2026-10-26T21:49:12Z https://nostr.now Ianagol https://nostr.now/npub1jgyrd4zu8kdc4xpeyqq75hflnf7vupwmqkxmsk3cts2eqakejcvqc8rkt6 https://media.mathstodon.xyz/accounts/avatars/108/201/208/221/876/637/original/e83e51a2a40343a0.png https://media.mathstodon.xyz/accounts/avatars/108/201/208/221/876/637/original/e83e51a2a40343a0.png https://nostr.now/nevent1qqsrhhn0l7rg2n63nrpph2kh7zz45ws4gkaf7tlhzkqlur94upckq7czyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps379h5z In reply to <a href='/nevent1qqsxc64shr7xufkuxtyjsrm0zfvawcfds7n2n79hxntyw0rlgccakkcc2nlu7'>nevent1q…nlu7</a><br/>_________________________<br/><br/>see also the tv show Numb3rs<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/117/509/410/648/952/366/original/e72405be53c93a12.png"> <br/> 2026-10-26T21:49:02Z https://nostr.now/nevent1qqsdaez8k6yur3t3y8feyc8jqgq2prt0h9rgajj64ss0ga95p27an3gzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsv8drg5 In reply to <a href='/nevent1qqs22uyxepedqch75vrdqvpcgrm3cfswgdwnqh4xkqgdgs4hrsuc6nsy5henr'>nevent1q…henr</a><br/>_________________________<br/><br/>The Leiden declaration also states about training AI on mathematics: “The rationale for this strategy often rests on a further assumption: that capabilities developed through mathematical theorem proving will extend to broader general reasoning.” <br/><br/><a href="https://leidendeclaration.ai/">https://leidendeclaration.ai/</a> 2026-10-25T03:37:54Z https://nostr.now/nevent1qqsyumlsjzq4ul5rac6ury6nh47v0kaewqkkwftzfafwg6he4vgtnqgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpszmzwch In reply to <a href='/nevent1qqsghzzv9pyu6vrnvefjahya4krgv4h6ws8x9hpt4cltvg42hxv3wmg4ccpkh'>nevent1q…cpkh</a><br/>_________________________<br/><br/>This is a result of Kuperberg. <a href="https://arxiv.org/abs/1112.0845">https://arxiv.org/abs/1112.0845</a> A non-trivial knot has a non-cyclic SU(2) representation by a result of Kronheimer-Mrowka. Reducing modulo an ideal, one gets a non-cyclic representation to SL(2,p) for some p. GRH (or now quasi-GRH) allows one to bound the size of the prime polynomially in the crossing number. Baldwin and Sivek are writing a note explaining this new result (assuming the OpenAI result is correct). 2026-10-25T03:30:26Z https://nostr.now/nevent1qqsx952mjmzn6jd7pzx00t0lq44zlest6de0y7z3cknndrjudkz2lzqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps7e045w RE: <a href="https://mstdn.social/@QuantaMagazine/117496960947355286">https://mstdn.social/@QuantaMagazine/117496960947355286</a><br/><br/>An interesting (to me) consequence of this result (or rather some further advanced building on it) is that the unknot recognition problem is in coNP (ie, there is a certificate that a knot is knotted which is polynomial size in terms of its crossing number). One also has certificates that a knot is hyperbolic or torus. This was previously proved by Kuperberg and Baldwin-Sivek based on the generalized Riemann hypothesis. But the quasi version (for Dedekind zeta functions) is enough. Lackenby proved unknotting is coNP unconditionally using a different approach, but this approach gives different information.<blockquote class="border-l-05rem border-l-strongpink border-solid"><div class="-ml-4 bg-gradient-to-r from-gray-100 dark:from-zinc-800 to-transparent mr-0 mt-0 mb-4 pl-4 pr-2 py-2">quoting <br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Article"><a itemprop="url" href="/note1fanu5n6px8g73cqw6x3ut60s2z9sxzsenn7dsnkmjdjfyrga9k7qlas2ry" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1">note1fan…s2ry</a></span><br/> </div> The Riemann hypothesis has been an open problem for over 160 years. Resolving it would enable mathematicians to better understand the nature of prime numbers, one of math’s most crucial building blocks. And that’s just for starters.