John Kerl
kerl.john.r@gmail.com
Feb. 25, 2007
Now that you’re majoring in one of the technical disciplines
(engineering, science, or math), you’re going to be spending a
significant amount of time communicating in writing with others. You may find
that previously unimportant details, such as crossing your z’s,
now become essential — not only so that others can understand you, but
also so that you can avoid mistaking your own 2z for
z2 and so on. This is especially important if your
handwriting (like mine!) is less than perfect.
Before I continue, take a fresh look at our Roman alphabet, the digits, and
the Greek alphabet:

Notice that these mechanically typeset symbols are all clear and distinct
(except that lowercase omicron and most of the uppercase Greek letters look
like Roman letters — we don’t use these “duplicates”).
When we write by hand, though, symbols can become ambiguous —
we’re not machines, and things get a little loopy when we hurry. In
prose, surrounding letters can disambiguate a questionable letter — e.g.
you can guess that the fourth letter of hou*e has to be an s.
But in mathematical expressions we mix symbols from different alphabets, in
different orders, so context can’t assist us — and when we guess,
we often guess wrong. So it now becomes very important that each letter be
clearly recognizable on its own merits.
Here are samples, followed by the points I consider most important.

Lowercase Roman letters:
- Always make the lowercase l cursive —
otherwise it looks like a 1.
Make sure it’s taller than an e:
,
,
.
The lowercase l isn’t a good variable name to use (since it can
look like a 1), but lots of people use it and so yo
28 Comments
jovas
Pretty much exactly how I write. (My lower case zeta is prettier)
thaumasiotes
He doesn't mention that many people have identical handwritten "u" and "n" (both written "и").
This barely matters at all; context will tell you what symbol is being used, just like it does in prose, and most material is typeset.
It really is a very bad idea to use lowercase Ls, though.
sideshowb
While we're here, any suggestions on what works better for writing math to a digital whiteboard? Wacom type tablet with no display, or an ipad type tablet with pen?
fifilura
My tip is to use white paper. No lines no squares, just white.
In Sweden you were expected to use paper with squares but it adds a lot of clutter.
Unearned5161
nice writeup, I always like taking extra care to view the actual motions a professor uses when writing the symbols on the board as it can sometimes be non-obvious the order or direction to start in.
would also love tips on making right curly brackets not be the bane of my existence. I don't get it, I write a right one basically for every left and yet they feel so different!
dieselgate
Crossing the Z is a good one. I cross 0 but understand the point with phi. Something that’s not mentioned is y (lowercase) and how they can look like a 4
dang
Related. Others?
Tips for Mathematical Handwriting (2007) – https://news.ycombinator.com/item?id=32665846 – Aug 2022 (2 comments)
Tips for Mathematical Handwriting (2007) – https://news.ycombinator.com/item?id=22983274 – April 2020 (76 comments)
moi2388
I personally prefer to use dotted paper.
And I write every Latin letter in its capital form, however actual capitals twice as large. Put a dot in zero.
That way everything looks distinct
Kwpolska
> Make a point come out of the top of the p, to distinguish it from a rho.
Or make it varrho (ϱ).
> Keep the slash in the phi vertical; keep the slash in the empty-set symbol slanted.
Again, varphi (U+1D711 which HN doesn’t seem to like) is easier to distinguish.
The author silently chose varepsilon in their TeX, but chose to ignore the rest of the variants.
My grammar school math teacher used a very large ascender for the alpha, almost into serif-£-sign-without-the-line-through territory.
lagrange77
> Put a hook on the x to distinguish it from a times sign […] In 3rd-semester calculus and onward you’ll be using the times sign quite often.
I wonder if he's talking about the cross product.
mturmon
I used to work in a field that used Sigma for covariance matrices, and pervasively needed discrete summations which also use Sigma (and often with an understood index set, so the Sigma appears without clarifying adornment).
I ended up writing my discrete summation Sigma's with a little serif on the bottom, and ordinary Sigma's as in OP, with 4 quick back-and-forth strokes.
rhelz
chuckle I'm teaching high school math, and I have students who are jedi knights of making ambiguous mathematical signs. They make their "1"'s with a long top serif, which make it look like it could be either a "1" or a "7". A "4" written with a curly hook on the bottom can be mistaken for an "8", etc etc.
