Blog (mostly math)

Post

Speculation. The “right kind of upskilling” can, effectively all by itself, uplift economies. To study: Report “Upskilling for shared prosperity”. Read more

Hahn-Banach Theorem

Ref: Functional Analysis lectures by Casey Rodriguez. Lecture on the Hahn-Banach theorem. Link to the lecture: Link. Updated: 3/3/26 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

Post

How do we know if everything is secretly already determined and unfolds to the T, or if there is randomness in the World? Is randomness an illusion? Does God play dice? Instinctually: Randomness exists in the World. Can we prove it? Read more

Udacity-1 Intro Programming-1 Intro Web Dev

Introduction to Programming Updated: 1/3/26 Link to Udacity subscription: Link. Link to Udacity course: Link. We will learn the foundations of four of the most popular languages: HTML, CSS, Javascript, and Python. \[{ \underline{\textbf{Introduction to Web Development}} }\] [The Web and HTML] HTML is used to structure and write web pages.... Read more

Closed Graph Theorem

Updated: 25/2/26 Ref: Functional Analysis lectures by Casey Rodriguez. Lecture on the Closed Graph Theorem. Link to the lecture: Link. Obs [Product of Banach spaces] Let ${ B _1 , }$ ${ B _2 }$ be Banach spaces. Then ${ B _1 \times B _2 }$ under \[{ \lVert (b _1, b _2) \rVert = \lVert b _1 \rVert + \lVert b _2 \rVert }\] is a Banach s... Read more