<br/><br/>AI just made a major advance toward an answer. <a href="https://www.quantamagazine.org/ai-proved-the-quasi-riemann-hypothesis-what-happens-now-20261019/">https://www.quantamagazine.org/ai-proved-the-quasi-riemann-hypothesis-what-happens-now-20261019/</a> </blockquote> 2026-10-24T18:40:06Z https://nostr.now/nevent1qqsz8lj0383fnk2y92ylup45tgt7yrg4ve8xxz62kwj07gkdmzvvzuczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsk09p0y In reply to <a href='/nevent1qqs8639ylfad2zg0nepl4z5myw9r6vw4aq653gd7q22m5xht56z2mysza97nj'>nevent1q…97nj</a><br/>_________________________<br/><br/>Here’s an excerpt from an article about Hamilton.<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/117/453/984/099/179/729/original/934d1024cc467363.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/117/453/984/317/343/519/original/8680aabf841f2c5a.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/117/453/984/923/776/227/original/c3f2e6e2af9a944b.png"> <br/> 2026-10-17T02:53:26Z https://nostr.now/nevent1qqsyx5ufsq28zklsyss4xwtcy4pryuqz652w898pj8j6a2cu4tkvr9szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps4jzqwp In reply to <a href='/nevent1qqsd92lw8x5n37pr7mwppx9lxjkkw5gungrwrydetq9znkhn3hku7mgmn67y8'>nevent1q…67y8</a><br/>_________________________<br/><br/>Now the challenge is for a chemist to synthesize a molecule that fits together in this pattern. 2026-09-24T17:11:07Z https://nostr.now/nevent1qqs286uwcanjfck56sc0ehzc588k593eel4z3vxn0hmvq2zu94efumczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsyt2vqh In reply to <a href='/nevent1qqs85q2fmsvucqa82qxd0k8cdc9ger7277nj2r29ydse3xdwqpvlhzsx6nd8k'>nevent1q…nd8k</a><br/>_________________________<br/><br/>Multiple groups wrote up Perelman’s proof of the geometrization conjecture in detail, which held up to scrutiny (modulo the lack of details). So I can imagine a similar thing happening here (although maybe the proof is like the proof of the 4-color theorem, where some parts are too complicated to be human checkable). 2026-09-10T15:22:20Z https://nostr.now/nevent1qqsz2u9w5y0dt7c6z3th3755qc8lh4jum86k8yp289n30smcv0vf07szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsqnnt96 In reply to <a href='/nevent1qqsxczwvgxyuz0gx4q9vhtku2e2ftx6hzcgdqhgvs6f2cphv6ckc8tc43jlaj'>nevent1q…jlaj</a><br/>_________________________<br/><br/>That will keep this lady busy <br/><br/><a href="https://youtu.be/OIsN0kiL9fI?is=M1SxFjxTDP27r02w">https://youtu.be/OIsN0kiL9fI?is=M1SxFjxTDP27r02w</a> 2026-08-17T14:50:10Z https://nostr.now/nevent1qqsquzt9he9ps38f0nww87xfknefy6qhzmh8ac3k3p6lzqh5mfz6sgszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps3wr576 In reply to <a href='/nevent1qqsd3jnuvyrdj5t67f6j4cyd6dy7pwgua0p86hsvqe4r0w4nctyul8cq3dqpq'>nevent1q…dqpq</a><br/>_________________________<br/><br/>Vasudha has claimed that the Gassner representation is faithful, which is maybe a less well-known problem, but probably a bigger deal (it implies linearity of the braid groups with a much simpler to describe representation than the Lawrence-Krammer representation proved to be faithful by Bigelow &amp; Krammer). <a href="https://arxiv.org/abs/2208.12378">https://arxiv.org/abs/2208.12378</a> 2026-07-27T15:49:35Z https://nostr.now/nevent1qqsr5euqayhx5y7kt82kl5r2vf2mqxg2mygpsavjwfklgtz2xxq9rgczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps33d49a In reply to <a href='/nevent1qqswwy7plu9mtvurmx0dgqnsw7wes0jswqj7flpwyyuzkxzu46w3k5qgq8cmg'>nevent1q…8cmg</a><br/>_________________________<br/><br/>When the cone angles on the spherical polyhedron are rational, there is a connection with translation surfaces. One can take a branched cover over the vertices so that the cone points all have cone angles a multiple of 2π, and so that there is a global holomorphic 1-form, hence a translation surface. Properties of this translation surface, such as closed geodesics or geodesics connecting vertices, can correspond to those of the polyhedron. For example, it underlies these results: <a href="https://arxiv.org/abs/1802.00811">https://arxiv.org/abs/1802.00811</a><br/><br/><a