
Tips for Mathematical Handwriting (2007) - bumbledraven
https://johnkerl.org/doc/ortho/ortho.html
======
c3534l
When I went back to school I had to take math again, which wasn't my best
subject in school. I was determined to figure out why I could understand the
material, yet consistently never quite did as well as I thought I should have
on tests. So I kept a journal of every mistake I made so I could categorize
them and understand them. Most of the mistakes were very specific handwriting
mistakes, but they were very particular to how I personally tended to write
things. By changing how I wrote a few numbers and letters, I eliminated all of
those mistakes. I didn't have to come up with an overly elaborate system that
puts way too much thought (and not enough evidence) like in the OP. It was
quite surprised that I tended to mistake 7s, qs and 9s (if the loop is too
small and there's another character written above it, you can misread some of
my more atrocious attempts at writing 9), or that I would fail to properly
coil the 6 and make it look like an overly spiraled 0. Meanwhile, I never once
mistook a 1 for a 7 and my solution to the letter O is just to never, ever use
them in math.

My advice is actually that mistake journal: it was the single best thing I
ever did for a math class. Figure out what mistakes are actually happening and
develop a system or habit to avoid that actual mistake.

~~~
_0ffh
>my solution to the letter O is just to never, ever use them in math

That seems reasonable. My solution was to slash my zeros, to the point that it
takes conscious effort not to.

~~~
pbhjpbhj
How do you visually differentiate nulls from zeroes? That's what stopped me
from slashing my zeroes, I've considered dotting them, but it's not relevant
for me anymore. I slash my 7s though, and form my 1 like that character, I
don't miss off the up-tick.

Primarily nowadays I'm writing on a tablet and need to be very precise to make
it readable.

~~~
_0ffh
>How do you visually differentiate nulls from zeroes?

My zero is a continuous line, starting top right and angling sharply left-down
after a ~360° oval. That nicely makes it writable in one fluid motion.

My null/empty set is a somewhat smaller circle and a separate slash starting
and ending visibly outside the circle.

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JadeNB
The response from a(nother) mathematician: don't worry too much about this
specific advice; it's one guy's convention, not dogma. But _do_ have very
definite conventions of your own to which you adhere carefully and faithfully,
whether they're this author's or anyone else's, or your own custom blend. As
the author mentions, too many undergraduates don't pay attention to
distinctions among similar-but-different symbols, but I've seen even
professional mathematicians who don't distinguish properly among, for example,
w, ϖ, and ω. (I even refereed a paper once whose author didn't distinguish
between o and 0 as subscripts!) Don't be one of them!

~~~
exmadscientist
This, exactly.

One other consideration is to pay attention to your colleagues. Sometimes more
specific fields have conventions, and it's probably a good idea to follow
them. For example, physicists universally* write a cursive v, not the shape
preferred by the article author. You should do that too, if you want to
communicate with physicists.

(*At least in my experience as a US almost-PhD in physics. And yes, it does
help if you have to, say, calculate the velocity of a neutrino beam....)

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supernova87a
I'm of mixed feelings about all the Greek letters used in physics, math, etc.
Eventually (after years of hard learning how to understand the underlying
equations physically) I got over the hurdle of them always instantly making
any equation more complicated and hard to understand -- and instead seeing
them as just constants that could be basically ignored for most of the
procedure (in many settings).

I do still feel though, that they are a legacy of when all these fancy old
Greek-reading scientists could flex their knowledge of unfamiliar symbols and
choose to make it hard for people who couldn't grasp it immediately. ("Now to
simplify the equation let's introduce the zeta function into this
expression!")

Lowercase Xi and Zeta were the worst. Never mind that they were the rarest and
always most complex (visually) of letters to be used -- but also always
horribly written by students/teachers, and made it even more incomprehensible.

I have similar feelings about the bra/ket notations in QM.

~~~
filmor
I don't get the issue. It's just notation. You could "feel" the same way about
the integral sign or fractions or about underused letters in your own
alphabet.

When the greek letters are used, they usually give you a clear indication that
they are "something different" from the things written. It's much either to
understand that alpha, beta, gamma, delta are some counterpart to a, b, c, d
than if you had to use i, j, k, l (for example).

Lowercase Xi is indeed always written horribly (like a tornado), but at least
in my studies, everyone wrote it equally horribly and all in the same way.

~~~
kmill
For my first encounter with lowercase xi, I was sure the professor was taking
advantage of his tenure and trying to pass off a scribble as a variable, and
that was _with_ my having made a point to familiarize myself with the Greek
alphabet the previous semester. Somehow I don't remember him bothering to
pronounce it!

Then there are the German algebraists who developed ring theory, for whom
Greek letters were not sufficient -- they reached for their Fraktur. The
correspondences for certain letters -- like A and S -- can be inscrutable to
neophytes.

