question_id int64 25.6k 509k | title stringlengths 27 150 | link stringlengths 67 130 | score int64 0 73 | view_count int64 13 44k | answer_count int64 0 43 | is_answered bool 2
classes | has_accepted_answer bool 2
classes | accepted_answer_id int64 61.8k 509k ⌀ | tags stringlengths 8 106 | creation_date stringdate 2026-03-04 05:32:13 2026-03-05 10:24:18 | last_activity_date stringclasses 1
value | body_html stringlengths 0 6.26k | comments listlengths 0 5 | answers listlengths 0 30 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
508,744 | Possible numbers of integer points that an $n$-by-$n$ square can cover | https://mathoverflow.net/questions/508744/possible-numbers-of-integer-points-that-an-n-by-n-square-can-cover | 2 | 60 | 1 | true | false | null | discrete-geometry | 2026-03-05 10:24:18Z | <div class="s-prose js-post-body" itemprop="text">
<p>For positive integer <span class="math-container">$n$</span>, how many integer points can an <span class="math-container">$n$</span>-by-<span class="math-container">$n$</span> square in the plane possibly cover?</p>
<p>Let <span class="math-container">$E$</span> be ... | [
{
"author_id": 552730,
"author_name": "Oleg Orlov",
"author_url": "https://mathoverflow.net/users/552730/oleg-orlov",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">A square can cover less than $n^2$ integer points, e. g. for $n=1$ the tilted square with center $(0.5,0.5)$ doesn't cove... | [
{
"answer_id": 508778,
"author_id": 586494,
"author_name": "Elias Panholzer",
"author_reputation": 140,
"author_url": "https://mathoverflow.net/users/586494/elias-panholzer",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>Case 1: all 4 sides cover integer points: By... | |
508,767 | Capping off an almost complex structure over a cone on a link of a quotient surface singularity | https://mathoverflow.net/questions/508767/capping-off-an-almost-complex-structure-over-a-cone-on-a-link-of-a-quotient-surf | 1 | 48 | 0 | false | false | null | dg.differential-geometry;4-manifolds;orbifolds | 2026-03-05 10:05:53Z | <div class="s-prose js-post-body" itemprop="text">
<p>Let <span class="math-container">$Y$</span> be an oriented <span class="math-container">$3$</span>-dimesional manifold, given by a link of a surface quotient singularity. This means that <span class="math-container">$Y=S^3/G$</span> for some finite subgroup <span cl... | [
{
"author_id": 13061,
"author_name": "Johannes Nordström",
"author_url": "https://mathoverflow.net/users/13061/johannes-nordstr%c3%b6m",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">You say \"orbifold\", but you seem initially to not impose any conditions on Y that ensure that CY is ... | [] | |
508,689 | Nonlinear wave equation and the light cone | https://mathoverflow.net/questions/508689/nonlinear-wave-equation-and-the-light-cone | 0 | 113 | 0 | false | false | null | reference-request;ap.analysis-of-pdes;wave-equation | 2026-03-04 18:53:20Z | <div class="s-prose js-post-body" itemprop="text">
<p>I have a basic question about the nonlinear wave equation. I am looking to prove the existence of a self similar solution to a wave equation; say <span class="math-container">$u=u(x,t)$</span>
<span class="math-container">$$ u_{tt}-\Delta_x u = |u|^{p-2} u$$</spa... | [
{
"author_id": 586494,
"author_name": "Elias Panholzer",
"author_url": "https://mathoverflow.net/users/586494/elias-panholzer",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Vladimir Georgiev and Grozdena Todorova. \"Existence of a Solution of the Wave Equation with Nonlinear Damping ... | [] | |
508,160 | Counterexamples in Simon-Smith min-max theory | https://mathoverflow.net/questions/508160/counterexamples-in-simon-smith-min-max-theory | 1 | 88 | 1 | true | false | null | riemannian-geometry;geometric-measure-theory;minimal-surfaces | 2026-03-04 18:48:46Z | <div class="s-prose js-post-body" itemprop="text">
<p>I am reading about the Simon-Smith min-max method for constructing minimal surfaces in 3-manifolds, following <a href="https://www.math.ias.edu/delellis/sites/math.ias.edu.delellis/files/MinMax92.pdf" rel="nofollow noreferrer">this survey</a> by Colding and De Lelli... | [] | [
{
"answer_id": 508753,
"author_id": 1540,
"author_name": "Otis Chodosh",
"author_reputation": 7412,
"author_url": "https://mathoverflow.net/users/1540/otis-chodosh",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>Take <span class=\"math-container\">$S^3(\\sqrt{2})\\... | |