href="https://arxiv.org/abs/1811.04131">https://arxiv.org/abs/1811.04131</a><br/><br/><a href="https://mathemalchemy.org/2021/01/19/dodecahedral-trajectory/">https://mathemalchemy.org/2021/01/19/dodecahedral-trajectory/</a><br/> <img src="https://media.mathstodon.xyz/media_attachments/files/116/842/262/338/660/579/original/cd7a0e21aaf8ea70.png"> <br/> 2026-07-01T02:04:13Z https://nostr.now/nevent1qqsrmh5rg3x7zh2e7f9j9pkskh6kfqrds3j6vtc9dk2h2dnwyrfqe0szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpscakyyd In reply to <a href='/nevent1qqsr4zqxlk995x3ymlgf7vf6p0u0e44vtegsklyx0v7zf4fzqgavr8gym5uvj'>nevent1q…5uvj</a><br/>_________________________<br/><br/>There’s a textbook devoted to abelian groups: <a href="https://link.springer.com/book/10.1007/978-3-319-19422-6">https://link.springer.com/book/10.1007/978-3-319-19422-6</a> 2026-05-24T09:01:14Z https://nostr.now/nevent1qqspq65jl4k0k2udj5zsq0f3hlxqnkjdgkjt4prvfuzdtje2tzdzktgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsj737x6 In reply to <a href='/nevent1qqsreh6xzqg58td2vlyhd7rdm8rp29trf0qnqjq387zfrexknn3j8mgp9xd8v'>nevent1q…xd8v</a><br/>_________________________<br/><br/>Posted image of a high unit-distance graph from the lattice construction of OpenAI (from Alvaro Lozano-Robledo on Twitter), see comments at the above link.<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/116/616/924/632/787/627/original/4ef1f59c0ff1c00e.png"> <br/> 2026-05-22T06:58:27Z https://nostr.now/nevent1qqsreh6xzqg58td2vlyhd7rdm8rp29trf0qnqjq387zfrexknn3j8mgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps5uy7ft I was looking for images of the point configurations maximizing unit distances, and found this post. <a href="https://community.wolfram.com/groups/-/m/t/3719376">https://community.wolfram.com/groups/-/m/t/3719376</a> it would be nice to see some based on the construction in the paper. 2026-05-22T03:36:13Z https://nostr.now/nevent1qqspek56xq0kgeacrtvlmapyf96g6cjfgv6sa9k760m4e3jdu2j8axgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpszdxh6n In reply to <a href='/nevent1qqstpa702nqjjxs82wz3fru6zaekuu9gg5npzjsznjv6grjhfxdwrqcycrx70'>nevent1q…rx70</a><br/>_________________________<br/><br/>Looks like MacKay’s paper appeared in 1981, and Levine-Steinhardt 1984. The three jointly received the Buckley prize for this in 2010.<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/116/570/970/515/304/201/original/cf9c8009ff7bb275.png"> <br/> 2026-05-14T04:11:14Z https://nostr.now/nevent1qqsz0ks06r96l70ts4casksaghd3ynal59xyv5d0wql57fc569s7degzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsxq8nhk In reply to <a href='/nevent1qqspe48aqd9vt39dc57c96g4a4e3zsx9dn5ldwp39rmxd76tkfx77vqlj9grw'>nevent1q…9grw</a><br/>_________________________<br/><br/>Quasicrystals were first predicted by Alan Mackay (he knew Penrose and may have been inspired by Penrose tilings)<br/><br/><a href="https://en.wikipedia.org/wiki/Alan_Lindsay_Mackay">https://en.wikipedia.org/wiki/Alan_Lindsay_Mackay</a><br/><br/>I met his son Bob at a climbing gym in Berkeley. <a href="http://bobmackay.com/">http://bobmackay.com/</a> Bob met Penrose as a teenager through his father and made some of the first computer designs of Penrose tilings. 2026-05-13T16:02:06Z https://nostr.now/nevent1qqszvtfl8usj4q4l3ej6m7f6jwnpxurtezyk6y63e6vlg6jsagk63rqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsfks33r In reply to <a href='/nevent1qqsw822r49rp8mzecwad7czekhunrlt0yhzxz64j6juvqn28pqm5tdq20ydlt'>nevent1q…ydlt</a><br/>_________________________<br/><br/>It looks like the continued fraction expansion of the Friedman constant has period 66754.<br/><br/><a href="https://mathoverflow.net/questions/457086/simple-continued-fraction-of-freimans-constant">https://mathoverflow.net/questions/457086/simple-continued-fraction-of-freimans-constant</a><br/><br/>It would be nice if there is a geometric interpretation of this constant. 