# \#mathematics-and-foundations **URL:** https://community.wolfram.com/tag/mathematics-and-foundations/99.md [Latest](https://community.wolfram.com/latest.md) · [Categories](https://community.wolfram.com/categories.md) · [Tags](https://community.wolfram.com/tags.md) --- ## [Basel, Hankel, and a recent proof of ζ(5) irrationality](https://community.wolfram.com/t/basel-hankel-and-a-recent-proof-of-5-irrationality/28282)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [October 7, 2026, 2:52pm UTC](https://community.wolfram.com/t/basel-hankel-and-a-recent-proof-of-5-irrationality/28282 "2026-10-07T14:52:21Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (56.1 KB) --- ## [An intuitive exploration of OpenAI's Navier–Stokes singularity construction (for the $1M Millennium Prize Problem)](https://community.wolfram.com/t/an-intuitive-exploration-of-openais-navier-stokes-singularity-construction-for-the-1m-millennium-prize-problem/28013)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 4\ **Last updated:** [September 25, 2026, 2:34am UTC](https://community.wolfram.com/t/an-intuitive-exploration-of-openais-navier-stokes-singularity-construction-for-the-1m-millennium-prize-problem/28013 "2026-09-25T02:34:39Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.5 MB) --- ## [Hadamard matrix of order 668](https://community.wolfram.com/t/hadamard-matrix-of-order-668/28083)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [September 22, 2026, 7:55pm UTC](https://community.wolfram.com/t/hadamard-matrix-of-order-668/28083 "2026-09-22T19:55:03Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (212.1 KB) --- ## [Four-color graphical bioinformatics: the machinery behind phylogenetic trees](https://community.wolfram.com/t/four-color-graphical-bioinformatics-the-machinery-behind-phylogenetic-trees/27398)
**Author:** [@jessicaalfonsi](https://community.wolfram.com/u/jessicaalfonsi)\ **Replies:** 2\ **Last updated:** [August 31, 2026, 2:55pm UTC](https://community.wolfram.com/t/four-color-graphical-bioinformatics-the-machinery-behind-phylogenetic-trees/27398 "2026-08-31T14:55:10Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (324 KB) --- ## [\[BOOK\] Exploring Partial Differential Equations: A Computational Approach now available](https://community.wolfram.com/t/book-exploring-partial-differential-equations-a-computational-approach-now-available/27399)
**Author:** [@aramm](https://community.wolfram.com/u/aramm)\ **Replies:** 1\ **Last updated:** [August 3, 2026, 3:37pm UTC](https://community.wolfram.com/t/book-exploring-partial-differential-equations-a-computational-approach-now-available/27399 "2026-08-03T15:37:50Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK\_Updated\_by\_aramm.nb (1.94 MB) --- ## [A deeper peek at the AI assist to DSolve\[\]](https://community.wolfram.com/t/a-deeper-peek-at-the-ai-assist-to-dsolve/27351)
**Author:** [@mroge02](https://community.wolfram.com/u/mroge02)\ **Replies:** 1\ **Last updated:** [July 31, 2026, 2:00pm UTC](https://community.wolfram.com/t/a-deeper-peek-at-the-ai-assist-to-dsolve/27351 "2026-07-31T14:00:53Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (382 KB) --- ## [Jacobian conjecture counterexample by LLM](https://community.wolfram.com/t/jacobian-conjecture-counterexample-by-llm/27349)
**Author:** [@antononcube](https://community.wolfram.com/u/antononcube)\ **Replies:** 4\ **Last updated:** [July 26, 2026, 2:52pm UTC](https://community.wolfram.com/t/jacobian-conjecture-counterexample-by-llm/27349 "2026-07-26T14:52:15Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (493 KB) --- ## [\[WSRI26\] Non-Projectional Rigidity in Finite-Axiom Theorem Spaces, and the System-135 Phenomenon](https://community.wolfram.com/t/wsri26-non-projectional-rigidity-in-finite-axiom-theorem-spaces-and-the-system-135-phenomenon/27333)
**Author:** [@svetoslavivanov](https://community.wolfram.com/u/svetoslavivanov)\ **Replies:** 1\ **Last updated:** [July 18, 2026, 9:00pm UTC](https://community.wolfram.com/t/wsri26-non-projectional-rigidity-in-finite-axiom-theorem-spaces-and-the-system-135-phenomenon/27333 "2026-07-18T21:00:21Z")
--- ## [\[WSRI26\] Interpreting How Neural Nets Regress Cubic Polynomials](https://community.wolfram.com/t/wsri26-interpreting-how-neural-nets-regress-cubic-polynomials/27331)
