Use of different typefaces to convey meaning

Mathematicians love using a different font, or style, to get a semantically different symbol, instead of using diacritics or a different letter entirely.

It can be hard to differentiate instances of the same letter rendered in different styles, or to miss the difference altogether.

In computer representations of mathematics which only use plain text, this strategy doesn't work at all, unless you're able to type in Unicode characters.

When handwriting mathematics, many of these differences are hard or impossible to produce, so there are different conventions to produce the same meaning.[1]

Sometimes, the alternate font looks very different to the standard one, and produces false friends (Fraktur).

Examples

A bold lower-case letter for a vector: $$\mathbf{a}$$. In handwriting, a common convention is to underline the letter instead.

Upright instead of italic for matrices: $$\mathrm{A}$$. Very hard to reliably produce in handwriting.

Script font for measure spaces $$\mathscr{M}$$ or categories $$\mathscr{C}$$, especially when the calligraphic font ($$\mathcal{M}$$ or $$\mathcal{C}$$) is also in use.