2026-05-07T20:46:03Z https://nostr.now/nevent1qqspvajfhaw8q4heeg230k0gcyhxgey8vdtvjulp4ztp0zu8talg37qzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps6g5q9z In reply to <a href='/nevent1qqsq2hpvl3d5uz2phzeyjmla7vktm8cq9ycxzm7hwv6drxdgctn04hcm6a7yg'>nevent1q…a7yg</a><br/>_________________________<br/><br/>I hadn’t seen this before. Presumably these are the orbits of Z_10 x Z_10 subgroups of the 14400 - order symmetry group. The orientation preserving subgroup is generated by the product of binary icosahedral groups acting on the right and left on the unit quaternions (with center acting trivially). This is then extended by an orientation-reversing element. In the icosahedral group (which is A_5), there is a cyclic element of order 5. The preimage of this element in the binary icosahedral group is order 10. So one gets (Z_10xZ_10)/(-1,-1). Maybe one can adjoin an orientation-reversing element to get the full Z_10 x Z_10? Or maybe it’s some sort of Z/2-extension? In any case, this suggests that on the Clifford torus, the tetrahedra come in two mirror image groups of 50. This seems to be the case looking at the visualization. 2026-05-06T16:10:59Z https://nostr.now/nevent1qqs2ajfh3l3yfllwe5rmylq3x3nd03gm69nejgggscw0u3ttzpyd9sqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps9wkaxe In reply to <a href='/nevent1qqsx9c8g5dmgrtxcm0xcy73pmrpddsr056uc97ky67twl8cqm8lmz8syrj5eh'>nevent1q…j5eh</a><br/>_________________________<br/><br/>This is coming from Humbert’s volume formula for the quotient of hyperbolic space by a Bianchi group. <br/><br/><a href="https://en.wikipedia.org/wiki/Bianchi_group">https://en.wikipedia.org/wiki/Bianchi_group</a> 2026-04-22T17:04:56Z https://nostr.now/nevent1qqs8m6gwvc6rhs938836ramrqgtsu49nnvvh5dtfy59ts09gncpckfczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsv86r2t In reply to <a href='/nevent1qqsf7v6c9pl0vcnz4tuhrgg02dy3lf6s9ghy9t6f0nrm6pzzk8ad62qdl0rg6'>nevent1q…0rg6</a><br/>_________________________<br/><br/>The figure eight knot group Γ is generated by the Mobius transformations z-&gt; z+ω, z-&gt; 1/(1+z), acting on the upper half-space model of hyperbolic space, with coordinates (z,t), z in C, t&gt;0, and where ω is a third root of unity (-1+sqrt(-3))/2. There is a cusp H (or horoball) centered at infinity, which is the set of points t&gt; 1. Looking at the image of H under the group Γ, one gets balls tangent to the boundary t=0 and of height 1, centered at the lattice Z+Zω, as well as horoballs of various heights tangent to Q(ω). This is what is shown in the image. They are tangent to H, and so are the largest horoball whose interior is disjoint from all of its images. The volume of the image of H in the quotient is sqrt(3), and the volume of the quotient is 2.0298. This ratio is a rational multiple of their value (and I think I had it flipped, 1/ cusp density, so volume / cusp volume). 2026-04-22T15:47:01Z https://nostr.now/nevent1qqs24x9dm3f9mk9ew3z7gjg5gv5332ztnyv4x7vzel6chcpzvsyfujgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsjdvu8y In reply to <a href='/nevent1qqs9lzvqx7ysev9l02yfr0nff3njhcuajyv00myp5utaq8tzswulmuswu6aqf'>nevent1q…6aqf</a><br/>_________________________<br/><br/>This is a rational multiple of the cusp density of the hyperbolic structure on the figure eight knot complement.<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/116/445/727/091/866/085/original/ea0dcde2a62cd1b8.png"> <br/> 2026-04-22T01:20:57Z https://nostr.now/nevent1qqsweemjtqu3fc5mwflad67d8u94g8zh7ntujgels7x066yvwa9ggnszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsxs2jma How technology in the classroom can distract from learning.