508,721 | Is the set of all hypergeometric identities finitely generated? | https://mathoverflow.net/questions/508721/is-the-set-of-all-hypergeometric-identities-finitely-generated | 8 | 352 | 2 | true | false | null | hypergeometric-functions | 2026-03-04 18:33:07Z | <div class="s-prose js-post-body" itemprop="text">
<p>If we look at Wikipedia's <a href="https://en.wikipedia.org/wiki/Generalized_hypergeometric_function#Identities" rel="noreferrer">list of hypergeometric identities</a>, we find classic results such as Saalschütz's theorem—
<span class="math-container">$${}_3F_2 (a,b... | [
{
"author_id": 7092,
"author_name": "Steven Stadnicki",
"author_url": "https://mathoverflow.net/users/7092/steven-stadnicki",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Would all the sorts of things you're thinking about be covered by W-Z pairs? <a href=\"https://en.wikipedia.org/w... | [
{
"answer_id": 508745,
"author_id": 3106,
"author_name": "Timothy Chow",
"author_reputation": 91241,
"author_url": "https://mathoverflow.net/users/3106/timothy-chow",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>I did what I should have done before posting to MO, ... | |
61,773 | $p$-adic Langlands correspondence | https://mathoverflow.net/questions/61773/p-adic-langlands-correspondence | 23 | 3,000 | 2 | true | true | 61,808 | reference-request;nt.number-theory;galois-representations | 2026-03-04 18:00:02Z | <div class="s-prose js-post-body" itemprop="text">
<p>Basic question: Is it correct that the $p$-adic Langlands correspondence is known for $GL_2$ only over $Q_p$ but not other $p$-adic fields? If so, I would like to request some light to be shed on this restriction, i.e., why only $Q_p$ but not its extensions. Any ref... | [
{
"author_id": 2821,
"author_name": "Chandan Singh Dalawat",
"author_url": "https://mathoverflow.net/users/2821/chandan-singh-dalawat",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Start with Pierre Berger's recent Bourbaki exposé 1017 <a href=\"http://arxiv.org/abs/1002.4111\" rel=\... | [
{
"answer_id": 61808,
"author_id": 13024,
"author_name": "vytas",
"author_reputation": 433,
"author_url": "https://mathoverflow.net/users/13024/vytas",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>Yes, this is correct.</p>\n<p>The problem is that when you replace ... | |
488,840 | Binomial coefficient C(2k,n-1) alternative formula equivalent to the Vandermonde identity? | https://mathoverflow.net/questions/488840/binomial-coefficient-c2k-n-1-alternative-formula-equivalent-to-the-vandermonde | 1 | 467 | 3 | true | true | 488,880 | reference-request;co.combinatorics;linear-algebra;binomial-coefficients;recurrences | 2026-03-04 17:31:53Z | <div class="s-prose js-post-body" itemprop="text">
<p>I am working with a binomial sum that arises in some combinatorial arguments (and also appears in certain generating‐function manipulations). Specifically, I have this identity</p>
<p><span class="math-container">$$
\sum_{j=0}^{n}
\binom{k}{j}\,\binom{k}{n-j}
\;=\;
... | [
{
"author_id": 7076,
"author_name": "Max Alekseyev",
"author_url": "https://mathoverflow.net/users/7076/max-alekseyev",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Why is it important to link the two sums rather than link the second sum directly to the binomial coefficient $\\binom{... | [
{
"answer_id": 488880,
"author_id": 10744,
"author_name": "Ira Gessel",
"author_reputation": 17728,
"author_url": "https://mathoverflow.net/users/10744/ira-gessel",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>The identity is a special case of <a href=\"https://en... | |
472,830 | Show that $\|P(f\circ\varphi_{\lambda})-\widetilde{f}(\lambda)\|_p=\|P(f\circ\varphi_{\lambda}-\overline{P(\overline{f}\circ\varphi_{\lambda}}))\|_p.$ | https://mathoverflow.net/questions/472830/show-that-pf-circ-varphi-lambda-widetildef-lambda-p-pf-circ-va | 2 | 316 | 1 | true | false | null | fa.functional-analysis;measure-theory;operator-theory;function-spaces;toeplitz-operators | 2026-03-04 17:11:15Z | <div class="s-prose js-post-body" itemprop="text">
<p>Let <span class="math-container">$\Omega = \mathbb B_n,$</span> the unit ball in <span class="math-container">$\mathbb C^n$</span> and <span class="math-container">$L^2_a(\Omega)$</span> be the Bergman space endowed with the normalized volume measure on <span class=... | [] | [
{
"answer_id": 473110,
"author_id": 153260,
"author_name": "an_ordinary_mathematician",
"author_reputation": 3226,
