All keyboards are more or less the same, the only difference is in the symbols printed on the keys. Hence the question is really about math keyboard layouts.
My keyboard layout has a lot of math symbols and use them every time I type math. Some examples (typed using my keyboard layout!): α β Γ Δ ψ Ψ (all greek letters are included), ≤ ≥ ⊗ → ∈ ∞ ↦ ≠ 〈 〉 ⊂ ⊃ ⊆ ⊇ ≅ ≃
TeX has about 230 math symbols (including Greek letters). You can easily encode them all, but my keyboard layout has only about 50 most commonly used symbols and 24*2=48 Greek letters.
And note that you can easily setup TeX to recognize Unicode math symbols in UTF-8 encoding.
Incidentally, I also have commonly used punctuation marks that are absent from ASCII: “ ” ‘ ’ – — …