A maths book from a painter

One of my interests is the development of scientific publishing following the invention of moving type printing in the middle of the 15^th century. The first real maths book, that is excluding reckoning books which are textbooks for commercial arithmetic, to be printed and published in German was written by the artist Albrecht Dürer who was born 540 years ago on the 21^st May 1471.

Born in Nürnberg the son of a Hungarian goldsmith he originally started to learn this trade with his father but then apprenticed to the leading Nürnberger artist Martin Wolgemut. As a journey man painter and printmaker he made his first journey to Italy from 1494 to 1495 where he learnt much about the new Renaissance style of Italian art and in particular the then still relatively new method of linear perspective. Dürer became convinced that this mathematically based style of composition was the true core of art and returned to Italy from 1505 to 1507 specifically to learn more about this technique.

Dürer devoted his artistic life to the study of linear perspective and proportion and to developing the mathematical knowledge necessary to carry out this type of drawing. He was one of the people most responsible for introducing this technique into Northern Europe. Convinced that the secret of true beauty lies in the theory of mathematical proportions he devoted twenty years to writing his major thesis on the subject his Hierinn sind begriffen vier bücher von menschlicher Proportion (Four Books on Human Proportion) printed and published posthumously in Nürnberg in 1528. When this book was almost complete Dürer realised that the book was much too mathematically advanced for apprentice artists, its targeted readership, and so he compiled an elementary geometry textbook, his Underweysung der Messung mit dem Zirkel und Richtscheyt (Instruction in Measurement with Compass and Straightedge), which was printed and published in Nürnberg in advance of his magnum opus, to which it was supposed to provide an introduction, in 1525.

Underweysung der Messung mit dem Zirkel und Richtscheyt Title Page

As already mentioned this was the first maths book to be printed and published in German, all previous mathematical works having been printed in Latin. Although aimed at apprentices of art the book found a much wider audience and went on to become a scientific bestseller not only in Germany. It was translated into Latin and several major European languages and became a standard textbook throughout Europe for most of the next century. It was still actual at the beginning of the 17^th century as Kepler was writing his geometrical works and he criticises Dürer’s construction of the heptagon as only an approximation and not mathematically precise. One of Dürer’s illustrations from the book on how to construct linear perspective is thought to have inspired Kepler to his experimental solution of the pinhole problem in optics.

Dürer’s textbook also plays an important role in the history of typography. It is printed in a typeface especially created for the book by the Nürnberger writing master Johannes Neudörfer (1497 – 1563) brother in law of the printer publisher Johannes Petreius. The typeface is a fraktur script and although this was not the first fraktur typeface, all fraktur typefaces developed and used since then are derived from Neudörfer’s creation.

Sample page showing text typeface and constructions within a circle.

Several years ago the City of Nürnberg decided to relaunch itself on the world market as “Dürer City”. The local newspaper conducted a survey and asked the people on the street if they knew who Albrecht Dürer was. As usual with these things something like 70% of the good citizens of Nürnberg didn’t have the faintest idea of the identity of the city’s most famous son. I was not asked but if I had been I would have answered, “an important German Renaissance mathematician”, which would almost certainly have convinced the questioner that I was one of the clueless!

Illustrations taken from, Albrecht Dürer, Underweysung der Messung mit dem Zirkel und Richtscheyt: Faksimile-Neudruck der Ausgabe Nürnberg 1525 mit einer Einführung von Matthias Mende, 3. Aufl., Verlag Dr. Alfons Uhl, Nördlingen, 2000