数学で生きること─AI時代における知性
序章 2026年現在、私たちはAIとともに数学を語り、発見する時代に生きている。かつて数学の発見は、時間をかけ、専門文献を読み、問題の輪郭をゆっくりと捉える営みだった。未知の理論に触れ、数年に及ぶ忍耐と直感の積み重ねを経 … 続きを読む
Mathematics
The multi-filtration and the multi-persistence on a total object
Discussion and Verdict I have observed a tendency to conflate, or at least structurally identify, (multi-) fil … 続きを読む
The Fractions
Fractions are deceptively difficult. I have seen many parents agonize over how to explain concepts like 1/4 or … 続きを読む
Sheafification as a free construction
In the world of algebra, we often encounter “free” constructions. Think of the free group or the p … 続きを読む
Why we prefer “the right-side” of a critical value?
One found that there is the convention where denotes the upper-tail critical value such that , as a standard n … 続きを読む
Introduction to Central Limit Theorem + α
In short, CLT (Central Limit Theorem) theoretically supports the intuitive phenomena. Averaging things out ten … 続きを読む
Note on extrema
For an optimization problem, we want to find an efficient way of calculating For 1, the Newton’s method … 続きを読む
Conditionally i.i.d.の謎
応用の文脈では、サンプリングの際に(現実の世界で)そのサンプルが表す実体とは別に、サンプルに対応した取り得る値の空間 (range space)[1]例えばYES/NOで回答する問いについて調査をする例の場合、 {0,1 … 続きを読む
Note on the element generation of an algebraic colimit
This is a revised version of a previous note, originally posted on February 20, 2023.
Note on the finality
The finality is a functorial property that induces a sort of surjectivety in the diagram of hom-set of codomai … 続きを読む