From boiling lead and black art: An essay on the history of mathematical typography

Math fonts from six different type systems, courtesy Chalkdust

I’ve always felt like constructing printed math was much more of an art form than regular typesetting. Someone typesetting mathematics is less a “typist” and more an artist attempting to render abstract data on a two-dimensional surface. Mathematical symbols are themselves a language, but they are fundamentally a visual representation of human-conceived knowledge—knowledge that would be too inefficient to convey through verbal explanations. This brings the typesetting of mathematics closer to a form of data visualization than regular printed text.

No matter how hard it’s ever been to create printed text, creating printed math has always been even harder. In pre-digital times, equation-laden texts were known as “penalty copy” because of the significant additional time and expense it took to set math notation for printing presses.

Even when modern word processors like Microsoft Word include equation editors, they tend to be difficult to use and often produce unpleasing results. While LaTeX and similar variants produce the highest quality digital math type, these frameworks also have much more of a learning barrier than general word processing.

But these modern quibbles are much more the fault of hedonic adaption than any of the tools available to us today. We have it vastly easier than any previous stage of civilization, and I think it’s critically important for those of us that write math to have at least a basic awareness of the history of mathematical typesetting.

For me, knowing this history has had several practical benefits. It’s made me more grateful for the writing tools I have today—tools that I can use to simplify and improve the presentation of quantitative concepts to other actuaries. It’s also motivated me to continue to strive for elegance in the presentation of math—something I feel like my profession has largely neglected in the Microsoft Office era of the last twenty years.

Most importantly, it’s reminded me just how much of an art the presentation of all language has always been. Because pre-Internet printing required so many steps, so many different people, so much physical craftsmanship, and so much waiting, there were more artistic layers between the author’s original thoughts and the final arrangement of letters and figures on pages. More thinking occurred throughout the entire process.

To fully appreciate mathematical typography, we have to first appreciate the general history of typography, which is also a history of human civilization. No other art form has impacted our lives more than type.

The first two Internets

While the full history of printing dates back many more centuries, few would disagree that Johannes Gutenberg’s 15th-century printing press was the big bang moment for literacy. It was just as much of an Internet-like moment as the invention of the telegraph or the Internet itself.

Before Gutenberg, reading was the realm of elites and scholars. After Gutenberg, book production exploded, and reading became exponentially more practical to the masses. Literacy rates soared. Reformations happened.

The Gutenberg Printing Press

I would argue that the invention of the printing press was on par with the evolutionary “invention” of human language itself. In The Origins of Political Order, Francis Fukuyama explains that spoken language catalyzed the separation of humans from lower forms of primates:

The development of language not only permits the short-term coordination of action but also opens up the possibility of abstraction and theory, critical cognitive faculties that are unique to human beings. Words can refer to concrete objects as well as to abstract classes of objects (dogs, trees) and to abstractions that refer to invisible forces (Zeus, gravity).

Language also permits practical survival advantages for families and social groups:

By not stepping on the snake or eating the root that killed your cousin last week, you avoid being subject to the same fate, and you can quickly communicate that rule to your offspring.

Oral communication became not only a survival skill, but a tool of incredible influence. Rhetoric and the art of persuasion were highly valued in Greek and Roman societies.

If spoken language was the first human “Internet,” mass printing was the next key milestone in the democratization of human knowledge. Mass production of printed material amplified the human voice by incalculable orders of magnitude beyond oral communication.

Of boiling lead and black art

Like all inventors, Johannes Gutenberg didn’t really make anything new so much as he combined existing materials and technologies in new ways. Gutenberg didn’t invent printing. He didn’t invent the press. He didn’t even invent movable type, which typically involves arranging (typesetting) casts of individual letters that can be brushed or dipped...