--- name: math-unicode description: Use whenever you need to express mathematical notation — equations, filters, set-builder, statistics, calculus, logic, ratios, drops, counts. Emit Unicode math glyphs INLINE; never wrap in `$…$`, `\(...\)`, or `$$...$$`. Terminal coding agents (Claude Code, Codex CLI, and others) do not render LaTeX, so raw delimiters appear as noise. This skill activates automatically when math is involved, in both Claude Code and Codex. --- # math-unicode When emitting mathematical notation in a terminal coding agent (Claude Code, Codex CLI, or similar), **always use Unicode glyphs inline** — never wrap math in `$…$`, `\(...\)`, or `$$...$$`. These terminals do not render LaTeX; raw delimiters appear as plain dollar signs and reduce readability. ## When this skill applies Triggers (use Unicode math): - Equations, formulas, derivations - Filter conditions, set-builder notation - Statistics: probabilities, expectations, distributions - Calculus, linear algebra, logic - Counts, ratios, fractions, drops where precision matters Skip (do not transform): - The user explicitly asks for LaTeX or a `.tex` file - Math inside fenced code blocks (preserve source syntax) - Strings being passed to a system that consumes LaTeX (KaTeX MCP, etc.) ## Glyph cheatsheet ### Greek ``` lowercase α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω uppercase Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω variants ϵ ϑ ϕ ϖ ϱ ς ``` ### Operators ``` arithmetic + − × ÷ ± ∓ · ∗ ⋅ ∘ ⊕ ⊖ ⊗ ⊘ ⊙ big ∑ ∏ ∐ ∫ ∮ ∬ ∭ ⨁ ⨂ ⨅ ⨆ roots √ ∛ ∜ calculus ∂ ∇ Δ ∆ ⅆ ⅇ constants ∞ ∅ ℵ ℶ ``` ### Relations ``` equality = ≠ ≈ ≅ ≡ ≜ ≝ ≐ ∝ ∼ ≃ ≢ order < > ≤ ≥ ≪ ≫ ⋘ ⋙ ⊴ ⊵ set ∈ ∉ ∋ ∌ ⊂ ⊃ ⊆ ⊇ ⊊ ⊋ ⊏ ⊐ ⊑ ⊒ set ops ∪ ∩ ⊎ ⊔ ⊓ ∖ ``` ### Logic & arrows ``` logic ∧ ∨ ¬ ⊕ ⊻ ⊼ ⊽ ⊢ ⊨ ⊥ ⊤ quantifiers ∀ ∃ ∄ ∴ ∵ arrows → ← ↔ ⇒ ⇐ ⇔ ↦ ↪ ↩ ↑ ↓ ⇑ ⇓ ⟶ ⟵ ⟷ ⟹ ⟸ ⟺ ⊸ ``` ### Number sets & brackets ``` sets ℕ ℤ ℚ ℝ ℂ ℙ ℍ 𝔽 brackets ⟨ ⟩ ⌈ ⌉ ⌊ ⌋ ‖ ‖ 〈 〉 ``` ### Sub/superscript glyph blocks ``` superscript ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ⁱ ⁿ ᵃ ᵇ ᶜ ᵈ ᵉ ᶠ ᵍ ʰ ʲ ᵏ ˡ ᵐ ᵒ ᵖ ʳ ˢ ᵗ ᵘ ᵛ ʷ ˣ ʸ ᶻ subscript ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ ₐ ₑ ₕ ᵢ ⱼ ₖ ₗ ₘ ₙ ₒ ₚ ᵣ ₛ ₜ ᵤ ᵥ ₓ ``` ### Common LaTeX → Unicode | LaTeX | Unicode | LaTeX | Unicode | LaTeX | Unicode | |---|---|---|---|---|---| | `\alpha` | α | `\sum` | ∑ | `\in` | ∈ | | `\beta` | β | `\prod` | ∏ | `\notin` | ∉ | | `\gamma` | γ | `\int` | ∫ | `\subset` | ⊂ | | `\delta` | δ | `\partial` | ∂ | `\subseteq` | ⊆ | | `\epsilon` | ε | `\nabla` | ∇ | `\cup` | ∪ | | `\theta` | θ | `\infty` | ∞ | `\cap` | ∩ | | `\lambda` | λ | `\emptyset` | ∅ | `\setminus` | ∖ | | `\mu` | μ | `\leq` | ≤ | `\wedge` | ∧ | | `\pi` | π | `\geq` | ≥ | `\vee` | ∨ | | `\sigma` | σ | `\neq` | ≠ | `\neg` | ¬ | | `\phi` | φ | `\approx` | ≈ | `\Rightarrow` | ⇒ | | `\omega` | ω | `\equiv` | ≡ | `\Leftrightarrow` | ⇔ | | `\sqrt` | √ | `\propto` | ∝ | `\forall` | ∀ | | `\pm` | ± | `\cdot` | · | `\exists` | ∃ | | `\times` | × | `\to` | → | `\mathbb{R}` | ℝ | ## Style rules ### Rule 1 — Inline math: Unicode, no delimiters Bad: `The filter $f(T; m) = \{(s,r) : n_{s,r} \geq m\}$ produces the cohort.` Good: `The filter f(T; m) = { (s,r) : n_{s,r} ≥ m } produces the cohort.` ### Rule 2 — Block math: own line(s), still no delimiters Bad: $$|Q| / |T| = 5238 / 31075 \approx 16.9\%$$ Good: |Q| / |T| = 5 238 / 31 075 ≈ 16.9 % ### Rule 3 — Subscripts - Single Unicode-renderable index: prefer the glyph (x₁, x₂, xᵢ, xⱼ, xₙ) - Multi-character or non-mappable subscript: keep `_{...