I loathe American textbooks from the bottom of my heart. I learned math from these tiny 100 page books that made the point directly and succinctly and trusted the reader’s intelligence to figure out the rest. Textbooks here seem to be written for people who are incapable of thinking for the . . . Read more

Dummit and Foote has a fun way of classifying Pythagorean triples. It is a classic fact that if $(a, b, c)$ is a reduced Pythagorean triple then there exists integers $m, n$ such that $$ \begin{align*} a &= m^2 - n^2, \ b &= 2mn, \ c &= m^2 + n^2. \end{align*} $$ To prov . . . Read more

Came across this really cool short video about identities in a Sudoku square: . . . Read more

I was formalizing some linear programming in Lean and came across one of the most surprisingly difficult to prove theorems. ::: {#thm-closed-convex-cones} Let $A : \mathbb{R}^m \to \mathbb{R}^n$ be a linear transformation. Then the set $$ { A x : : : x \ge 0 } $$ is closed in . . . Read more

I came across this fun theorem in a talk about tree colorings: Combinatorial Nullstellensatz. Let $f \in F[x_1, x_2, \ldots, x_n]$ be a polynomial of degree $t_1 + \cdots + t_n$. If $S_1, S_2, \ldots, S_n$ are nonempty subsets of $F$ such that $\left| S_i \right| \geq t_i . . . Read more

I came across this video by NumberPhile and 3Blue1Brown about the density of primes that are 1 mod 4 vs the density of primes that are 3 mod 4. The main fact is quite cool but there was something that he said during in the middle of t . . . Read more

xD . . . Read more

$\tau$ manifesto The Tau Manifesto is dedicated to one of the most important numbers in mathematics, perhaps the most important: the circle constant relating the circumference of a circle to its linear dimension. For millennia, th . . . Read more

LMFDB Github The LMFDB is a database of mathematical objects arising in number theory and arithmetic geometry that illustrates some of the mathematical connections predicted by the Langlands prog . . . Read more

I came across this essay by Rodrigo Ochigame exploring possible future impact of math formalization and automation. Automated Mathematics and the Reconfiguration of Proof and Labor Abstract: This essay examines how . . . Read more