Not to mention a glyph which is maximally ambiguous between "T" and "F" so that when grading true/false questions, could stand in for either :-)
If the students would put half as much effort into learning the material as they do in trying to trick teachers they would get straight A's ;-)
joshdavham
It's incredible to realize how many of the habits mentioned in this post that I've unintentionally picked up while studying applied math. Even after graduation, I still follow a lot of these 'conventions'.
gnatolf
Most important to me was something not mentioned here: to make i/j les ambiguous, I but effort into explicitly add the right swoop at the bottom of the i, which allowed for the j to be a straight longish line dotted at the top.
buescher
For Greek I like this:
https://www.covingtoninnovations.com/pens/GreekChartLarge.jp…
There’s an old joke about “mathematical maturity” meaning being able to write a lowercase zeta, but I took enough classes from professors that would confuse xi and zeta that it probably doesn’t matter that much.
paulluuk
Mostly unrelated, but I wish the field of math would step away from greek letter notatation and just make variable and function names readable as programmers do. I know there are historic reasons, and I'm sure that mathematicians' time is so valuable that they can't be bothered to write more than 1 character, but it's a real barrier to entry in my opinion.
lynguist
I came up with similar rules over decades (I still write sometimes mathematical symbols), and I have to only take care of my "u" vs "n" and "r" vs "v", and write these pairs especially slowly because in my handwriting (especially u and n) look the same.
But for all the others I’ve developed similar disambiguations.
xyproto
Dotted 0 (number) and a regular round O (letter) should also be possible, instead of a round blank 0 (number) and an O (letter) with a top curl.
mysteria
For distinguishing between the lowercase "a" and "α" without switching to cursive you can also use a double storey a.
jebarker
People that use xi should lose their math credentials
dogmatism
learned this by experience in…1998
thanks for the insight
queuebert
The blog writer has particularly bad handwriting, and maybe that's why he needs these tricks. I've seen a lot of math handwriting, and seriously his is among the worst. Maybe he was drawing the letters with a mouse.
mkasberg
I changed the way I wrote my y's (now very curly) and z's (now crossed) in college while studying math after realizing I was making silly mistakes changing y's to x's and z's to 2's.
bluenose69
This is a good resource, and pretty much what I tell students in my classes. I take great care to explain how to write symbols, and I also give multiple pronunciations of the Greek letters.
Students with math and physics backgrounds are fine with Greek letters and other mathematical symbols, but the biologists in the class are mystified. They also get terribly confused when I reuse symbols for different purposes.
What I've discovered is that the students who have trouble with mathematical notation and reasoning got derailed when a teacher, in an early grade, said "let x be the unknown". That is a phrase that never comes up in other contexts, and I think it throws them off track. Many find it difficult to get back on-track later, so they memorize and sleep-walk their way through other mathematics classes until the system no longer insists that they take them. A shame, really.
milesrout
Why do Americans write x as a cross instead of like )(?
I have always written and seen written the variable x as )( and I was very surprised when I met Americans and they didn't do this.
gerdesj
This is all very well but surely all mathematicians/engineers/scientists (n that) have considered this both for themselves and had it mentioned when being taught in relevant subjects, or simply noticed.
Who on earth screws up writing rho with a p? Yes, I know that someone will but they need to write the symbol properly.
Zed and two? RLY? (Crossing your Z is a Germanic thing for me, which is why I do it – I grew up in W Germany). Despite that, you would be in no doubt if I wrote a 2 or Z, because I know how to use a fucking pen and I am able to write.
To be fair, I come from an age where cursive means something!
We are heading into an era where being able to use a pen or pencil will border on arcane skills. Calligraphy isn't hard nor is ensuring you get your message across.
Cross your zeros but leave your Os alone (or dot them if you like – I do sometimes). Cross your zeds if you like. Write Greek letters as they should be – a lower case rho starts from the bottom right and is written in a single stroke – it never looks like a "p".
x (eks) is two curves and not a diagonal cross. Multiplication is . or adjacency of symbols, however it might be x depending on context.
The given advice is don't slash the zero. I disagree. Phi is fatter than tall – its not hard to be precise, which I would hope a mathematician might manage.
In the end can you write or not? If not, use a keyboard. Nothing wrong with that per se …
ch3cooh
This is remarkably thorough! But it's missing one very common case: lowercase a vs. u (or v). If you're trying to make your handwriting more legible, don't skip this case– figure out a way to be intentional about it because it's so common. :)
Here's mine:
My u's have the little curved tail to distinguish them clearly from v's. And then, to further differentiate a vs. u, I deviate from the norms for fonts and make my handwritten lowercase a look like a half-height uppercase a with a curved top.
Honestly I only really use about 1/4 of the tips in this cheat sheet. But, the a vs. u trick is where I actually make the most impact by being intentional about my handwritten 'font' (with l/i vs 1, t vs. +, and x vs. × being the runner ups).
And the main reason I don't use the 'a' that fonts like this HN font use is that can look a lot like a 2 with the loop when drawn quickly (and I draw my 2's with loops so that they don't look like uncrossed z's or equal signs with an 'I failed to pick up my pen completely ' diagonal) ;-P
layer8
> Put a hook on the x to distinguish it from a times sign
This is counterproductive IMO, because it makes it look like a chi. (The article notes the problem.) That seems more likely to cause issues than the possible ambiguity with the “times” symbol (“×”). If you need a multiplication symbol, use the middle dot (“·”) instead.