Three typefaces for mathematics (2007) [pdf] | Hacker News Reader

Three typefaces for mathematics (2007) [pdf]

ultrasparky.org

149 pointsjstrieb48 comments

In my opinion, the Monotype caster with a competent operator, the Modern Series 7 typeface, and the 4-line system produced mathematical typesetting not yet surpassed. There is no contemporary system for typesetting mathematics that can produce such beautiful compositions as the Monotype did.

TeX is phenomenal. And Computer Modern was a Herculean effort by Knuth, but in my opinion, it’s wholly lacking in many departments. It’s spindly, clinical, and vapid. But I don’t blame Knuth; we just need a serious typographer to learn METAFONT and make a beautiful typeface for mathematics that is not gimmicky.

Your criticism of Computer Modern as "spindly" makes sense only digitally, not in print (or, at least, print of the era Computer Modern was designed for).

Optimized for printers of a different era (and relying heavily on ink bleed), Computer Modern's default configuration looks less than great on today's printed page. However, if you make some small adjustments (as METAFONT was designed to do), it suddenly becomes rather pleasant. Here's a page with an example of how it looked initially compared to how it looks on modern printers, and a modification of the METAFONT parameters that looks pleasant on screens:

https://www.typografie.info/3/topic/22238-ist-die-computer-m...

Most modern digital adaptions are done poorly, and without considering this.

METAFONT is really simple, and more people should consider playing around with it. It's really fantastic.

This is not usually noticeable, because TeX distributions now use a Type 1 version of CM, distributed by AMS, when compiling documents to PostScript or PDF. (Or, they use Latin Modern, which is based on this Type 1 version which is so spindly in the first place.)

To use an adaptation which is thicker in print, and which uses the original METAFONT settings, check out mpfonts: https://ctan.org/pkg/mpfonts.

However, note that on screen, mpfonts usually doesn't look so great, since the fonts are Type 3 adaptations of the METAFONT programs and not Type 1 fonts.

It would be nice to have a PDF filter to imitate ink bleed.

> we just need a serious typographer

Well, that is why Hermann Zapf was commissioned to design AMS Euler. Knuth supplied the METAFONT and critiqued it in iterations by trying it out.

I’ll be honest. I consider AMS Euler to be a gimmick. Yes, real books by serious mathematicians have used it, but it’s so non-traditional that it has not been broadly accepted. (Zapf is a real typographer of course. But the project, to me, is more of an exercise in avant garde typography than one to supplant “standard” mathematical type.)

I think that depends on whether you want your stuff to look like some definition of traditional.

The equations in AMS Euler look good to me. [1]

[1] https://en.wikipedia.org/wiki/AMS_Euler#/media/File:AMS_Eule...

They look terrible, in fact. This is no way to typeset equations. (For example, variables should be set in italics.)

Variables have their own style here. Compare i sin y and the difference between the variable i and the i in sin.

Yes AMS Euler is very nontraditional as mathematical typesetting goes — to put it in terms of Zapf's oeuvre, it's not Palatino or Optima but rather Zapfino. :-) Looking at what was written/expected before it was created, it can probably be seen as somewhat of a disappointment.

But it was created to mimic the style of mathematicians writing by hand on a blackboard, and I must say that in the book Concrete Mathematics (reading which was, in retrospect, one of the highlights of my life) it works very well, going well with the book's conversational style, the irreverent margin graffiti by students, etc.

I used Palatino for my thesis. The only downside is that the typefacing of mathematics is less standardised than Computer Modern. You have to play around with things in that regard.

Edit: I think AMS Euler for the equations and Palatino for text is not a bad idea.

What is your opinion of Concrete Roman? [0]

>Concrete Roman is a slab serif typeface designed by Donald Knuth using his METAFONT program. It was intended to accompany the Euler mathematical font which it partners in Knuth's book Concrete Mathematics. It has a darker appearance than its more famous sibling, Computer Modern. Some favour it for use on the computer screen because of this, as the thinner strokes of Computer Modern can make it hard to read at low resolutions.

