### TeX: A Boon for Mathematicians

Donald E Knuth, designer of the \TeX mathematical typesetting system.

Mathematicians owe a great debt of gratitude to Donald Knuth. A renowned American computer scientist and mathematician, Knuth is an emeritus professor at Stanford University. He is author of many books, including the multi-volume work, The Art of Computer Programming.

Knuth is the author of the powerful and versatile mathematical typesetting system called TeX. The original version, designed and written by Knuth, was released in 1978.

TeX is a powerful system for typesetting mathematical formulae. It is ideal both for simple mathematical notes with few formulas and for more complex documents and books involving subtle and sophisticated mathematical typography. TeX is used by almost all research mathematicians. It is also popular in computer science, engineering, physics, statistics, and and many other sciences.

The name TeX is pronounced “tech” like the first syllable of “technical”. The letters of TeX are the Greek letters tau, epsilon and chi, and TeX is an abbreviation of ${\tau\epsilon\chi\nu\eta}$, which means “art” or “craft”, and which is the origin of our word “technical”.

Some History

Knuth had two main goals in mind in designing TeX: to enable mathematicians to produce high-quality books — beautiful books — with ease, and to provide a program that would give results independent of the particular computer used. He also wanted the system to be unchanging over time to the greatest practicable extent.

Around 1977, Knuth received galley proofs of one of his many books. Finding the quality inferior, he determined to design a typesetting system that would enable writers “to produce beautiful books”. It was to be ten years or so before the TeX system was “frozen”, after which only essential changes, such as bug-fixes, could be made to the core program.

TeX is now very stable, and only minor updates are permitted. The current version of TeX is 3.14159265. Updates are indicated by adding an extra decimal digit. This is done so that the version number approaches ${\pi}$.

LaTeX: a de facto standard for writing maths

Almost nobody uses the raw TeX program any more. The most popular `wrapper’ system is LaTeX, originally developed by Leslie Lamport. This allows design at a higher level, and includes document styles for books, letters, slides and many more formats.

Many thousands of books have been prepared for publication using LaTeX. The leading publishers Addison-Wesley, Cambridge University Press, Elsevier, Oxford University Press and Springer use the system. The majority of mathematical journals are produced using LaTeX.

Authors prepare their documents in plain text files, including the LaTeX commands and using whatever editor they prefer. The .tex files they produce are in ASCII format and are normally quite small (at least compared to the dreadful binary files produced by many word-processing programs).

Simple Commands

TeX commands commonly start with a backslash and are grouped with curly braces. For example, the definition of the Gamma function may be written

\Gamma(\alpha) = \int_0^\infty \exp(-z) z^{\alpha-1}\,\mathrm{d}z \,.

When compiled in LaTeX, this produces the following (beautiful) output:

$\displaystyle \Gamma(\alpha) = \int_0^\infty \exp(-z) z^{\alpha-1}\,\mathrm{d}z \,.$

Thanks to the generosity of the designers, Knuth, Lamport and many others, TeX is free software. The source code is in the public domain, and is accessible to all mathematicians and others without any payment.

LaTeX is not as simple to learn as many other (inferior) typesetting systems, but it is well worth the effort. There are numerous websites and videos to help beginners. If you do not have the system installed, you can try an online version such as Overleaf, a cloud-based LaTeX editor at https://www.overleaf.com. Progress is rapid and, with a little effort, you may soon become a TeXpert.