<br/><br/><a href="https://www.theatlantic.com/ideas/2026/04/teachers-screens-edtech-students/686681/?gift=G0hU6ohQGLGJfrFtwMSWpVILzN_BAXtiLF-_MUq-2cE">https://www.theatlantic.com/ideas/2026/04/teachers-screens-edtech-students/686681/?gift=G0hU6ohQGLGJfrFtwMSWpVILzN_BAXtiLF-_MUq-2cE</a> 2026-04-09T03:33:13Z https://nostr.now/nevent1qqsqqyfkxpx0rfltpehzyemyel4889v53c0llt9tdk05lv9xsgfhkzszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsrq9df4 In reply to <a href='/nevent1qqsya0685z2fyd7ne9t0m9dvv7q4m35akfwqfcummrrwsramgzyr0kqwvfdn7'>nevent1q…fdn7</a><br/>_________________________<br/><br/>I clicked on it to check that the date wasn’t April 1. 2026-04-05T04:41:41Z https://nostr.now/nevent1qqsy22vuvfx6f00fqxzhlq3y300tszc2ndt2fmcx4mfvpr249guufgczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpslqzqj7 In reply to <a href='/nevent1qqs298exmkwzeergcd834f9pks26sh6u4m2vztt8edkmpcdkvzaesgcm3ns4l'>nevent1q…ns4l</a><br/>_________________________<br/><br/>I didn’t look at the petition, but I can imagine a host of reasons not to hold the ICM in the US right now. 2026-03-15T18:33:19Z https://nostr.now/nevent1qqsq5r7njysvw45gk4df5328uz29jqpw9xcl698w94kgdedghukjvfczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsxr5yw2 In reply to <a href='/nevent1qqsqussdjm2ygsylacvd5t20vyzg6nmqts0d7kxkaue42xrhpjlmw2g2w3cvc'>nevent1q…3cvc</a><br/>_________________________<br/><br/>Anyone that figures out dark matter will be walking on cloud 9. 2026-01-11T05:14:34Z https://nostr.now/nevent1qqsg2knf984vzc2lcr5nzyarvqfl5whh9zavf6fvt3489f2xtde9cdgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps2h0pha In reply to <a href='/nevent1qqsgshfmaqqyu69t2mdv2m7mu8yhmr0ztpj49vte6uxvurvq7s8qwgc4vfcr5'>nevent1q…fcr5</a><br/>_________________________<br/><br/>This seems impressive. <br/><br/><a href="https://www.linkedin.com/posts/axiommath_yesterday-thousands-of-bright-undergrads-activity-7403482884361093120---sC/">https://www.linkedin.com/posts/axiommath_yesterday-thousands-of-bright-undergrads-activity-7403482884361093120---sC/</a> 2025-12-07T22:24:49Z https://nostr.now/nevent1qqsp3gg7npelsx5cvsdkl8flwznwtcq78wme8mw2s8mwg6wj87wtc2szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps00pvnm In reply to <a href='/nevent1qqsgshfmaqqyu69t2mdv2m7mu8yhmr0ztpj49vte6uxvurvq7s8qwgc4vfcr5'>nevent1q…fcr5</a><br/>_________________________<br/><br/>Ken Ono is all in on this. <br/><br/><a href="https://www.wsj.com/tech/ai/math-ken-ono-carina-hong-axiom-startup-649bc417">https://www.wsj.com/tech/ai/math-ken-ono-carina-hong-axiom-startup-649bc417</a> 2025-12-07T22:20:22Z https://nostr.now/nevent1qqsg4c592hmraznrx4vhasvk0msrtemhzjv47trp7za45apjqaarcwszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps777g75 In reply to <a href='/nevent1qqsvvvm24gccn2pvvuwhxrfh4zgeqqu70xp55ff20yp98t60tmfgtlcwhgv8u'>nevent1q…gv8u</a><br/>_________________________<br/><br/>The classification of finite simple groups begs to differ. 2025-12-07T22:12:52Z https://nostr.now/nevent1qqsde3rfne5y6m2t3sqfxyeqc9gr9x0cujlm7zn622jpatzgzkduc0szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsmfekj4 In reply to <a href='/nevent1qqs8kx8u6e4tzns5g96ysq9cx6scvl0vr7u8rzh33797qsy6n697aggylysxj'>nevent1q…ysxj</a><br/>_________________________<br/><br/>An equivalent way to see it: take a linear transformation sending the parallelopiped to a cube. Then the inscribed ellipse will be sent to a sphere. Now note that the ratio between the volumes is constant. 2025-11-06T16:35:00Z https://nostr.now/nevent1qqsglszlmxgffrph268m4h4k0j0s5w7p6g3hk494tl299s5c3c2fpsszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpspankyp In reply to <a href='/nevent1qqs9rzwzh0fsdp9ac59x9ngqeguf9ht72cdz0rncft3mppqwhdjulvc90xpum'>nevent1q…xpum</a><br/>_________________________<br/><br/>It’s too bad this hasn’t been worked out completely yet. I’m not sure what the issues are. Someone told me a while ago that there are some tricky differential topology issues that haven’t been resolved. 