While I get why notation shouldn't matter, I do find it to be more tiring to
read new notation where I don't already have an internal pronunciation.

~~~
jks
Apparently set theorists weren't satisfied with Greek, Fraktur or blackboard
bold, so they use (at least) aleph and beth from Hebrew.

~~~
sidpatil
I wish we used more Cyrillic characters in math, just to keep things varied.

------
rahimnathwani
I wish we'd been taught this in high school.

One habit I _did_ learn in high school is writing x as two 'c' shapes in a
mirror image. This is clearly an x rather than a multiplication symbol. I
prefer it to the version listed in the article.

I find it hard to distinguish the author's X/χ

~~~
jackpirate
X written as )( is the absolute worst. It always looks like two parenthesis
when I'm grading student writing and I have no idea how to parse what they
write.

~~~
jhanschoo
In high school my teacher preferred that to distinguish it from the
multiplication symbol. These days I write it as a times with a hook at the
top-left to distinguish (a la most cursive styles, but disjointed), with the
added bonus that I write uvwxyz all with the same top-left hook that helps
visually group them together, matching their typical role in mathematical
writing.

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aesthesia
It’s not entirely true that context can’t help disambiguate mathematical
notation. The situations in which it’s common to use a lowercase omega are
quite distinct from those where it’s common to use a lowercase w. Even if both
appear in the same formula, they will tend to have very different roles. Good
notational choices also try to avoid these ambiguities. You probably shouldn’t
use v and nu at the same time, even in typeset math.

------
phorkyas82
Reminds me of my first analysis professor. He managed to explain the proofs
while writing them with chalk on the blackboard, all equations nice an clean
like the Latex in our scripts - while we struggled to keep up with his pace,
was impossible for us to copy it all. He came across a bit dry,
overstructured, exact, but also kind and humble - maybe like you imagine a
German mathematician.

~~~
lonelappde
Don't waste time in lecture taking notes. Pay attention and think.

Save your rote copying for homework time.

~~~
FreeFull
Often people take notes because it actually helps memorise and pay attention
what's being said, without any intention to read the notes at all afterwards.

~~~
nachexnachex
I'm like this, and many I know. I suspect the actual memorising comes when
writing, creating the muscle memory. If not written, I can't ensure I'll
remember.

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xzcvczx
"Put a loop on the q, to avoid confusion with 9"

yet the given example looks like a (badly drawn) 8 to me

~~~
mkl
Yes, a tick up and right at the bottom of the q's tail is clearer.

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anonytrary
Loop your l's, and cross your sevens and your z's to avoid confusing them with
ones and twos. Exaggerate the differences between your i's and your j's by
looping your j's. Curve the base of your t's to avoid confusing them with f's.
Math is a lot harder to do when you cannot distinguish your variables from
each other and numbers.

~~~
h-cobordism
And also make sure to distinguish between your pi's and your n's! I can't
count the number of times I've mixed the two up while finding Fourier
coefficients.

~~~
anonytrary
This is why I exaggerate the pi's top cross (like a capital T with two legs).
A lot of people write pi in a way such that the top cross has no dangling
edges[0]. I always try to exaggerate the unique features of symbols. One can
avoid a lot of these problems by first exhausting the least overlapping
symbols.

[0] See left variant:
[https://pm1.narvii.com/6331/cb50e106b141735ad714b934eb18ea55...](https://pm1.narvii.com/6331/cb50e106b141735ad714b934eb18ea55b8d6b66d_hq.jpg)

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mynegation
"Put a loop on the capital O so it doesn’t look like a zero"

I do no put loops on O's, but to this day I have a habit of writing a stroke
(in forward slash direction) inside zero.

~~~
coopsmgoops
But now it looks like a Theta!

~~~
mynegation
My printed or cursive thetas have horizontal or tilde like bar in the middle.

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analog31
The most maddening for me was using letter pairs such as u and v, or zeta and
xi, that are just handwriting death traps. No matter how good you are, you're
going to screw up once, and kiss your derivation goodbye.

Plus, as good an idea as it sounds, telling my hands to make the same letter
the same way twice is hopeless.

------
bluenose69
In my teaching, I tend to write a lot of Greek letters on the board. Students
from physics and mathematics are comfortable with this and can make out my
squiggles easily. To make things easier for students coming from biology, I
write out the names of the symbols, the first few times I use them. This helps
a lot, because they are not just unfamiliar with the symbols, but also the
words I use when I talk about them.

Another thing I do is to pronounce symbols in both the Greek and the American
ways. That helps them in other classes, because where I teach, the professors
are about evenly divided in their pronunciation.

PS. my squiggles are basically identical to those in the article under
discussion here.

------
djcjr
_Don 't_ loop the 2 or you'll have the problem with alpha, as they show a few
lines later.

Crossing the Z resolves the need to loop the 2.

