Ref: “Linear Algebra and Matrices” by Helene Shapiro. Chapter on Simultaneous Triangularization. Math StackExchange answer here. Thm [Commuting matrices share an eigenvector] Let ${ A, B \in \mathbb{C} ^{n \times n} . }$ Suppose ${ AB = BA . }$ Then ${ A, B }$ share an eigenvector. Pf: Let ${ \lambda }$ be an eigenval... Read more 06 Mar 2026 - 2 minute read
Reddit posts regarding use of AI in Mathematics. Updated: 1/8/26 OpenAI post: Ten advances in Mathematics and Theoretical Computer Science. Link to post: Link. OpenAI’s internal model disproves Unit Distance Conjecture of Erdos. Link to r/math post: Link. MathOverflow post on use of AI. Link. A paper b... Read more 04 Mar 2026 - 1 minute read
To read: “Claude’s Cycles” by Knuth. Link to r/math post: Link. Link to the paper: Link. Read more 04 Mar 2026 - less than 1 minute read
Speculation. The “right kind of upskilling” can, effectively all by itself, uplift economies. To study: Report “Upskilling for shared prosperity”. Read more 03 Mar 2026 - less than 1 minute read
Ref: Functional Analysis lectures by Casey Rodriguez. Lecture on the Hahn-Banach theorem. Link to the lecture: Link. Updated: 5/3/26 For a normed space ${ V , }$ let ${ V ^{’} }$ denote ${ V ^{’} = \mathcal{B}(V, K) . }$ Q) Given a general nontrivial normed space ${ V , }$ how large is ${ V ^{’} }$? Is it ${ V ^{’} = \lbrace 0 \rbrace }$... Read more 03 Mar 2026 - 5 minute read