Math unicode

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."