"author_url": "https://mathoverflow.net/users/153260/an-ordinary-mathematician",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>I think it goes like th... | |
195,938 | Grothendieck on polyhedra over finite fields | https://mathoverflow.net/questions/195938/grothendieck-on-polyhedra-over-finite-fields | 26 | 1,000 | 1 | true | false | null | reference-request;co.combinatorics;ho.history-overview;discrete-geometry;finite-fields | 2026-03-04 16:04:28Z | <div class="s-prose js-post-body" itemprop="text">
<p>In Grothendieck's <em>Sketch of a Programme</em> he spends a few pages discussing polyhedra over arbitrary rings and concludes with some intriguing remarks on specializing polyhedra over their "most singular characteristics". I am having trouble understanding what h... | [
{
"author_id": 50846,
"author_name": "Matthias Wendt",
"author_url": "https://mathoverflow.net/users/50846/matthias-wendt",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Could the singular characteristic have something to do with the modular representation theory of the automorphism g... | [
{
"answer_id": 423573,
"author_id": 429204,
"author_name": "user234212323",
"author_reputation": 934,
"author_url": "https://mathoverflow.net/users/429204/user234212323",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>Not an exact answer to your question but maybe i... | |
488,866 | Generalization of Chebyshev polynomials with connection to K-bonacci sequence number | https://mathoverflow.net/questions/488866/generalization-of-chebyshev-polynomials-with-connection-to-k-bonacci-sequence-nu | 3 | 183 | 1 | true | true | 508,749 | co.combinatorics;computability-theory;binomial-coefficients;recurrences;trigonometric-polynomials | 2026-03-04 15:49:13Z | <div class="s-prose js-post-body" itemprop="text">
<p>I have been exploring a combinatorial approach to express Chebyshev polynomials and generalizing them through a recurrence relation. I would like to know whether this recurrence relation can be proven using induction or a combinatorial approach.</p>
<p><span class="... | [
{
"author_id": 2530,
"author_name": "darij grinberg",
"author_url": "https://mathoverflow.net/users/2530/darij-grinberg",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Without getting into anything deep, a few comments: Have you seen the work of Arthur Benjamin and others, e.g., <a hr... | [
{
"answer_id": 508749,
"author_id": null,
"author_name": "TigranNersissian",
"author_reputation": 1,
"author_url": "",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p><b>Proof.</b> <i>Given the generalized Chebyshev polynomial:</i>\n<span class=\"math-container\">$$G... | |
508,702 | Intuitive explanation why the radii converge in this sequence of eights? | https://mathoverflow.net/questions/508702/intuitive-explanation-why-the-radii-converge-in-this-sequence-of-eights | 19 | 1,000 | 4 | true | true | 508,712 | mg.metric-geometry;sequences-and-series;limits-and-convergence;intuition | 2026-03-04 15:46:01Z | <div class="s-prose js-post-body" itemprop="text">
<p>In the diagram, circles of the same color are congruent.</p>
<p><a href="https://i.sstatic.net/4XXO2ILj.png" rel="noreferrer"><img alt="Sequence of nested figure eights" src="https://i.sstatic.net/4XXO2ILj.png"/></a></p>
<p>I have a <a href="https://math.stackexchan... | [
{
"author_id": 172802,
"author_name": "Saúl RM",
"author_url": "https://mathoverflow.net/users/172802/sa%c3%bal-rm",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Why is the proof non-intuitive? If you mean all the big formulas, they can be avoided in a proof, i.e. one does not need a... | [
{
"answer_id": 508712,
"author_id": 36721,
"author_name": "Iosif Pinelis",
"author_reputation": 146947,
"author_url": "https://mathoverflow.net/users/36721/iosif-pinelis",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>As <a href=\"https://mathoverflow.net/questions... | |
508,490 | Proving Kashiwara–Schapira's micro-local cutoff lemma $\infty$-categorically | https://mathoverflow.net/questions/508490/proving-kashiwara-schapiras-micro-local-cutoff-lemma-infty-categorically | 7 | 271 | 0 | false | false | null | sheaf-theory;micro-local-analysis | 2026-03-04 15:14:22Z | [] | [] | ||
508,585 | Improperness of regular conditional probabilities | https://mathoverflow.net/questions/508585/improperness-of-regular-conditional-probabilities | 1 | 86 | 0 | false | false | null | pr.probability;measure-theory | 2026-03-04 14:47:17Z | [] | [] | ||