I have the referenced book Concrete Mathematics by Graham, Knuth and Patashnik. To my uninformed eye it looks pleasing.

[0] https://en.wikipedia.org/wiki/Concrete_Roman

Concrete, AMS Euler, and Computer Modern are all perfectly legible. Concrete suffers from being incomplete in terms of headings, lack of sans-serif, and not having a complete matching mathematical typeface. (The math in Concrete, especially with integrals and sums, looks awful.)

It is still leagues behind Modern Series 7, though.

> Computer Modern was a Herculean effort by Knuth, but in my opinion, it’s wholly lacking in many departments. It’s spindly, clinical, and vapid.

I strongly agree, I hate how Computer Modern looks, especially because of what you describe as being "spindly" - it's exceptionally light. If you use any other font for body text then the contrast is overwhelming, when the maths and text ought to just flow together. You can use it for body text too but then the whole page looks a mess.

> ... make a beautiful typeface for mathematics that is not gimmicky.

My favourite text/maths combinations:

* Palatino for text and Pazo [1] for maths. I am a big fan of Palatino, and Pazo is derived from it - I'm not sure what the exact relationship is but to me they look like basically the same font. For me, this is the direct answer to your question of a "beautiful typeface for mathematics". Perhaps not every symbol in the TeX package was hand-designed for the font, but I haven't noticed any real clash. The only problem is that it's such a radical departure from traditional TeX fonts that it might be a bit ubrupt for some people. My PhD supervisor certainly didn't like me using it (he thought I had used totally different typesetting software and told me to "just use TeX like everybody else").

    \usepackage[slantedGreek]{mathpazo}
    \usepackage{upgreek} % Euler upright Greek; matches Palatino quite well

* This is a very unfashionable opinion but I actually think Times is a very readable font and works well with mathematics. I used the times [4] package (although I note it now says you should load the font a different way) with the commercial but very affordable mtpro2 [5]

* I often used Utopia for both text and maths [3]. This is more of a compromise as it looks a tiny bit like Computer Modern (to its discredit) but is more like more conventional fonts and definitely doesn't have CM's weight problem. It's actually somewhat similar to Microsoft's Cambria and Cambria Math.

    \usepackage[utopia,greekuppercase=italicized]{mathdesign} % for math
    \usepackage{esint} % make integrals look less silly
    \newcommand{\mathbold}[1]{\boldsymbol{#1}}

* I found people (maybe just my supervisor!) still had a problem with using Utopia as the text font so I settled on the super-compromise of Times text with Utopia math for my thesis; I'd have prefered the fonts to be identical but these go fairly well and certainly their weights don't clash (unlike CM with anything else).

* For presentations I think it's best to use a san-serif font. The most complete combination I've been able to find is CM Bright for text/math [6] and esstixbb for blackboard bold (with beramono for fixed-width)

    \usepackage[slantedGreek]{cmbright}
    \usepackage{esstixbb}
    \usepackage[scaled]{beramono}

[1] https://ctan.org/tex-archive/fonts/mathpazo?lang=en

[2] https://ctan.org/pkg/upgreek?lang=en

[3] https://tug.org/FontCatalogue/utopia-mathdesign/

[4] https://ctan.org/pkg/times?lang=en

[5] https://www.pctex.com/mtpro2.html

[6] https://tug.org/FontCatalogue/computermodernbright/

Was Modern Series 7 compatible with the 4-line system? The thesis seems to imply the 4-line system and Times New Roman Series 569 were linked.

(page 13 compares hand-set Series 7 with 4-line set Series 569).

That is a great question, and I might be misremembering that detail.

The 4th paragraph on the 29th page names the students involved with the Euler effort in alphabetical order, giving the incorrect impression that I made a significant contribution. All credit goes to the others listed.

What are some good sans-serif math fonts? I'm aware of sansmathfonts [1] and FiraMath [2]. I'm particularly looking for a font like Open Sans or Roboto. FiraMath is close.

