This is the first post. It exists mostly to confirm the layout and to verify that MathJax renders inline and display math the way we want it to.

Inline math

Euler’s identity is $e^{i\pi} + 1 = 0$, which packs five fundamental constants into a single equation.

Display math

A classic — the Gaussian integral:

\[\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}.\]

A small proof

Claim. For all $n \in \mathbb{N}$, $\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$.

Proof. By induction on $n$.

Base case. For $n = 1$, the left side is $1$ and the right side is $\frac{1 \cdot 2}{2} = 1$. ✓

Inductive step. Assume the identity holds for some $n \geq 1$. Then

\[\sum_{k=1}^{n+1} k = \left(\sum_{k=1}^{n} k\right) + (n+1) = \frac{n(n+1)}{2} + (n+1) = \frac{(n+1)(n+2)}{2},\]

which is the formula with $n+1$ in place of $n$. $\blacksquare$

A bit of prose

Posts here can mix prose, math, and code blocks freely. A short code sample:

def gauss_sum(n: int) -> int:
    return n * (n + 1) // 2

That’s all for the first post.