2025-10-18T21:28:36Z https://nostr.now/nevent1qqsrgnujkx3jy3drlmmx4jrr5mgd5p99py44d8pcdjxu5957h5xqk5szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsfhcxm0 In reply to <a href='/nevent1qqsxwptk4l8djr4fj2dee3jm56c9nfh6pux3675f6yxm2ze3hlfyhfgn46r8q'>nevent1q…6r8q</a><br/>_________________________<br/><br/>Another option is to consider “long knots”. I’m not sure who invented this, but I learned about it from Ryan Budney. This is just where you imagine the two ends going off to infinity, asymptotic to lines. <a href="https://arxiv.org/abs/math/0309427">https://arxiv.org/abs/math/0309427</a> 2025-10-13T15:26:27Z https://nostr.now/nevent1qqsp9apnn4awt7cf3wqm3w80lfykdnunclulq668vn38nmyuwmrmxzczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsucfedt In reply to <a href='/nevent1qqszmdfp3rsd83cnx2qhd6p5sylkzk4r0a56922py8fxez7vwe02uecnm0re6'>nevent1q…0re6</a><br/>_________________________<br/><br/>I like that, Ed could be Edinburgh or Education. 2025-09-28T18:57:39Z https://nostr.now/nevent1qqsgld8xns7ryddfpkwdpp6gzxfnthgynk5uvmu9zwh265fe28c4t4qzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps5km7zk In reply to <a href='/nevent1qqs99jg76re9qp7wrm4t5v499yflqynzsr9t9vg8u7cdrt5u8vvue4gr85cqh'>nevent1q…5cqh</a><br/>_________________________<br/><br/>TEDinburgh - might run into copyright issues. 2025-09-27T04:57:17Z https://nostr.now/nevent1qqsq3du22zaf95kj5u4tejuthf5t60fvhj2xnkl6hvm7wzjsa50l5eqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsgyn64f In reply to <a href='/nevent1qqsqm9x8al957rt6m7p8uwhf3t8daz0u3csyrsaz0mz8rcm99f2ungqxj9ehj'>nevent1q…9ehj</a><br/>_________________________<br/><br/>Hint: the answer is invariant under area preserving transformation. 2025-09-03T01:39:26Z https://nostr.now/nevent1qqspt8uw5rz48q8r6kxr0vy2tnz425lt2p0y4rr8dd2rhew74g7f96czyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpstmdjr3 Math puzzle (inspired by recent posts of James Tanton). Take some points in Euclidean space z_1,…,z_k , what is the locus of points x such that the sum of the squares of the distances of x to z_1 through z_k is constant? I.e. |x-z_1|^2+ … + |x-z_k|^2 = c. 2025-08-07T06:44:11Z https://nostr.now/nevent1qqsqfj4w8gspu7l94ktss4fa666qtfhwatlzcezlwywnn0eze4f6zjczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsz47z4t In reply to <a href='/nevent1qqs8n65j86lv2vfrcq4g3p9gfql2j7he6uqvqvstvq225560dhakrsq9z3kq9'>nevent1q…3kq9</a><br/>_________________________<br/><br/>A reminder that the reason we don’t have unique representations for real numbers is that the Cantor set is totally disconnected but the real numbers are connected (I think I didn’t learn about this explanation until I was an assistant professor). 2025-08-05T16:48:32Z https://nostr.now/nevent1qqsfse4ngg88fmvcs33ylcrw8hxlzdn0nrex7kxyg75nzpxnezaf87szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps0aj5w9 In reply to <a href='/nevent1qqsdsvz6q6fst97atnt3rmn5vquh37xcpmt8ljcffff6z7sez7efw9c4l8f9j'>nevent1q…8f9j</a><br/>_________________________<br/><br/>Giving a new meaning to Hamiltonian mechanics. 2025-08-04T18:38:21Z https://nostr.now/nevent1qqsr36jrf8kq7g5wn57em4m6jzmdkau5hnmwdvd978zuxnam47wq8zqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps0tz5x3 In reply to <a href='/nevent1qqsfhsdt5k9epepy93w8huw00uz4usdcpwhyuvhhe8hu376d09szsssew3lxr'>nevent1q…3lxr</a><br/>_________________________<br/><br/>It feels like this should be related to Faulhaber’s formula, but I’m not sure how. 2025-07-21T18:18:55Z https://nostr.now/nevent1qqsw0nmzl6ufg7nuz9jkssgvldu8ynewhn362h4h967nzhfu6ye4lmgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsgjmcs8 In reply to <a href='/nevent1qqs854rvcgx2rsrzu9ec3mnlszwk9el89zu5she8aptnk3wymsy32rc6wq55h'>nevent1q…q55h</a><br/>_________________________<br/><br/>I shared a gifted version of this article here: (for people without a subscription). <a href="https://mathstodon.xyz/@Ianagol/114835860905798385">https://mathstodon.xyz/@Ianagol/114835860905798385</a> 2025-07-13T11:50:10Z https://nostr.now/nevent1qqsg00apnhu0cncrnelxln73g7xt690u3554r98f9cap04l3kpttjsczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsa4gfy6 Record lattice sphere packings discovered. <a href="https://www.quantamagazine.org/new-sphere-packing-record-stems-from-an-unexpected-source-20250707/?mc_cid=a20fe07f36&amp;mc_eid=284cf6a352">https://www.quantamagazine.org/new-sphere-packing-record-stems-from-an-unexpected-source-20250707/?mc_cid=a20fe07f36&amp;mc_eid=284cf6a352</a> This also seems to optimize the “lattice kissing” bound. 