What is a good handwriting font for mathematics?

68

26

My students frequently mix up my $t$'s with my $+$'s and my $y$'s with my $4$'s.

What is a good handwriting font for distinguishing these and other easily confused symbols?

Brian Rushton

Posted 2014-03-14T00:10:40.183

Reputation: 5 998

This is an excellent question for one of my math profs used a "font" that made $i j ! l 1 \iota r n m w \nu \omega$ indistinguishable on the blackboardHagen von Eitzen 2015-01-14T21:41:19.680

1Anyone coming here and looking to provide an additional answer: I would still love to see an answer that shows a good strategy for differentiating between 5 and s. Making sure the right angle at the top of the 5 is very pronounced is not enough, and this specific issue is not addressed in the (excellent) answers from Jim and Joel.Chris Cunningham 2014-03-26T15:06:27.507

4

I think it's probably worth linking this question to an old one on MathOverflow that deals with a similar problem http://mathoverflow.net/q/5853/45

Loop Space 2014-03-27T08:26:33.667

This is an excellent question. I once had a professor who said he'd worked hard to completely change his handwriting to make it more legible on the board. I had another professor whose k, r, t, x, and kappa were all indistinguishable to me.Mark Meckes 2014-03-14T14:26:08.507

I have just began writing my "x"'s with two swift curves and I prefer this very much. I didn't know how many other wrote it this way as I live in America.Andrew Moawad 2017-02-24T22:37:38.783

9Sometimes spacing helps, but my students would almost always mix $z$ and $2$, until I stroke my $z$'s with a middle bar, like ƶ or Ƶ. Very useful question!dtldarek 2014-03-14T01:08:13.640

I think it would be good to collect the advice from the answers in a small table, for convenience (in a letter-how to make it recognizable format).dtldarek 2014-03-14T02:36:52.447

Answers

68

I changed my handwriting font years ago for precisely this purpose, and I have continued to tweak my letterforms over the years, using the algorithm of changing the form of whichever letters seem to generate the most confusion. Here is my current font: enter image description here

A few notes about these letters:

  1. Capital letters aren't listed, but my experience is that they're all fairly straightforward. Just make sure to use print letters instead of cursive.

  2. It's crucial to have versions of a, b, d, p, and q that can be written using a single stroke. If you draw your circles and stems separately, they will constantly get disconnected, which vastly decreases legibility.

  3. I often omit the bottom "tail" on the f when writing it in the middle of a word, but I always include it when it's part of an equation. Similar statements hold for the top curve on the i. I will also draw a 1 as a simple vertical line if I think it's clear from context.

  4. The l (ell) is my newest letter, and I'm not really sure about it yet. I tried using a cursive $\ell$ for a while, but it never looked good inside of words, and it still wasn't very legible as a variable. At present, I am often omitting the top and bottom curves when the l is part of a word.

  5. In general, I've had bad experiences with vertical loops. I've tried loops on $\ell$'s, g's, j's, d's, and q's, and all of them seemed to make the letters less recognizable. (This is probably because such loops hardly ever appear in computer or typewritten fonts.)

  6. The tail curve on the t is crucial to avoid confusion with a + sign.

  7. The initial curves for the v and w are quite helpful for legibility. I also think v's and w's are more legible with relatively sharp angles, as opposed to a curvy cursive approach.

  8. The initial curve on the x is absolutely essential. This will be one of your most used letters, and it really helps to get it right. Curves on any of the other three stems don't seem to improve legibility, and make the letter annoying to write.

  9. I also think this curvy version of a y is easier to read than a two-sticks version. Among other advantages, it can be drawn in a single stroke, which avoids disconnection problems.

  10. The line across the z helps avoid confusion with the number 2, and the line across the 7 helps avoid confusion with a variety of symbols.

