How much math does a paper need

Exactly as much as your claims require, and not one symbol more. Math in a paper is not a sophistication signal; it is a precision tool. The best-written papers use notation where prose would be ambiguous and prose where notation would be noise.

Notation is precision, not decoration

Write $f: \mathcal{X} \to \mathcal{Y}$ when the reader needs to know the domain and codomain exactly. Write “the model maps images to labels” when they do not. A paragraph that could be plain English but is rendered as symbol soup does not look rigorous, it looks evasive, and reviewers translate it back to check whether anything is actually being claimed. Before formalizing a statement, ask: does the symbol version rule out a misreading the prose version allows? If not, keep the prose.

Define every symbol once, then never redefine it

The reader’s working memory is your scarcest resource. The discipline:

• Introduce each symbol at first use: “let $n$ be the number of samples.”
• One meaning per symbol for the whole paper. If $\alpha$ is a learning rate in Section 3, it cannot be a significance level in Section 5.
• For notation-heavy papers, a small notation table early on pays for itself.

Number equations only when you reference them

An equation number is a promise: “we will point back to this.” Numbering everything buries the equations that matter under ones that do not.

\begin{equation}
  \mathcal{L} = \mathcal{L}_{\text{task}} + \lambda \mathcal{L}_{\text{reg}}
  \label{eq:loss}
\end{equation}

Reference it with \eqref{eq:loss}; for display math you never cite, use \[ ... \] or the starred environments and skip the number. The referencing machinery is covered in cross-references.

Theorem environments, in one breath

If your paper proves things, wrap claims in theorem, lemma, and proof environments rather than bolding “Theorem 1” by hand: they number themselves, cross-reference cleanly, and signal exactly what is claimed versus what is commentary. Setup and usage live in theorems and proofs.

Consistency is half the battle

Pick conventions and hold them for the entire paper:

• Vectors bold ($\mathbf{x}$) or arrowed, never both.
• Matrices uppercase bold, scalars italic lowercase.
• Sets in blackboard or calligraphic ($\mathbb{R}$, $\mathcal{D}$), consistently.
• Same convention in figures and tables as in the text.

Custom macros make consistency cheap: define \newcommand{\vx}{\mathbf{x}} once and a late notation change is a one-line edit instead of a paper-wide hunt.

Calibrate to the venue

A theory venue expects formal statements and complete proofs. An applied venue expects a clean problem setup and maybe one loss function. Read three accepted papers from your target venue and match their density. For the mechanics of writing any of it, start with math mode and keep the math symbols cheatsheet open in a tab.