Good Maths ⇔ Good Typography

A few days ago, I sent out a throw-away tweet commenting that I’m always careful to write “4 × 4” and not “4 x 4” because the multiplication symbol “×” and the character “x” are different things.

This sparked an unexpected volume of interest in my use of various mathematical symbols in tweets.

Thanks to the power of unicode, almost all electronic devices can display a huge range of symbols beyond the normal letters and numbers we use most frequently. This is particularly useful if you love both maths and typography.

i.e.: you ∈ {love maths} ∩ {love typography}

But while ASCII and its friends might give you the potential to use all manner of symbols, there is no easy way to do it. Twitter gives you the power but not the convenience.

My solution is to keep a document titled “Maths Symbols” on my phone and just copy and paste from there as I need them. After a few requests, I dumped a fistful of these symbols onto twitter for other people to copy, but it was rather desultory collection. I’ve since gone through and put my typographical house in order. They’re now all neatly laid-out, with a space before and after all symbols for ease of selecting. They are vaguely in categories and ordered roughly according to how often I use them. For most of them I’ve noted a name or use for the symbol; many symbols are used different ways in different branches of maths (it was a brave topologist who chase “π” as the symbol for homotopy groups) and so I’ve noted my most common use for them. Your use may vary.

You can download this whole list of maths symbols and greek letters as a text file by right-clicking here. Or else, I’ve put the whole thing at the end of this post for you to just copy+paste. If I’ve missed any characters, put them in the comments below and I’ll keep growing the list.

I should also mention that there are various apps for smart-phones which are effectively glorified lists with simplified copy+paste options. For users of the information-phone: “Character Pad” is good for its easy-of-use while “FancyChars” has an impressive but disorganised range of characters.

In a perfect world though, someone would develop a twitter client which can parse LaTex and convert it to the closest possible unicode text. Unfortunately at the moment: ∄

HERE THEY ARE:
π pi
∞ infinity
ℵ aleph
∆ delta
∑ sigma

× multiplication
÷ division
– subtraction (m dash)
√ square root
± plus and minus
∓ minus and plus

≠ not equal sign
≈ approximately equal
≥ greater than or equal to
≤ less than or equal to
≪ much less than
≫ much greater than
≅ congruent to
~ approximately, similarity
≡ equivalence
≜ equal by definition
∝ proportional to

¬ not
⇒ implies
⇔ equivalent
∀ for all
∃ there exists
∄ there does not exists
∴ therefore
∵ because
→ arrow
↔ double arrow
⇐ back arrow
⇑ up arrow
⇓ down arrow

⊗ circled cross (tensor product)
⊖ circled dash
⊕ circled plus

∈ element of
∉ not element of
∩ and, intersection
∪ or, union
⊆ subset
⊂ strict subset
⊄ not subset
⊇ superset
⊃ strict superset
⊅ not superset
Ø ∅ empty set
Ƥ power set

ℕ natural numbers
ℤ integers
ℚ rationals
ℝ real numbers
ℂ complex numbers
ℍ quaternions (Hamiltonian)
ℙ projective space

∘ composition
∙ dot scalar product
· and

∠ angle
º degrees
∡ measured angle
∢ spherical angle
∟ right angle

‰ per-mille
‱ per-ten-thousand
∇ del
† Hermitian matrix
⌊x⌋ floor brackets
⌈x⌉ ceiling brackets

∂ partial derivative
∫ integral
∬ double integral
∭ triple integral
∮ closed line integral
∯ closed surface integral
∰ closed volume integral
ℒ Laplace transform
ℱ Fourier transform

GREEK ALPHABET: Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω

RANDOMS: ⊥ ⊧ ⊢ ≺ ⋉ ⋊ ≀ ◅ ▻ ↦ ⋈ ∐ … ∤ ■ □ ∎ ▮ ‣ ⊻ ≜ ≝ ≐

SUPERSCRIPTS: ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ᵃ ᵇ ᶜ ᵈ ᵉ ᶠ ᵍ ʰ ⁱ ʲ ᵏ ˡ ᵐ ⁿ ᵒ ᵖ ʳ ˢ ᵗ ᵘ ᵛ ʷ ˣ ʸ ᶻ ᴬ ᴮ ᴰ ᴱ ᴳ ᴴ ᴵ ᴶ ᴷ ᴸ ᴹ ᴺ ᴼ ᴾ ᴿ ᵀ ᵁ ⱽ ᵂ ⁿ ʰ ʱ ʲ ʳ ʴ ʵ ʶ ʷ ʸ ˀ ˁ ˠ ˡ ˢ ˣ ˤ ᴬ ᴭ ᴮ ᴯ ᴰ ᴱ ᴲ ᴳ ᴴ ᴵ ᴶ ᴷ ᴸ ᴹ ᴺ ᴻ ᴼ ᴽ ᴾ ᴿ ᵀ ᵁ ᵂ ᵃ ᵄ ᵅ ᵆ ᵇ ᵈ ᵉ ᵊ ᵋ ᵌ ᵍ ᵎ ᵏ ᵐ ᵑ ᵒ ᵓ ᵔ ᵕ ᵖ ᵗ ᵘ ᵙ ᵚ ᵛ ᵜ ᵝ ᵞ ᵟ ᵠ ᵡ ᵸ ᶛ ᶜ ᶝ ᶞ ᶟ ᶠ ᶡ ᶢ ᶣ ᶤ ᶥ ᶦ ᶧ ᶨ ᶩ ᶪ ᶫ ᶬ ᶭ ᶮ ᶯ ᶰ ᶱ ᶲ ᶳ ᶴ ᶵ ᶶ ᶷ ᶸ ᶹ ᶺ ᶻ ᶼ ᶽ ᶾ ᶿ

SUBSCRIPTS: ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ ₐ ₑ ₒ ₓ ₔ ᵢ ᵣ ᵤ ᵥ ᵦ ᵧ ᵨ ᵩ ᵪ

FRACTIONS: ½ ↉ ⅓ ⅔ ¼ ¾ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅐ ⅛ ⅜ ⅝ ⅞ ⅑ ⅒ ⅟