391,124 | Are hypergeometric series not taught often at universities nowadays, and if so, why? | https://mathoverflow.net/questions/391124/are-hypergeometric-series-not-taught-often-at-universities-nowadays-and-if-so | 52 | 8,000 | 7 | true | false | null | mathematics-education;hypergeometric-functions | 2026-03-04 14:28:14Z | [] | [] | ||
508,738 | Reference for colimits in comma categories F ↓ G in which F and G are not assumed cocontinuous | https://mathoverflow.net/questions/508738/reference-for-colimits-in-comma-categories-f-%e2%86%93-g-in-which-f-and-g-are-not-assume | 3 | 57 | 0 | false | false | null | reference-request;ct.category-theory;limits-and-colimits | 2026-03-04 11:08:40Z | <div class="s-prose js-post-body" itemprop="text">
<p>Given functors <span class="math-container">$F : \mathbf A \to \mathbf C$</span> and <span class="math-container">$G : \mathbf B \to \mathbf C$</span>, it is <a href="https://ncatlab.org/nlab/show/comma+category#completeness_and_cocompleteness" rel="nofollow norefer... | [] | [] | |
456,780 | Reference for understanding Shelah-Harrington-Makkai's proof of Vaught's conjecture for $\omega$-stable theories | https://mathoverflow.net/questions/456780/reference-for-understanding-shelah-harrington-makkais-proof-of-vaughts-conject | 6 | 359 | 0 | false | false | null | reference-request;lo.logic;model-theory | 2026-03-04 09:41:17Z | <div class="s-prose js-post-body" itemprop="text">
<p>I'm looking for a source to help me better understand Shelah-Harrington-Makkai's proof of Vaught's conjecture for <span class="math-container">$\omega$</span>-stable theories (<a href="https://doi.org/10.1007/BF02760651" rel="nofollow noreferrer">DOI</a>, <a href="h... | [
{
"author_id": 83901,
"author_name": "James E Hanson",
"author_url": "https://mathoverflow.net/users/83901/james-e-hanson",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Hopefully someone will come in with a reference but my impression is that there isn't a lot of good exposition of s... | [] | |
508,666 | Cutting squares and rectangles into mutually similar but non-congruent rectangles -2 | https://mathoverflow.net/questions/508666/cutting-squares-and-rectangles-into-mutually-similar-but-non-congruent-rectangle | 3 | 163 | 1 | true | true | 508,673 | co.combinatorics;discrete-geometry;tiling | 2026-03-04 08:39:15Z | <div class="s-prose js-post-body" itemprop="text">
<p>We try to go a step beyond <a href="https://mathoverflow.net/questions/508628/cutting-squares-and-rectangles-into-mutually-similar-but-non-congruent-rectangle">Cutting squares and rectangles into mutually similar but non-congruent rectangles</a> and record a couple ... | [
{
"author_id": 46140,
"author_name": "Peter Taylor",
"author_url": "https://mathoverflow.net/users/46140/peter-taylor",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Trivially, if a rectangle is dissected into two rectangles which are similar to each other and have side ratio $a$ then... | [
{
"answer_id": 508673,
"author_id": 46140,
"author_name": "Peter Taylor",
"author_reputation": 8178,
"author_url": "https://mathoverflow.net/users/46140/peter-taylor",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>As noted in a comment, but for completeness: if we ... | |
415,209 | Exposition of Grothendieck's mathematics | https://mathoverflow.net/questions/415209/exposition-of-grothendiecks-mathematics | 40 | 7,000 | 13 | true | false | null | ag.algebraic-geometry;soft-question;textbook-recommendation;books;exposition | 2026-03-04 08:04:30Z | <div class="s-prose js-post-body" itemprop="text">
<p>As <a href="https://en.wikipedia.org/wiki/Alexander_Grothendieck" rel="noreferrer">Wikipedia</a> says:</p>
<blockquote>
<p>In Grothendieck's retrospective <em>Récoltes et Semailles</em>, he identified twelve of his contributions which he believed qualified as "great... | [
{
"author_id": 148448,
"author_name": "Aravindh Krishnamoorthy",
"author_url": "https://mathoverflow.net/users/148448/aravindh-krishnamoorthy",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">May I suggest to include the two examples into (separate) answers just to know (as someone else... | [
{
"answer_id": 415212,
"author_id": null,
"author_name": "Francesco Polizzi",
"author_reputation": 68975,
"author_url": "",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>A good roadmap for FGA (topic 4, with glimpses on topic 6) is</p>\n<p><em>Fantechi, Barbara; Gö... | |