  11. I don't seem to be able to draw a curvy-bottom 9 that looks good. I wish I could.

  12. This version of a 2 is much clearer than any version with a loop on the bottom.

  13. I tried drawing a final loop on my o's for a while (like a cursive o), and it didn't work out.

Edit: By request, here are my capital letters. Unlike my lowercase letters, my capitals are really quite standard, and I don't have much to say about them. I've also included by Greek letters.

enter image description here

Jim Belk

Posted 2014-03-14T00:10:40.183

Reputation: 6 186

After commenting, I gave a lecture and tried to observe my own habits. I found that I could "push" the chalk so long as I was writing in the centre (vertically) of the board, and that my writing deteriorated significantly near the bottom, so w near the centre could be done as one stroke but near the bottom needed four. Nevertheless, I still disagree with (2), my 'p' (and 'x', but I defy anyone to do a one-stroke 'x'!) is two strokes and looks better that way than done as a single stroke.Loop Space 2014-03-21T08:53:02.523

@AndrewStacey To each his own. It is true that my writing tends to deteriorate near the bottom of the board, and I suppose that problem could be exacerbated by some of my letter forms. Also, it is of course true that my x, t, and z are all two strokes -- I think two strokes work out fine as long as the strokes cross. But for me, at least, it's hard to consistently draw circles and squares that are tangent in two strokes.Jim Belk 2014-03-21T12:42:46.673

3@Andrew: I've seen one-stroke x's. The results are not good.Mark Meckes 2014-03-22T12:42:25.410

@AndrewStacey I don't remember where it was, but there was a guy who would write on chalkboard as with a brush, i.e. he would always "pull" the chalk in all directions (adjusting with the wrist and fingers). I must admit it was quite amazing to watch (he was fast and efficient). Also, his font was rather large, but that was actually good. It happens that I copy him while drawing diagrams.dtldarek 2014-03-23T17:56:47.093

That's really great advice. Might I humbly ask you to post a picture of your capital letters as well (I'm in Germany and we really like Capital Letters here and use them and use them a lot in Lectures…).Dirk 2015-01-15T12:41:00.607

@Dirk I've added them above.Jim Belk 2015-01-15T20:43:48.247

Thank you very much!Dirk 2015-01-15T21:20:25.863

The only thing I might add is to add a strike through the NUMBER 0... to differentiate from the letter O??? – None – 2014-03-26T14:41:10.987

6Isn't that confusing when people will think of the empty set?Markus Klein 2014-03-26T14:44:22.893

@InvaderGzim I've never been able to make a version of this that looks good. What direction is your strike? How far does it go on both ends?Jim Belk 2014-03-26T19:50:50.787

@JimBelk Just to make it clear, my comment posted after I gave a lecture should be read as negating my earlier comment. My initial objections were theoretical in nature and once I'd actually observed what I do, then I discovered that I pretty much followed your advice anyway.Loop Space 2014-03-27T08:25:14.567

Beautiful answer! I just wonder, why do you consider the initial curve on x essential? What is its purpose?avakar 2015-12-16T14:10:27.683

1@avakar Not only does it make x's clearly distinguishable from some sort of multiplication symbol, but it also just makes an x look a bit more like typical x's in math books. Almost all math books use some sort of italic serif font for variables, and in such a font the stems on an x are almost always curved on the ends. For a handwritten font, just having a curve on the upper left end seems to suffice for conveying this same visual impression.Jim Belk 2015-12-17T00:50:05.207

7That list is great. I especially like the second point; it seems obvious in retrospect but until just now it never occured to me while I have considerable problems with this. I changed away from writing in my usual handriting style to 'printed' letters on the blackboard, and this was always an issue since then.quid 2014-03-14T23:45:52.977

@quid Thanks. I was taught to draw circles and stems separately in elementary school, and the result for me was about two decades of terrible handwriting.Jim Belk 2014-03-14T23:53:13.207

Great! I think I use almost the same handwriting. I just use a 1 without the lower horizontal bar, to avoid confusion with the 7, and my l has a loop. Also, care should be taken when writing uppercase letters that look the same as their lowercase variant, but bigger. (c and C, k and K, o and O, p and P, s and S, x and X, u and U, v and V, w and W, z and Z)Ruben 2014-04-19T21:16:29.053

What medium are you using here? I'm not sure I'd agree with all the criteria in all cases. For example, with chalk it's best not to push the chalk making (2) a little tricky.Loop Space 2014-03-20T10:12:52.000

@AndrewStacey I write almost exclusively on chalkboards. I can't say I've noticed any problems related to "pushing".Jim Belk 2014-03-20T21:42:00.670

14

enter image description here

$\times\ \ +\ \ 4\quad 2\quad \omega\quad 9\quad a\quad 1\quad i\\ x\quad t\quad y\quad z\quad w\quad g\quad q\quad l\quad j$