**Author:** [@enricobottazzi](https://community.wolfram.com/u/enricobottazzi)\ **Replies:** 1\ **Last updated:** [July 18, 2026, 7:08pm UTC](https://community.wolfram.com/t/wsri26-interpreting-how-neural-nets-regress-cubic-polynomials/27331 "2026-07-18T19:08:29Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (6.43 MB) --- ## [\[WSRI26\] Observer Theory in Cellular Automata](https://community.wolfram.com/t/wsri26-observer-theory-in-cellular-automata/27326)
**Author:** [@mariajoserenza](https://community.wolfram.com/u/mariajoserenza)\ **Replies:** 3\ **Last updated:** [July 18, 2026, 12:08pm UTC](https://community.wolfram.com/t/wsri26-observer-theory-in-cellular-automata/27326 "2026-07-18T12:08:42Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (1.25 MB) --- ## [\[WSRI26\] A Computational Study of Benford's Law in Integer Sequences](https://community.wolfram.com/t/wsri26-a-computational-study-of-benfords-law-in-integer-sequences/27318)
**Author:** [@wolgamot](https://community.wolfram.com/u/wolgamot)\ **Replies:** 1\ **Last updated:** [July 17, 2026, 11:00pm UTC](https://community.wolfram.com/t/wsri26-a-computational-study-of-benfords-law-in-integer-sequences/27318 "2026-07-17T23:00:32Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (3.57 MB) --- ## [\[WSRI26\] Lie Algebras from Strings to Hyperstrings](https://community.wolfram.com/t/wsri26-lie-algebras-from-strings-to-hyperstrings/27298)
**Author:** [@fli044](https://community.wolfram.com/u/fli044)\ **Replies:** 1\ **Last updated:** [July 17, 2026, 5:39pm UTC](https://community.wolfram.com/t/wsri26-lie-algebras-from-strings-to-hyperstrings/27298 "2026-07-17T17:39:57Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (7.68 MB) --- ## [\[WSRI26\] Inverting the Sitnikov Problem](https://community.wolfram.com/t/wsri26-inverting-the-sitnikov-problem/27313)
**Author:** [@suryansharyan01](https://community.wolfram.com/u/suryansharyan01)\ **Replies:** 1\ **Last updated:** [July 17, 2026, 3:32pm UTC](https://community.wolfram.com/t/wsri26-inverting-the-sitnikov-problem/27313 "2026-07-17T15:32:25Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.39 MB) --- ## [\[WSRI26\] Solving the k-ary Density Classification Task](https://community.wolfram.com/t/wsri26-solving-the-k-ary-density-classification-task/27305)
**Author:** [@ahmeterhanavci](https://community.wolfram.com/u/ahmeterhanavci)\ **Replies:** 2\ **Last updated:** [July 17, 2026, 2:15pm UTC](https://community.wolfram.com/t/wsri26-solving-the-k-ary-density-classification-task/27305 "2026-07-17T14:15:04Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (1.59 MB) --- ## [Get snarky: the cycle double cover conjecture -- an AI proof?](https://community.wolfram.com/t/get-snarky-the-cycle-double-cover-conjecture-an-ai-proof/27275)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [July 15, 2026, 2:53pm UTC](https://community.wolfram.com/t/get-snarky-the-cycle-double-cover-conjecture-an-ai-proof/27275 "2026-07-15T14:53:04Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (5.82 MB) --- ## [Branch-correct affine expansions for log, power and arg](https://community.wolfram.com/t/branch-correct-affine-expansions-for-log-power-and-arg/27280)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 