}` syntax — the underscore reads unambiguously as a subscript and stays more legible than bracket-style indexing: - `n_{s,r}` ← (s,r) has no Unicode subscript form - `x_max`, `σ_obs` ← multi-letter - Never mix: don't write `x_₁` or `x_{1}` when `x₁` works. ### Rule 4 — Superscripts (powers) - Simple / Unicode-mappable exponent: prefer the glyph — x², x³, xⁿ, eˣ, A⁻¹, and the transpose xᵀ / vᵀ. - Multi-character or expression exponent: use **caret + parentheses**, never `^{...}` — `x^(k+1)`, `x^(i)`, `e^(iπ)`. A bare `x^{T}` / `x^{(i)}` leaks LaTeX source; write `xᵀ` (single glyph) or `x^(i)` (parenthesized). ### Rule 5 — Big operators with bounds Unicode operator + a **bracketed inline range** — never `_{...}^{...}`. Use `..` for a numeric/expression range, `∈` for set membership, `→` for a limit target: ``` ∑[i=1..n] aᵢ ∏[k ∈ K] pₖ ∫[a..b] f(x) dx ∫[-∞..∞] e^(-x²) dx ⋃[i=1..n] Aᵢ lim[x→0] f(x) ``` ### Rule 6 — Fractions - Inline: `a/b`, `(a + b) / (c + d)` - Block (only when it aids clarity): ``` a + b ───────────── c² + d² ``` ### Rule 7 — Matrices / vectors ASCII art with corner glyphs: ``` A = ⎡ a b ⎤ v = ( v₁ , v₂ , v₃ )ᵀ ⎣ c d ⎦ ``` ### Rule 8 — Sets and conditions Prefer set-builder with `|` or `:`: ``` Q = { (s,r) ∈ T : n_{s,r} ≥ 18 ∧ p⁰_{s,r} < 0.9 } ``` ### Rule 9 — Numbers - Thousands: thin space (` `) — `5 238`, `34 601` — not commas (locale ambiguous). - Decimal: dot — `16.9 %`. - Percent: space before `%` — `16.9 %` (typographic convention; readable). - Approximations: ≈, ∼. Order of magnitude: ~. Confidence: `x = 5.2 ± 0.3`. ### Rule 10 — When Unicode hurts, fall back explicitly If a glyph chain becomes denser than the LaTeX it replaces, switch to readable ASCII pseudo-LaTeX and annotate it. Example: ``` H(p) = − ∑[x ∈ X] p(x) · log p(x) (∑ = sum over the support X) ``` The reader's comprehension is the only metric. Choose whichever form is clearest, then stay consistent within a passage. ### Rule 11 — Plain letters for variables; never style with math-alphanumeric codepoints Write variable names and identifiers with ordinary letters (x, A, Var, RSS). Do **not** reach into the Unicode *Mathematical Alphanumeric Symbols* block (𝐀 bold, 𝐴 italic, 𝓐 script, 𝔸 styled double-struck) to *style* ordinary letters. Those codepoints garble on copy/paste, terminal search, and screen readers — the same failure Claude Code hit in issue #61558. Exception: the standard, semantically meaningful blackboard-bold sets and operators are correct notation, not styling — keep using ℕ ℤ ℚ ℝ ℂ ℙ 𝔽 (number sets) and 𝔼 (expectation). Use those; don't hand-style anything else. ## Quick reference — common forms ``` Mean / std μ ± σ x̄ ± s Probability P(A | B) ℙ(A ∩ B) = ℙ(A) · ℙ(B | A) Expectation 𝔼[X] = ∫ x · f(x) dx Variance Var(X) = 𝔼[X²] − 𝔼[X]² Gradient ∇f = ( ∂f/∂x₁ , ... , ∂f/∂xₙ ) Norm ‖x‖₂ = √(Σᵢ xᵢ²) Big-O T(n) = O(n log n) Limit lim[n → ∞] aₙ = L Sum bounds ∑[i=1..n] i = n(n+1)/2 Quantile q_α = inf{ x : F(x) ≥ α } ``` ## Anti-patterns — never emit these in the terminal (Claude Code / Codex) ``` ✗ $f(x) = \sum_{i=1}^{n} x_i$ ✗ \( a^2 + b^2 = c^2 \) ✗ $$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$$ ✗ \[ |Q|/|T| \approx 16.9\% \] ✗ ∑_{i=1}^{n} or ∫_a^b or x^{T} (stacked bounds / brace exponent leak source even without $…$ — write ∑[i=1..n], ∫[a..b], xᵀ) ✗ Let 𝑉𝑎𝑟 = … or matrix 𝐀 = … (math-alphanumeric styling; garbles on copy/search — write Var, A) ``` If asked to produce raw LaTeX (e.g. for a `.tex` file or a KaTeX-rendering tool downstream), do so — and call it out explicitly: *"Raw LaTeX as requested; this will not render in the terminal."*