2025-07-11T17:53:29Z https://nostr.now/nevent1qqswmpdkrpdtwh8j8nqzjpncg584y3jaha8a4w9zkygy5xghuej9m3qzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps5qjwpx In reply to <a href='/nevent1qqs2j7eu6734dpzm32v5pd77sme2l2xa3nuemh8nftlvg7gts2m5dwg5se6a4'>nevent1q…e6a4</a><br/>_________________________<br/><br/>More signs<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/483/426/704/602/original/1b1d76c6f5020bd0.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/483/628/763/708/original/57c89bce25621aa5.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/483/833/523/040/original/473284744f6c62bb.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/484/061/024/015/original/81a2607e02891a49.png"> <br/> 2025-06-14T20:00:22Z https://nostr.now/nevent1qqs2j7eu6734dpzm32v5pd77sme2l2xa3nuemh8nftlvg7gts2m5dwgzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsyptlks In reply to <a href='/nevent1qqs0wseg6lmppy5yks4js73vw8tc57h2a93jsz69kqeakhrz5fzx93gj9e36f'>nevent1q…e36f</a><br/>_________________________<br/><br/>No Kings protest at Larkspur Landing<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/470/524/300/530/original/f8b5eebca8776d2f.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/470/751/067/343/original/294000509bc9ef2c.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/471/055/396/484/original/6eb14015e049623e.png"> <br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/683/471/390/206/074/original/27ee94864a67e82f.png"> <br/> 2025-06-14T19:56:46Z https://nostr.now/nevent1qqspq95x8thqkdeadfx3gl0s5ewjscv4zrekevjvnkr3zzkrza7fdgqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsf0wrga In reply to <a href='/nevent1qqsfaagzuxguu3x3a5tcsnmrkcz853l6pw70jdmyg68uvxu2np2mklcd3lhl0'>nevent1q…lhl0</a><br/>_________________________<br/><br/>This is the whole point, these deportations are a drop in the bucket compared to the number of immigrants, but news of these deportations are intended to scare current and potential immigrants into leaving or not coming. That was also the point of separating children from their families - who would want to risk that? 2025-06-12T23:06:56Z https://nostr.now/nevent1qqswtcu2tvsqrgjxa9emcyfun29lfxu4uull4stve40sfwp2k42yecczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps3vdznp In reply to <a href='/nevent1qqsp6x8uy9l6yw7m4k7guqk4fevxfmskqvz8yezccz6zryeqqng42rsqmjf5r'>nevent1q…jf5r</a><br/>_________________________<br/><br/>Thanks, the link was at the end of the article so I didn’t include it in the posting.<br/><br/>A conceptually simpler formula is to compute the arc of the circle between tangent circles in the ring. Then the sum of these angles is 2π. Of course, this is not an algebraic equation, but could be made algebraic via the application of trig identities.<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/286/674/233/640/598/original/03abd54b517b7f9d.png"> <br/> 2025-04-05T18:04:37Z https://nostr.now/nevent1qqst4jr3h7tq27lrxse0ch6vz87c3k23z9mq7n8fa2pzwtedlxecatszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps5ed4gw Formula relating the radii of a ring of circles. <br/><br/><a href="https://scitechdaily.com/descartes-unfinished-mystery-mathematicians-solve-380-year-old-geometry-problem/">https://scitechdaily.com/descartes-unfinished-mystery-mathematicians-solve-380-year-old-geometry-problem/</a><br/><br/>I recall learning about the ring lemma as a graduate student, but I didn’t realize that there wasn’t an explicit formula known relating the radii. <br/><br/><a href="https://en.m.wikipedia.org/wiki/Ring_lemma">https://en.m.wikipedia.org/wiki/Ring_lemma</a> 2025-04-05T01:02:33Z https://nostr.now/nevent1qqspkzmaqvesgw50h3tzxeeaqpdfkzkc0qgr5amh7nt8l2h5m5gwa4qzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps7m4twr In reply to <a href='/nevent1qqsped0fzh7x7g28n5ugsgc5pwfpvk3t3stxzjsnuqlwuf3phrgjeqgz0qw5w'>nevent1q…qw5w</a><br/>_________________________<br/><br/>I hadn’t heard of it before, I just looked at the gif of the McGee graph and identified the Cayley graph minor via groupprops. 