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bmn__
I can tell the design is ad-hoc. There is a science to manual writing, the
author appears to be unaware of it (I guess by virtue of being born into an
English speaking nation which afaict never saw fit to follow other ones who
had already developed relevant standards in the 1960s). I see a couple
improvements so that the proposal falls more in line with those standards:

1 should have an upstroke.

0 should have a loop, dot or stroke, not O.

q descender should have a stroke, not a loop.

9 should have a round bottom.

g descender should have a loop.

Latin letters should be written in script form, not block letter form,
notably: ℰ, 𝒢, ℐ, 𝒥, ℒ, 𝒴, not E, G, I, J, L, Y.

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yanestra
I guess the tip with the "hooked x" is not so perfect because the result can
be confused with a chi (which is in fact rather a hooked x than a slashed wave
like in the article).

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cik2e
I was a math major and started doing all of this very quickly because I
couldn’t read my own work. I would put this in the realm of common sense.

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Xophmeister
My cursive “x” looks quite similar to my cursive “n”. In my Real and Abstract
Analysis exam, IIRC, I remember writing a limit expression, as n goes to
infinity, that involved no “x” variable. The professor read it as an “x”,
despite the context, and promptly marked it incorrect. It taught me to make my
handwriting unambiguous, but I’m still bitter about this, some 15+ years later
:P

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huffmsa
My biggest gripe in school and now isn't legibility, but wondering if the
professor / author is using his Greek letters as some magic, universal
constants or just throwing them in as variables because it's "convention".
Spend more time hunting down context and the "With {} as {}" section than
understanding the equation.

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amelius
> Put a loop on the q, to avoid confusion with 9

I already put a loop on g. I put a little "serif" bar on the stem of the q.

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throwawaysea
Do we need everyone to memorize these guidelines or do we need an alphabet
that is designed to be naturally distinguishable despite stylistic
differences? I feel like with cursive and handwriting focus going out of
style, it isn’t practical to expect convention to be followed more strictly
than it already is(n’t).

~~~
adiabatty
Since my penmanship isn't all that great, I use quite a few of these
guidelines when I'm writing out math problems. At any rate, you can ignore a
lot of them if, like most people, all you need is A-Za-z0-9πθ+.

------
daffy
The lowercase zeta isn't right, and the lowercase chi looks just like the xes.

------
dan-robertson
I have somewhat strong opinions on this. I uploaded a similar set of symbols
here: [https://imgur.com/a/gKJ3KO2](https://imgur.com/a/gKJ3KO2)

I’ve added notes in red, some baselines in blue and some lines at x-height in
yellow.

I want to point out a few things:

1\. OP misses out the need for script and blackboard bold letters and various
symbols. You want them to not be confused with letters. In particular U and
set union, epsilon and set membership, and oplus and capital theta.

I think OP’s eta looks wrong. Too much like an m.

One trick to use is that letters can have ascenders and descenders. Numbers
can too but I don’t use that. I also incorrectly write a rho as a letter with
an ascender and no descender to help to distinguish it from a p. I also try to
impart a big curve at the top so you won’t think there could be the top of a
straight line hidden in there.

I draw the top of a tau just below x-height while the bar on a t is somewhat
above it. This and the rest of the t being higher helps to disambiguate.

Never use an o (“oh”) or omicron and probably not upsilon either (I missed out
capital upsilon because OP did too and I didn’t notice). An exception is
big/little O notation but I don’t really like it.

I don’t like OP’s q. It looks too much like a double bowled g. I prefer a tick
to a loop.

I tend to not have issues with 2 vs z but I do with nu vs v. I kinda dislike
using nu because of it. In print I have trouble with v vs u.

I often use variant letters for some Greek letters (in particular my epsilon
is what TEX calls varepsilon because it is more like handwriting and less like
a print font. Similarly for theta kappa, and phi. I don’t use varpi which
looks too much like an omega, cardigan which is only really to go on the end
of a word in Greek, varrho because I don’t like it, and I don’t write capital
omega the modern Greek way (a horizontal line with a circle above it).

Other tricky symbols are: Angle brackets vs lt/gr. Usually context suffices.
Angle brackets vs parens: just don’t rely on this distinction.

Or vs v can and union vs U can usually be solved by context and spacing (you
have a bigger space between a term and an operator than between factors or
arguments in a term)

A final note is that I tend to write mathematics more upright than my normal
handwriting. This helps distinguish inline mathematics from the rest of a
sentence.

I looked through some random old notes to see if I could still read my writing
and I can. The only thing I struggled with was the script C for conjugate
classes because I was missing the context and struggling to guess what ccl
stood for. At first I thought it was a script G.

Having written this, I realise I omitted forall, exists, nabla/del, integral
sign, partial sign, therefore dots, infinity, approxequal and hbar.

A final note is that spoken names matter to o. “Twiddle” is a much better name
than “tilde” because it is more naturally made into a verb. You can say
“define the relation twiddle on the naturals such that a twiddles b if ...”
and then you can easily use that verb when talking through a proof of eg
transitivity.

