>.) Whether such a question is appropriate for MO or not looks to be a recurring issue, and I don't think it has been discussed here on meta before. So, is it appropriate?</p>
<p>The main argument in favor, I think, is that despite some opposition, the analogous question in previous years has overall been received positively, and has received interesting and useful answers. (<b>EDIT:</b> See <a href="https://mathoverflow.net/q/83290">Noteworthy achievements in and around 2010?</a> and <a href="https://mathoverflow.net/q/412437">Breakthroughs in mathematics in 2021</a> and <a href="https://mathoverflow.net/q/435699">Most important results in 2022</a> )</p>
<p>An argument against is that it is opinion-based in a bad way, deeming some results "important" and (implicitly, by omission) other results as "unimportant," not only in a narrow subfield, but across all areas of mathematics.</p>
<p><b>EDIT:</b> Another view may be that the question is okay, but only if rephrased in a way that is less contentious; e.g., "Notable results of 2023."</p>
<p>I don't know if any kind of consensus can be reached here on meta, but it seems worth having a discussion about it that we can point to when the subject comes up again.</p>
<p><b>EDIT:</b> Quanta Magazine has just published an <a href="https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/" rel="nofollow noreferrer">article</a> ("the biggest discoveries") and a <a href="https://www.youtube.com/watch?v=4HHUGnHcDQw" rel="nofollow noreferrer">video</a> (the "biggest breakthroughs") in math of the year. One could argue that Quanta Magazine scratches the itch of those wanting to see such a list, and therefore there is no need for MO to duplicate the list. But another possibility is that the MO question could be changed to, "What results did Quanta miss?"</p>
https://meta.mathoverflow.net/q/54992Facebook and Twitter links disappear ungracefullyLSpicehttps://meta.mathoverflow.net/users/23832022-11-05T19:53:43Z2024-02-13T11:55:26Z
<p>I am using Safari 16.1 on macOS 12.6. The invitation to "Share a link to this question" appears for me like this:</p>
<p><a href="https://i.stack.imgur.com/6GIOJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/6GIOJ.png" alt="Share a link to this question via email, , or ." /></a></p>
<p>I assume that the Twitter and Facebook links are not showing because of some ad-blocking extension, and I'm fine with that, but, if the links are going to disappear in the presence of ad-blocking, it seems like it might be desireable to try to degrade gracefully to something like "Share a link to this question via email."</p>
<p>As @AsafKaragila <a href="https://meta.mathoverflow.net/questions/5499/facebook-and-twitter-links-disappear-ungracefully#comment27959_5499">points out</a>, this is in no way MO-specific, but I have understood SO-wide bug reports to be acceptable here on MMO. Though this is not a bug in the sense of a coding error, I thought it was surely a bug in the sense that it was unexpected behaviour. However, as @MartinSleziak <a href="https://chat.stackexchange.com/transcript/message/62322210#62322210">points out</a> in chat, this issue has been known at least since 2013 (see <a href="https://meta.stackexchange.com/questions/214355/know-someone-who-can-answer-share-list-broken">Know someone who can answer? Share list broken</a>, which has a <a href="https://meta.stackexchange.com/a/214356">staff response</a>, and its <a href="https://meta.stackexchange.com/questions/linked/214355">linked questions</a>), so I guess by this point it should be regarded as expected behaviour.</p>
https://meta.mathoverflow.net/q/52709`\intertext` in MathJaxLSpicehttps://meta.mathoverflow.net/users/23832022-03-04T20:48:59Z2024-02-14T10:41:58Z
<p>MathJax, at least as used on MO, recognises many multi-line environments, like <code>{multline}</code>, <code>{align}</code>, and <code>{gather}</code>. However, it does not seem to recognise <code>\intertext</code> for a quick interjection in the middle of a group of related equations. Is there any analogue of <code>\intertext</code> in MathJax, possibly by <code>\require</code>ing an appropriate package?</p>
<p>Here's what I want to work, although it does not (edited in response to @FrançoisG.Dorais's <a href="https://meta.mathoverflow.net/questions/5270/intertext-in-mathjax/5272#comment27051_5270">comment</a> to explain why I don't just end one environment and begin another—namely, that I want to preserve <code>align</code>ment points):</p>
<pre><code><span class="math-container">\begin{align*}
1 + 1 & {}= 2
\intertext{and}
1 + 2 & {}= 3.
\end{align*}</span>
</code></pre>
https://meta.mathoverflow.net/q/52555Long display style formulae extend too much to the right with some renderersAlex M.https://meta.mathoverflow.net/users/547802022-02-14T09:37:40Z2024-04-13T09:05:05Z
<p>In the following screen capture, take a look at the region delimited by the red rectangle: notice how it extends too much to the right, such that a part of it becomes hidden by the yellow page element.