2025-03-24T15:38:52Z https://nostr.now/nevent1qqs0ktzuffhddqkhhwgxnt9qs5k73dde04y2ymfz3ej5lkqe4h3dw8szyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpse3rw3k In reply to <a href='/nevent1qqs843quhlyn2ragc6wq3wfyws8n4ukkxjqt5ydakksepys9lfzlatcxd45l8'>nevent1q…45l8</a><br/>_________________________<br/><br/>Cool, are you visiting the topos institute? We are on spring break this week. 2025-03-24T04:32:27Z https://nostr.now/nevent1qqsggnu7wsn4yhkga07emgcy0ps66ykyqd08cp96x2vu5fta84nkl9qzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtps24w6a7 In reply to <a href='/nevent1qqs2f04tr8dkehdcu40xcv6fjh0y7wgx7sq97t50qzxdj0t33y2mlegs0hetw'>nevent1q…hetw</a><br/>_________________________<br/><br/>Deleting the red edges (and erasing the red vertices), one gets the Cayley graph for the semidihedral group of order 16 with respect to the generator of the cylic group Z8 and the involution automorphism of Z8 (in the Cayley graph, one may draw one green edge for each involution instead of two directed edges). This group is a subgroup of the McGee group. <a href="https://groupprops.subwiki.org/wiki/Semidihedral_group:SD16">https://groupprops.subwiki.org/wiki/Semidihedral_group:SD16</a> Pairs of opposite green edges, fixed by the other involutions of the McGee group (corresponding to the D16 subgroup, or extension of Z8 by the -1 involution) have midpoints of edges connected by a red edge to recover the McGee graph from the Cayley graph of SD16.<br/> <img src="https://media.mathstodon.xyz/media_attachments/files/114/215/401/119/908/336/original/9dc95725475a0ff4.png"> <br/> 2025-03-24T04:00:58Z https://nostr.now/nevent1qqsfwzxn5jk4p0ztjnn4mvhtdqgnfxjlr6rtm55whcevzcl9lurg7ugzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpskanry5 In reply to <a href='/nevent1qqs8rf5zgwz8tk4axq9492cy87s3gny3ws9tecle7j3knawynpel7pgazyyjs'>nevent1q…yyjs</a><br/>_________________________<br/><br/>Rent an electric car? Driving up the 101 from SB is nice. Highway 1 is still closed in Big Sur I think. 2025-03-02T21:49:48Z https://nostr.now/nevent1qqs2kgaptc02cacrqq5skemgpf64nmx42xljfetls496m97l7kxp4cszyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpstvw452 In reply to <a href='/nevent1qqsrl6nhg0x5qq8yyzwzdhsmkvypjr7vpfwqvyuzvchmdk9npns3krgdlaqqj'>nevent1q…aqqj</a><br/>_________________________<br/><br/>Not sure if this counts, but first and second fundamental theorems of calculus are pretty famous. 2025-02-28T03:43:39Z https://nostr.now/nevent1qqst52x64tdlfu7epaycx4kkddavx75lwerxyh29jad6v0g3vak4lmczyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsujn7dk In reply to <a href='/nevent1qqs8ymqvjsq9q0hdnx87lhqnlh6qv7ezeq8n88zxf7ddlxm55xmf4qg5wy56u'>nevent1q…y56u</a><br/>_________________________<br/><br/>My wife canceled our subscription too (I would only read it occasionally). 2025-02-27T05:54:29Z https://nostr.now/nevent1qqsq98maet6uv25jghh40tem7yf7gy66d2zpyt2x79sdsulf5rg9kcqzyzfqsdk5ts7ehz5c8ysqr6ja87d8ens9mvzcmwz68pwptyrkmxtpsg5clcr In reply to <a href='/nevent1qqs8cpq680xnkfrzd8ae9nsw9cr3hlv6n9tqz87apl2u0rzw90rfwuqvhrj6l'>nevent1q…rj6l</a><br/>_________________________<br/><br/>reading the question, it wasn’t immediately clear to me that a solution should exist, since one is given one parameter of freedom (α) to try to hit the identity, but the Lie group SO(3) has dimension 3. So potentially this could trace out a curve in SO(3) that doesn’t pass through the identity (except for α=0). But somehow the symmetry allows a non-trivial solution. 2025-01-21T03:05:55Z