Joel Reyes Noche

Posted 2014-03-14T00:10:40.183

Reputation: 4 090

3I am impressed that you distinguish $\omega$ and $w$. – None – 2014-03-25T02:16:21.863

5Some years ago, when I was a student, I was doing a calculation, and a z became a 2. Needless to say, the result was wrong. Since then I crossed my z's as seen here. Same for a curl on the bottom of a t.Gerald Edgar 2014-03-14T13:22:02.203

My only issue is with your 4. When written quickly, that style tends to resemble a 9. I prefer the open topped one and giving y a loop at the bottom off the tail.David G 2014-03-27T03:15:52.043

3A friend of mine in undergrad used his bad handwriting to his advantage. He once found that he had to change a partial derivative symbol into a 2 in order to get the correct answer, which he did deliberately over the course of a few lines. (Or so he said; he never explained what happend to the other partial derivative symbol.)Toby Bartels 2014-03-27T16:41:19.760

@TobyBartels, you make a good point about $\partial$ and $2$.Joel Reyes Noche 2014-03-28T02:03:49.967

Like @JimBelk, I also put a horizontal line across my $7$ to distinguish it from $1$.Joel Reyes Noche 2014-03-15T01:10:21.023

14

I would like to add a point that I've not seen explicitly mentioned in the other answers. That is that context can often be your aid in clarifying your lettering. As a trivial example, no one is going to misread they as +hey. So the "special alphabet" is primarily for mathematics in your lectures. (That said, you should cultivate a clear hand writing for normal text but it doesn't need to be as extreme as for the mathematical part.)

Similarly, if you never write $\times$ then the students will soon realise that x means $x$ and not $\times$. And I doubt that someone will mistake $x_k$ or $\vec{x}$ for $\times_k$ or $\vec{\times}$.

On the other hand, scale is often hard to see on a board so X and x are not easy to distinguish. It can be awkward to avoid using these together (consider the common desire to have $x \in X$) and distinguishing them visually can be difficult, but then context can help.

Here are some practical tips:

  1. Go in to a large lecture hall, write some random equations on the board, and then go to the back and try to read what you wrote. Then modify your handwriting until you think it is clear. This won't be perfect (since you know what you wrote), but it'll at least be a lot better than not doing it.

  2. Say what you write as you write it, and make sure that before you write anything on the board then the students are at the same point as you so that they are paying attention to what you say as you write it.

  3. Cultivate writing "the wrong way". It's a bit trickier for those not blessed with sinister tendencies, but if you can learn to write so that you do not stand in front of what you just wrote then it will be much easier for the students to see what you write as you write and say it. This doesn't mean writing with your left hand, it is possible to do this with the right hand but the body position takes a bit of getting used to. This has the added bonus of making you more turned towards the students as you write.

Having just given a lecture, I'd add one more practical point: ensure that the board is clean before you write on it. Stray squiggles left over from before you erased it can be confusing.

Loop Space

Posted 2014-03-14T00:10:40.183

Reputation: 2 873

13

alphabet alphabet with stroke order

Here are what my alphabet and numbers have ended up looking like. For the sake of clarity, I've included a stroke order chart, where the first stroke is red, the second green, the third blue, and the fourth cyan.

I try to make distinctions between every character, but I agree with those above who have noted that "o" is, in general, a terrible name for a variable. I tend to only use the "O" with a flourish where I have to make a distinction between "o" and "O".

I use the double-story "g" to distinguish from "y", and "S" with a serif to distinguish from "5". I use serifs to distinguish between uppercase and lowercase ("c" and "C", "s" and "S", "k" and "K", "v" and "V", "w" and "W", "p" and "P"), but where I don't have to make that distinction, "c" and "s" get serifs to distinguish from "(" and "5", respectively.

Nyan Cat

Posted 2014-03-14T00:10:40.183

Reputation: 131

1I also sometimes put serifs on $Z$ to differentiate it from $z$ or $2$.Joel Reyes Noche 2014-03-27T02:30:18.517

11

This is my handwriting font for mathematics. (Excuse the shakey-ness, this was made using the stylus on my phablet.)

It isn't as minimalist as some of yours, but I have never had anyone tell me they had trouble reading my writing. I make it clear which letters are which by using size and giving attention to negative space.

I find that using big loops and serifs is really good for board work, where it can otherwise be difficult to distinguish capital letters. (Spencerian cursive is actually pretty good for board work too, just not for equations.)

