# Distinguishing calligraphic or script letters from regular letters in handwritten mathematics

What is a good handwriting font for mathematics? addresses handwriting on a board. How do you clearly distinguish calligraphic letters, such as $$\mathcal{ABCDEFG}$$, or script letters, such as $$\scr{ABCDEFG}$$, from regular letters $$ABCDEFG$$ in handwritten mathematics?

Edit: Since posting this question, I have discovered How to write \mathcal letters by hand? on MSE and Andrew Stacey's article: Old Pappus' Book of Mathematical Calligraphy, although his main example is how to write a Fraktur $$\mathfrak{g}$$.

I always give this piece of advice to my students: only use letters that you can distinguish yourself. (Some people really don't do this unless told so.) When you teach, apply the same more strictly: only use letters that most students can distinguish. This includes avoiding using $v$ and $\nu$ in the same context. If you run out of letters, use something else: overlines, underlines, accents... Or just use different letters for different things.

I make my curly letters more curly than the regular ones, but this distinction is not always easy. If my students (or I myself) seem to have hard time following, I change my notation. Script letters should never be absolutely necessary.

• Your last remark that "script letters should never be absolutely necessary" has prompted me to ask a new question on the advantages of using script letters.
– J W
Commented Sep 20, 2014 at 10:32
• Maybe are not necessary, but often highly desirable, e.g. when one has a number of corresponding concepts, like $a$, $A$, $\mathcal{A}$ and $\alpha$ which are all related in the same way as $b$, $B$, $\mathcal{B}$ and $\beta$. Of course, you can use things like $\aleph$ or $A'$, $A_2$, $\check{A}$, but in my experience accents and indexes are not as good as calligraphic letters: after some time the results become messy (after you have to use forward indexes like ${}^i_j{}\tilde{A}^*_l$, you know you should refactor). A good solution to this is to use names like $\cos$, $\mathrm{diam}$, etc. Commented Aug 23, 2016 at 6:47

If you have clear handwriting on the board (if you don't, forget about calligraphic letters and use diacritics instead), you can "invent" your own calligraphic set of letters for the blackboard. It just has to be clearly distinguishable from your normal one, e.g. like this:

• look at the top left corner of the capital letter
• if it is a corner (B,D,E,F,P,R), make it an arc instead
• if it is a line cap (H,I,J,K,L,T,W,Z), add an arc to it
• if it is an arc (C,G,O,Q,S), make it a corner instead
• if it is skipped (A), make it a corner instead
• for X and Y make the line from the top left corner a downward arc
• add a swoosh to the U (or don't use it, because it too easily gets confused with V, Y and the normal variants)
• make both lines of the V inward arcs (or don't use it)

So, except for V and U (and X and Y) the letters are easily distinguishable and the rules are fairly simple.

My advice is to avoid the use of script or fancy fonts. Even if you have the skills to pull it off--and I'm very impressed by the boardsmanship of people here, see some of the old threads--many of your students will struggle with it in notes. The work is hard enough on its own, so try to avoid anything that adds mental hurdles (fancy notation).

I have seen lots of books that show vectors, for example, in script or bold or the like. But an arrow over the top is much easier to scribble in notes. Especially for those like me, with poor handwriting.

I would also avoid the use of Fraktur or of those Greek letters that are easily confused (the v looking thing, nu?) The same point applies. Even if you are good at it, some of the notetakers will not be.

Like with the arrows on the top vectors, there are usually alternatives to show more variables (capital letters, underscores, etc.) that are simpler.

• I'm using cursive vs "normal" for physical quantities vs units on the boards and always emphasize that I don't expect students (age 14+) to follow this convention and there will be no deductions if they don't, but there are some students who get confused... Commented Jan 30, 2022 at 11:57