This is a work-in-progress English translation of Hermann Hankel's 1867 Vorlesungen über die complexen Zahlen und ihre Functionen, I. Theil: Theorie der Complexen Zahlensysteme ("Lectures on complex numbers and their functions, Part I: Theory of Complex Number Systems"), a textbook on complex analysis that played an important role in the transition to modern mathematics in nineteenth century Germany.

You can view the translation in its present state here.

The original text, with sometimes-workable OCR, is available from the Internet Archive.

Hankel's book is not very well known today, even among philosophers and historians of mathematics, but it was an important work in its time. For example, in Frege's Grundlagen der Arithmetik ("Foundations of arithmetic"), which is widely read among anglophone philosophers today, Hankel is Frege's most frequently cited interlocutor. Frege scholarship could learn a lot from Hankel, but because Hankel's text is difficult and hasn't been translated, it hasn't received much attention. By making this translation available, I am hoping to make the work more accessible to an English-speaking audience (and their search engines and browsers).

I am also using the project to experiment with the possibilities of publishing a translation in a "hypertext-first" format: linking to works Hankel cites, representing his formulas in MathML, showing the original phrase for certain translations in mouse-over text, and so on. Because digital texts are hard to cite by traditional means (e.g. with page numbers), I am also taking care to encode the features of the original text in the markup. See MARKUP.md for more information about how these features are represented.

At the moment, it is not my goal to translate the whole book, which is mostly just a mathematics textbook that is by now outdated. Its interest lies mainly in its historical importance and in the philosophical approach to the foundations of mathematics which Hankel sets out in the initial chapters of the book. The translation is focused on these initial chapters.

Comments, corrections, and contributions of any kind are welcome! There are plenty of ways to help, even if you don't read German. You can:

• continue transcribing and marking up the German text
• proof read the English translation and report any errors or inconsistencies
• improve the markup and CSS

If you do read German, you can also:

• proof read the German transcription
• suggest improvements to existing translations
• contribute new translations, or suggest that passages be translated

Open an issue, make a pull request, or simply send me an email (rwl followed by the usual commercial accounting symbol and recursewithless.net).

This work by Richard Lawrence is licensed under CC BY-SA 4.0

This research was funded in part by the Austrian Science Fund grant ESP 211-G, as part of the project "Frege among the Formalists".