The prototypical gesture here is the J, from left to right to down. That is the leftmost part of many capitals.

Keeping track of where the bottom line of the word is also important, for example the tail on the lower case t is just below thst bottom line, and it is crossed exactly on the middle letter line.

My biggest problem is that my vs look like nus.

Alexander Gruber

Posted 2014-03-14T00:10:40.183

Reputation: 1 311

3That's a nice handwriting font!Mark Fantini 2014-12-21T19:45:46.540

1It's a beautiful font, but I can see where students who are not used to it still might be confused. Especially g's with 8's, p's with ρ's, f's with j's, S's with ∫'s. Some students in the back row might even think the capital T is an i hat.user3932000 2016-03-25T21:05:07.793

10

I think you need to fix any problems you have by modifying a letter or two of the way you write. For example, I used to write my y's in two separate straight strokes, but they would get confused with my x's if I wasn't careful about where the stroke stops. To correct this, I started writing my y's more like the way you write a g, with a curly bottom. I also stroke my z's with a cross to keep them separate from my 2's.

To fix your t's, add a curl on the bottom.

mkasberg

Posted 2014-03-14T00:10:40.183

Reputation: 381

7

As others have suggested, adding a serif can make a big difference. I write my y's like g's, and I also stroke my z's through the middle. Lower-case l's are written cursive-style, with a loop, and I make sure to make the 'tail' of my q's big enough to ensure there's no confusion with 9's.

I also never use certain letters as variables (if I can help it) - especially o's.

Andy Mikula

Posted 2014-03-14T00:10:40.183

Reputation: 348

6

In response to Chris Cunningham's request, I think this sort of 5 is unlikely to be mistaken for an s:

5

The key is not just the right angle at the top left, but the sharp angle directly below it. The danger here is to make sure you don't come so close to closing up the bottom that it looks like a 6.

Mark Meckes

Posted 2014-03-14T00:10:40.183

Reputation: 1 026

I know this thread is really old, but I haven't seen my solution discussed. I don't alter the digit 5 to distinguish it from the letter s, because I write 5 so often in comparison. Rather, I just change the letter s (used in mathematics) by writing it with very pronounced serifs (top and bottom) in one stroke. This takes very little change in practice, and I stick to the plain old curvy s for normal, non-math writing.Nick C 2018-02-09T22:39:08.807

@NickC: Well, I don't alter my 5 either; this is just the way I write 5s. But it's a good point in general: modify symbols in inverse proportion to how often they're used. Hence (as discussed elsewhere on this page) change z instead of 2, and change t instead of +.Mark Meckes 2018-02-10T02:00:58.837

8My 5tudents will thank you.Chris Cunningham 2014-04-25T04:40:05.697

4

I write like this: enter image description here

And everybody can read what I'm writing. Especially, take look at letter x.

And here are my digits: enter image description here

enedil

Posted 2014-03-14T00:10:40.183

Reputation: 149

Ohhh, I love it. Looks right out of a Tim Burton movie. Cool Q, too. and j. and y.Alexander Gruber 2015-02-08T21:25:50.250

4

We discussed this, or more specifically the subject of handwritten $x$, a while ago at The Aperiodical.

I still don’t understand why the two-curves $x$ never caught on in the US. Newton wrote $x$ the way modern Brits do, so it predates American independence. Curious!

Christian Perfect

Posted 2014-03-14T00:10:40.183

Reputation: 41

3

The linked photo clearly shows that Newton usually wrote "x" by crossing two lines. There are only a few cases otherwise on a page with dozens of x's.

kundor 2015-01-15T17:04:40.880

4

Taking my cue from printed math (and particularly TeX), I use different fonts for text mode and math mode. The italic font (math mode) is cursive, while the roman font (text mode) is printed. This helps distinguish ‘a’ from ‘$a$’, for example. (And assuming that you and I are both using the default fonts on this site, then my handwriting looks pretty much like those two letters do on the screen.) When I started this, I had a somewhat too exaggerated cursive style, so the fonts look less different now than they used to, but I maintain a difference in all letters.

Also, after several false starts, I've settled on a little loop at the top of ‘0’ to distinguish it from ‘O’. (Much as TeX uses merely slanted letters for math-mode capitals, I don't distinguish text-mode and math-mode capitals at all, saving the fancy cursive stuff for calligraphic font, which I use only in extreme circumstances.)