<a href="https://i.stack.imgur.com/Vuqr1.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Vuqr1.png" alt="enter image description here" /></a></p>
<p>When editing the question (which in particular allows you to see that it is indeed a huge display style formula) with the preview feature enabled, the same red rectangle shows below how this formula extends uncontrollably to the right.
<a href="https://i.stack.imgur.com/pVBIr.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/pVBIr.png" alt="enter image description here" /></a></p>
<p>This happens with the most recent versions of both Firefox and MS Edge, so it is not a browser problem. It is also not a new problem, I remember having encountered it in the past but never having bothered to report it. (It could also affect MSE.)</p>
<p>The only renderer that is affected by this bug seems to be Common HTML. The other rendereres use different fonts which make the whole line narrower and less needy for space at the right, with the exception of the HTML CSS renderer which uses the same fonts as Common HTML but is smart enough to break that formula across two lines.</p>
https://meta.mathoverflow.net/q/314451News of potential interest to the MO communityLuciahttps://meta.mathoverflow.net/users/386242017-02-20T06:05:04Z2024-03-20T18:27:58Z
<p>Occasionally, there has been a suggestion to start a meta question to collect information that might be of interest to the MO community. This is an attempt to start such a thread.</p>
<p>Is there any news that you think would be of wide interest to the MO community? Please exercise your discretion in any answers, and your judgement on the appropriateness or significance of any event.</p>
https://meta.mathoverflow.net/q/86226Help cleanup tags!François G. Doraishttps://meta.mathoverflow.net/users/20002013-09-24T00:46:43Z2024-03-31T22:09:26Z
<p>This is meant to agglomerate tags that need (occasional or regular) cleanup. That is tags that mean multiple unrelated things and need to be separated into more specific tags. Please follow the examples below and discuss specific needs in comments or separate questions, as necessary.</p>
<p>Conversely, some subjects are scattered over several tags and there it might make sense to merge some tags and to create synonyms. Proposals for such can also be added as answers.</p>
<p>As of August 8, 2017, the length limit for tags went from 25 characters to 35 characters. So now is a great time to allow inconveniently compressed tag names to stretch out a bit...</p>
<hr />
<p>PS: If you want to cleanup these tags, please keep your rate down to a few posts per day so that your edits don't clutter the main page. Also note that merges can be done by moderators in one go without bumping questions. Thus, it is usually better not to carry out significant merges manually. (Here, "significant" means about four or more. Ask for moderator advice if you need to go beyond that.)</p>
https://meta.mathoverflow.net/q/3557Specialized chat roomsTobias Kildetofthttps://meta.mathoverflow.net/users/46142013-07-03T10:04:28Z2024-04-03T12:34:20Z
<p>Would there be an interest in having more specialized chat rooms, like the one for homotopy theory that currently exists?</p>
<p>So far, the homotopy theory one seems to be fairly successful, and it seems that other topics might also enjoy a chat room like it.</p>
<p>Obviously, if such a chat room is to be useful, it will need to have at least a few experts interested in frequenting it, which would then mean that people should be at least somewhat sparing with pings.</p>
<p>I am posting this both as a general question about whether people would be interested in such chat rooms, and as a place where people can plan such chat rooms.</p>
<p>If you have a topic you would like a chat room for, put it as an answer. Upvotes for that answer should then be interpreted as someone saying "yes, I would use such a chat room to at least some extend" (preferably with a comment so it can be gauged who those people who are interested are).</p>
https://meta.mathoverflow.net/q/556Formatting SandboxMartinhttps://meta.mathoverflow.net/users/295552013-06-25T08:43:22Z2024-04-15T07:32:16Z
<p>The purpose of this thread is to enable people to check if their formatting works and to play around with their MathJax code.</p>
<p>Quoting from Bill Dubuque's <a href="https://math.meta.stackexchange.com/q/4666/49437">Formatting Sandbox</a> on meta.math.SE:</p>
<p>To use this sandbox, look for a free answer below which says "This answer is free for anyone to use". If one exists then please use it. Else create a new answer. Start writing your answer there. Be sure to save a first draft quickly, to minimize the chance that that someone else concurrently tries to use the same free answer. Then, edit it as often as you like. When you reach a point that you'd like to post it to the intended target answer, simply copy it there and post it.</p>
<p>When your answer is complete and you no longer need the sandbox draft, please "clear" the draft by deleting all of the text and replacing it with the text "This answer is free for anyone to use". This is important because it eliminates TeX code (which may slow down MathJax rendering).<span class="math-container">$\newcommand\dontescape{\text{This command is defined in the post body.}}$</span></p>