math-unicode

name	math-unicode
description	This skill must be used whenever a response needs mathematical notation — equations, filters, set-builder notation, statistics, calculus, linear algebra, logic, ratios, drops, or counts. Load it before composing, including when the user explicitly mentions math-unicode. Emit terminal-native Unicode inline, never raw LaTeX delimiters or commands.
disable-model-invocation	false

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).
• Single index with no subscript glyph: use a bare underscore — I_ν, ∂_μ.
• Multi-character or grouped subscript: use _{...} 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.
• Single exponent with no glyph: use a bare caret — x^ν, (z/2)^a.
• 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 selectors

Unicode operator + a bracketed inline selector — never _{...}^{...}. Use .. for a numeric/expression range, ∈ for set membership, → for a limit target, and an equation/condition when that is the natural selector:

∑[i=1..n] aᵢ            ∏[k ∈ K] pₖ            ∫[a..b] f(x) dx
∫[−∞..∞] e^(−x²) dx     ⋃[i=1..n] Aᵢ           lim[x→0] f(x)
∑[m₁+...+mₙ=N] c_m      ∮[C] f(z) dz           Res[z=z₀] f(z)

Use ordinary letters for named functions: Γ, B, erf, det, tr, Re, Im, exp, log, sin, cos, argmin. Do not emit \operatorname. For a left-scripted named function, use available glyphs such as ₂F₁(a,b;c;z); when an index cannot be expressed as one glyph, use readable ASCII notation such as _{p}F_q rather than inventing a substitute.

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 ⎦

Declare variable types in prose instead of faking bold or italic: “Here z and n are vectors, and Ω is a matrix.”

Rule 8 — Tensor indices

Tensor indices are indices, not powers. Keep non-mappable tensor indices in bare ASCII form and group only when the index has multiple characters:

R^ρ_{σμν}        ∂_μ        Γ^ρ_{νσ}

Rule 9 — Piecewise forms and aligned derivations

Use the box-drawing brace glyphs for a short piecewise definition; keep equals signs in the same column for a derivation. If those brace glyphs are absent in a reader's font, use a semicolon-separated sentence instead.

f(x) =
  ⎧ x²    if x ≥ 0
  ⎩ −x    if x < 0

aₙ = bₙ + cₙ
    = dₙ

Rule 10 — Sets and conditions

Prefer set-builder with | or ::

Q  =  { (s,r) ∈ T  :  n_{s,r} ≥ 18  ∧  p⁰_{s,r} < 0.9 }

Rule 11 — Numbers

• Thousands: thin space ( , U+2009) — 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 12 — 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. Prefer common, well-supported glyphs. Do not use combining marks or obscure modifier letters just to force a super- or subscript; use readable bare ^x / _x notation instead. Choose whichever form is clearest, then stay consistent within a passage.

Rule 13 — 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 = √(∑[i=1..n] 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 }

Golden corpus — difficult terminal-native forms

These examples are deliberately chosen to exercise non-mappable indices, constrained sums, tensors, special functions, contours, and multiline output. They are normalized terminal forms of standard formulas (including DLMF §10.32.E2, §15.6.E1, §19.19.E1, and §21.2.E1).

I_ν(z) = (z/2)^ν / (√π Γ(ν+½)) ∫[0..π] e^(±z cos θ)(sin θ)^(2ν) dθ

F(a,b;c;z) = 1 / (Γ(b)Γ(c−b)) ∫[0..1] t^(b−1)(1−t)^(c−b−1) / (1−zt)^a dt

T_N(b,z) = ∑[m₁+...+mₙ=N] ((b₁)_{m₁} ··· (bₙ)_{mₙ}) / (m₁! ··· mₙ!) · z₁^(m₁) ··· zₙ^(mₙ)

θ(z | Ω) = ∑[n ∈ ℤ^g] exp(2π i(½ n · Ω · n + n · z))
  Here z and n are vectors, and Ω is a matrix.

R^ρ_{σμν} = ∂_μ Γ^ρ_{νσ} − ∂_ν Γ^ρ_{μσ} + Γ^ρ_{μλ} Γ^λ_{νσ} − Γ^ρ_{νλ} Γ^λ_{μσ}

f^(n)(z₀) = n! / (2π i) ∮[C] f(z) / (z−z₀)^(n+1) dz

∂u/∂t + (u · ∇)u = −∇p + νΔu + f,  ∇·u = 0

p(x) = exp(−½ (x−μ)ᵀΣ⁻¹(x−μ)) / √((2π)ᵈ det Σ)

F(ω) = ∫[−∞..∞] f(t)e^(−iωt) dt

f(x) =
  ⎧ x²    if x ≥ 0
  ⎩ −x    if x < 0

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."