Toby Bartels

Posted 2014-03-14T00:10:40.183

Reputation: 251

1I like this idea in general, but regarding 0/O, a loop at the top makes me think more of the letter, not the numeral.Mark Meckes 2014-04-18T09:38:21.680

I can see that, but since that would be a cursive letter and the capitals are printed (see the parenthesis above) it doesn't really look much like an O. At least, I don't think it does!Toby Bartels 2014-04-19T22:34:39.573

But it's surprisingly hard to get a distinguished zero! Sometimes people use a slash, but we need that for the empty set. I tried a dot for a while (like some computer displays have), but it was too much work for too little result. So now I have the curl; quick and easy, and can be made more or less noticeable as required. Still not ideal, however, I agree.Toby Bartels 2014-04-19T23:31:44.093

To me, it looks like a script O, so if you think of all capitals as printed, I see your point. But how often do you need an O in math mode anyway? I would think it would come up rarely enough to qualify as the kind of "extreme circumstances" for which you save the calligraphic font.Mark Meckes 2014-04-20T08:10:06.430

It's rare, but if it's an ordinary "O" then I still don't want the fancy font.Toby Bartels 2014-04-23T11:54:53.133

2

One thing I have run into is, when learning or tutoring probability, being able to distinguish the random variables with their density functions' support.

To that end, I typically put serifs on my capital letters only, and that helps me tell the difference. One big issue is telling the difference between $W$, $w$, and $\omega$. I typically put serifs on $W$, keep the angles crisp on the $w$, and exaggerate the round parts for the $\omega$.

Noel

Posted 2014-03-14T00:10:40.183

Reputation: 21

2

How about using cursive handwriting as shown below:

enter image description here

Aquarius_Girl

Posted 2014-03-14T00:10:40.183

Reputation: 123

And is this good?András Bátkai 2014-04-18T07:00:24.563

@AndrásBátkai With this at least y and 4 look "different". The word good is subjective and yes this is good for me.Aquarius_Girl 2014-04-18T07:12:26.847

Sorry, if I sounded rude. I thought some explanation why you think is good belongs to the answer.András Bátkai 2014-04-18T07:13:52.987

@AndrásBátkai you didn't sound rude, you sounded as if you disagree with this being good. :)Aquarius_Girl 2014-04-18T07:14:55.617

1I do this (see my answer), but I notice your "z" … students would complain that they couldn't recognize that as a "z", so eventually I had to heavily modify it. (Now it almost looks printed, but it still has a curl.)Toby Bartels 2014-04-20T00:15:19.987

2

The key is neatness. I am a student, and I take for granted that my lecturers will use neat handwriting. I don't like it when a lecturer's handwriting is scrawled hastily and messily because it makes it difficult to read. I also don't like it when a lecturer neglects to write down something they have said, or something that is helpful with understanding what is being communicated (e.g. writing "Proof" before a proof to let the class know that the theorem has ended). Below I have given some pictures of the best handwriting that I have encountered.

Picture 1

Picture 1: this lecturer gives a tail on his v's and w's. The only problem with this handwriting is that the difference between a u and a v can be confusing.

The following two pictures show writing done by a lecturer who is exceptionally neat when he writes on the board. His style of teaching is to have a lot of discussion, and to only write down the mathematical symbols which he is talking about.

enter image description here enter image description here

ahorn

Posted 2014-03-14T00:10:40.183

Reputation: 129

0

enter image description here

I tend to loop my ζ so it doesn't look like a Z and I also put the lines on the z so it is not a 2.I also make my 1 like shown in the picture so it is not an I. I make my lowercase g fancy so it is not a 9. I put lines on my Θ so they are not θs. I also make my α short so they are not a ∝. I do not make my Phis like a plain old circle with a line. I tend to make a loop and then come down. My μs have a loop on the side.

user9199

Posted 2014-03-14T00:10:40.183

Reputation: 1

0

I don't understand how you can mix up a t and a +-sign:

  • the letter t contains a curl at the bottom and the bar does not pass left of the vertical line
  • the +-sign consists only of straight lines.enter image description here
  • the letter y starts with a curl and has a hole at the bottom
  • the digit 4 consists only of straight lines.
  • the letter z is written in the French way, the hole is quite long.
  • the digit 2 has a small but clear hole.

Dominique

Posted 2014-03-14T00:10:40.183

Reputation: 513