508,715 | Representing a given vector field in any way I like around regular points | https://mathoverflow.net/questions/508715/representing-a-given-vector-field-in-any-way-i-like-around-regular-points | 6 | 163 | 2 | true | false | null | dg.differential-geometry;ap.analysis-of-pdes;differential-topology;differential-equations;smooth-manifolds | 2026-03-04 07:52:53Z | <div class="s-prose js-post-body" itemprop="text">
<p>The same question was asked <a href="https://math.stackexchange.com/questions/5126824/representing-vector-field-in-anyway-i-like-around-regular-points">on Mathematics Stack exchange</a> but has not received any response or comments.</p>
<p>Let <span class="math-cont... | [
{
"author_id": 5484,
"author_name": "Daniel Asimov",
"author_url": "https://mathoverflow.net/users/5484/daniel-asimov",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Shouldn't 1. read \"𝑎^1 ≡ 1, 𝑎^i ≡ 0 if i ≠ 1\" ?</span>",
"comment_id": 1325539,
"created_date": "2026-03-... | [
{
"answer_id": 508735,
"author_id": 24309,
"author_name": "Loïc Teyssier",
"author_reputation": 5632,
"author_url": "https://mathoverflow.net/users/24309/lo%c3%afc-teyssier",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>For question 2., even for analytic (or polyn... | |
508,718 | A series related to $\zeta(3)$ | https://mathoverflow.net/questions/508718/a-series-related-to-zeta3 | 3 | 379 | 2 | true | true | 508,731 | nt.number-theory;sequences-and-series;riemann-zeta-function;binomial-coefficients | 2026-03-04 06:33:42Z | <div class="s-prose js-post-body" itemprop="text">
<p>Inspired by <a href="https://mathoverflow.net/questions/508663">Question 508663</a>, I discovered the following identity</p>
<p><span class="math-container">$$\sum_{k=1}^\infty\frac{H_{2k}-H_{k}}{k^2\binom{2k}k}=2 \zeta(3)-\frac{\pi \sqrt{3}\, \Psi^{\left(1\right)... | [
{
"author_id": 110710,
"author_name": "Steven Clark",
"author_url": "https://mathoverflow.net/users/110710/steven-clark",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">Mathematica gives the result $$\\sum _{k=1}^{\\infty } \\frac{H_{2 k}-H_k}{k^2 \\binom{2 k}{k}}=2 \\zeta (3)-\\frac{2... | [
{
"answer_id": 508731,
"author_id": 124654,
"author_name": "Zhi-Wei Sun",
"author_reputation": 18678,
"author_url": "https://mathoverflow.net/users/124654/zhi-wei-sun",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>The formula is not new. It follows from (3.2) and ... | |
98,548 | In search of an early picture of Max Dehn | https://mathoverflow.net/questions/98548/in-search-of-an-early-picture-of-max-dehn | 20 | 1,000 | 3 | true | true | 98,550 | ho.history-overview | 2026-03-04 06:16:24Z | <div class="s-prose js-post-body" itemprop="text">
<p>I am trying to find a copy of a picture "Mathematische Gesellschaft:
Group Portrait, Faculty, University of Göttingen (1899)."</p>
<p>This picture was published by Springer-Verlag as a poster in 1985,
but Springer has been unable to find a copy for me. I also sent ... | [] | [
{
"answer_id": 98550,
"author_id": 9652,
"author_name": "Dirk",
"author_reputation": 13198,
"author_url": "https://mathoverflow.net/users/9652/dirk",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>As a matter of fact, the poster is right on the other side of the hal... | |
507,298 | Explicit derivation of the Artin-Schreier equation from a Kummer extension in non-discretely valued complete fields | https://mathoverflow.net/questions/507298/explicit-derivation-of-the-artin-schreier-equation-from-a-kummer-extension-in-no | 6 | 270 | 1 | true | false | null | nt.number-theory;field-extensions;valuation-rings | 2026-03-04 05:57:07Z | <div class="s-prose js-post-body" itemprop="text">
<p>Let <span class="math-container">$(K, |\cdot|)$</span> be a complete ultrametric field of characteristic <span class="math-container">$0$</span> with residue field <span class="math-container">$k$</span> of characteristic <span class="math-container">$p > 0$</spa... | [
{
"author_id": 11417,
"author_name": "Lubin",
"author_url": "https://mathoverflow.net/users/11417/lubin",
"body_html": "<span class=\"comment-copy\" itemprop=\"text\">In future, please have pity on an aged mathematician with failing vision, and avoid using “$a$” and “$\\alpha$” in the same paragrap... | [
{
"answer_id": 507322,
"author_id": 18060,
"author_name": "Will Sawin",
"author_reputation": 166969,
"author_url": "https://mathoverflow.net/users/18060/will-sawin",
"body_html": "<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>If <span class=\"math-container\">$a$</span> has the ... |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 14