[1] https://tug.org/FontCatalogue/sansmathfonts/

[2] https://github.com/firamath/firamath

Edit: Many more listed here but you need to filter out the serif fonts: https://tug.org/FontCatalogue/mathfonts.html

I've always really liked Rhatigan's (that is, the author of the linked piece) Gina typeface:

http://www.ultrasparky.org/work/typefaces/gina/gina_01.html

I read something about it evolving into an internally developed project somewhere but never saw it again. I really wish it were released publicly.

The LaTeX world is sorely missing a font that looks as good as the Springer Baskerville of legendary Bourbaki and IHES fame. No, the "baskervald" package is not up to par (just look at the ugly accent in the é character!).

I've been guilty of using Baskervald myself. But I agree that's it's not a very good variant of Baskerville (which I like a lot).

Do you happen to know what macOS's "Baskerville" font is exactly? That one looks much better than Baskervald.

Baskervald is not that bad, I use it almost exclusively and I am quite fond of it. Yet, it lacks the liveliness of classic Baskerville. I do not know exactly what it is the difference; but in the french accents it is very obvious.

No idea about your macos question.

The example of the classic 4-line math typesetting at the top of page 4 is the best you will ever see. Anything else would serve nothing but to distract and annoy the reader (not to say anything about the writer who now has less time to think about math proper.)

A tangent, but what about typesetting and typefaces for music sheets - anything like TeX for written music?

Totally different needs than mathematical notation, but seems to share common issues, like specialized symbols, placements and spacings.

I think Lilypond <https://lilypond.org/> is the TeX for music engraving.

For typesetting short snippets of music notation within TeX, you can use the MusixTeX package <https://ctan.org/pkg/musixtex>.

Thank you, those are exactly the kinds of music typesetting/engraving software (and notation syntax) I was curious about.

Following a few links, I found a great overview:

MusiXTEX - Using TEX to write polyphonic instrumental music

http://icking-music-archive.org/software/musixtex/musixdoc.p... (pdf)

For Lilypond, here's an introduction that demonstrates how to "write music by typing text":

Lilypond: "Compiling" Music

https://lilypond.org/text-input.html

Philip Hazel (author and maintainer of the Exim mailer) has written a memoir where is discusses writing a program for typesetting music.

It's well worth reading for that and other fascinating stuff: [pdf link](https://drive.google.com/file/d/10TAOEgIL--CmzqOl0fkdP-cagjS...).

Oh wow, what a fun read!

I started with the section on Music Typesetting, good stuff: Oxford Music Processor, his Philip's Music Writer, the language syntax to encode notation information.. This is right up my alley, thank you for the link.

So much of it is relevant to our current time, it's still not a solved problem and there's room for innovation.

I'll enjoy reading the rest of his memoir.

Out of idle curiosity, what’s the difference on page 5 between the two “x = a + 4” calculations?

The second one is "chi = alpha plus four." The general point he is trying to make here is that in a Greek word we would see the chi and alpha because of the context, but if you typeset an equation with letters intended for setting text there simply isn't enough distinction in the characters to prevent confusion because there isn't enough context to distinguish the "a" and the alpha. You need a mathematical typeface with characters that cannot be confused even though text set with those characters would look awful. In other words, a proper mathematical typeface requires more than just symbols.

I'm surprised there's no mention of eqn and troff.

Those are programs, not typefaces.

The author is talking about the difficulty of typesetting mathematics, and refers to TEX as an approach to solve this problem. eqn and troff preceded TEX. Heck, even Microsoft's and Open Office's approach to typing in equations are direct descendants of eqn.

I think the author is only interested in the box model that TeX uses insofar as it influenced the typeface design. He’s contrasting TeX’s “box and glue” setup with the rigid matrix design needed by Monotype faces, and the much more expressive non-box layout model used by Cambria.

Very true! Side note: I always admired the idea of eqn, loved reading about it from Kernighan and Cherry, but never saw it as powerful (or pretty) enough for serious use.

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