0\ **Last updated:** [July 13, 2026, 2:34pm UTC](https://community.wolfram.com/t/branch-correct-affine-expansions-for-log-power-and-arg/27280 "2026-07-13T14:34:51Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (474 KB) --- ## [\[WSRP26\] Spatial and temporal patterns of artificial satellites around earth](https://community.wolfram.com/t/wsrp26-spatial-and-temporal-patterns-of-artificial-satellites-around-earth/27194)
**Author:** [@hema87477](https://community.wolfram.com/u/hema87477)\ **Replies:** 2\ **Last updated:** [July 10, 2026, 7:39pm UTC](https://community.wolfram.com/t/wsrp26-spatial-and-temporal-patterns-of-artificial-satellites-around-earth/27194 "2026-07-10T19:39:35Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (4.39 MB) --- ## [\[WSRP26\] Combinatorial-geometric properties of proof spaces of structures in universal algebra](https://community.wolfram.com/t/wsrp26-combinatorial-geometric-properties-of-proof-spaces-of-structures-in-universal-algebra/27197)
**Author:** [@chenjiaxuan123456](https://community.wolfram.com/u/chenjiaxuan123456)\ **Replies:** 1\ **Last updated:** [July 9, 2026, 8:01pm UTC](https://community.wolfram.com/t/wsrp26-combinatorial-geometric-properties-of-proof-spaces-of-structures-in-universal-algebra/27197 "2026-07-09T20:01:12Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (15.9 MB) --- ## [\[WSRP26\] The topology of pentagon aggregation and resultant void shapes](https://community.wolfram.com/t/wsrp26-the-topology-of-pentagon-aggregation-and-resultant-void-shapes/27188)
**Author:** [@jamesbutterfield922](https://community.wolfram.com/u/jamesbutterfield922)\ **Replies:** 1\ **Last updated:** [July 9, 2026, 6:51pm UTC](https://community.wolfram.com/t/wsrp26-the-topology-of-pentagon-aggregation-and-resultant-void-shapes/27188 "2026-07-09T18:51:43Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (5.05 MB) --- ## [The Min and Max of the No-3-in-line problem](https://community.wolfram.com/t/the-min-and-max-of-the-no-3-in-line-problem/27121)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 5\ **Last updated:** [July 5, 2026, 2:11pm UTC](https://community.wolfram.com/t/the-min-and-max-of-the-no-3-in-line-problem/27121 "2026-07-05T14:11:21Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (3.92 MB) --- ## [OpenAI disproves Erdős unit distance conjecture](https://community.wolfram.com/t/openai-disproves-erdos-unit-distance-conjecture/26916)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 6\ **Last updated:** [June 30, 2026, 9:18am UTC](https://community.wolfram.com/t/openai-disproves-erdos-unit-distance-conjecture/26916 "2026-06-30T09:18:14Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.07 MB) --- ## [No-3-in-line problem solved for order 70 by Marijn Heule](https://community.wolfram.com/t/no-3-in-line-problem-solved-for-order-70-by-marijn-heule/27085)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [June 18, 2026, 5:52pm UTC](https://community.wolfram.com/t/no-3-in-line-problem-solved-for-order-70-by-marijn-heule/27085 "2026-06-18T17:52:15Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (50.4 KB) --- ## [Progress in the no-three-in-line-problem](https://community.wolfram.com/t/progress-in-the-no-three-in-line-problem/26861)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [May 11, 2026, 6:52pm UTC](https://community.wolfram.com/t/progress-in-the-no-three-in-line-problem/26861 "2026-05-11T18:52:00Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (3.53 MB) --- ## [All elementary functions from a single binary operator](https://community.wolfram.com/t/all-elementary-functions-from-a-single-binary-operator/26749)
**Author:** [@andrzejodrzywolek](https://community.wolfram.com/u/andrzejodrzywolek)\ **Replies:** 1\ **Last updated:** [April 19, 2026, 6:08pm UTC](https://community.wolfram.com/t/all-elementary-functions-from-a-single-binary-operator/26749 "2026-04-19T18:08:08Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (1.93 MB) SymbolicRegression.m (28 KB) --- ## [Spacefilling polyhedra: Voronoi cell tessellation & stereohedra classification in 3D Euclidean space](https://community.wolfram.com/t/spacefilling-polyhedra-voronoi-cell-tessellation-stereohedra-classification-in-3d-euclidean-space/26734)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [April 15, 2026, 7:06pm UTC](https://community.wolfram.com/t/spacefilling-polyhedra-voronoi-cell-tessellation-stereohedra-classification-in-3d-euclidean-space/26734 "2026-04-15T19:06:06Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (14.3 MB) --- ## [Rule 30 exact binomial-Lucas lifting: boolean logic to integer coefficients, Stirling & support sets](https://community.wolfram.com/t/rule-30-exact-binomial-lucas-lifting-boolean-logic-to-integer-coefficients-stirling-support-sets/26542)
**Author:** [@tigrannersissian](https://community.wolfram.com/u/tigrannersissian)\ **Replies:** 3\ **Last updated:** [March 26, 2026, 10:55pm UTC](https://community.wolfram.com/t/rule-30-exact-binomial-lucas-lifting-boolean-logic-to-integer-coefficients-stirling-support-sets/26542 "2026-03-26T22:55:20Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (378 KB) rule30\_wolfram.pdf (436 KB) --- ## [AI logic & Knuth's conjecture: Claude LLM's generalized rule for 3D toroidal Hamiltonian lattices](https://community.wolfram.com/t/ai-logic-knuths-conjecture-claude-llms-generalized-rule-for-3d-toroidal-hamiltonian-lattices/26551)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 2\ **Last updated:** [March 6, 2026, 10:29am UTC](https://community.wolfram.com/t/ai-logic-knuths-conjecture-claude-llms-generalized-rule-for-3d-toroidal-hamiltonian-lattices/26551 "2026-03-06T10:29:33Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (1.03 MB) --- ## [\[BOOK\] Special Functions: A Computational Approach now available in Wolfram Notebook format](https://community.wolfram.com/t/book-special-functions-a-computational-approach-now-available-in-wolfram-notebook-format/26552)
**Author:** [@tigrani](https://community.wolfram.com/u/tigrani)\ **Replies:** 1\ **Last updated:** [March 5, 2026, 1:25pm UTC](https://community.wolfram.com/t/book-special-functions-a-computational-approach-now-available-in-wolfram-notebook-format/26552 "2026-03-05T13:25:18Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (3.18 MB) --- ## [The entropy bagel: complex roots of Littlewood polynomials](https://community.wolfram.com/t/the-entropy-bagel-complex-roots-of-littlewood-polynomials/26534)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 2\ **Last updated:** [March 4, 2026, 6:28am UTC](https://community.wolfram.com/t/the-entropy-bagel-complex-roots-of-littlewood-polynomials/26534 "2026-03-04T06:28:52Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (3.42 MB) --- ## [Investigating fractal triangles and spectral graph analysis in recursive subdivision](https://community.wolfram.com/t/investigating-fractal-triangles-and-spectral-graph-analysis-in-recursive-subdivision/26495)
**Author:** [@rocketengn](https://community.wolfram.com/u/rocketengn)\ **Replies:** 1\ **Last updated:** [February 20, 2026, 6:29pm UTC](https://community.wolfram.com/t/investigating-fractal-triangles-and-spectral-graph-analysis-in-recursive-subdivision/26495 "2026-02-20T18:29:34Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (11.1 MB) [Next page](https://community.wolfram.com/tag/mathematics-and-foundations/99.md?match_all_tags=true&page=1&tags%5B%5D=mathematics-and-foundations)