There can’t be many Renaissance mathematici, whose existence was ennobled by a personal portrait by the master of the Renaissance portraits, Hans Holbein the younger. In fact, I only know of one, the German mathematicus, Nicolas Kratzer.
One might be excused for thinking that having received this singular honour that Kratzer had, in his lifetime, achieved something truly spectacular in the world of the Renaissance mathematical disciplines; however, almost the opposite is true. Kratzer appears to have produced nothing of any significance, was merely the designer and maker of sundials, and an elementary maths teacher, who was only portrayed by Holbein, because for a time they shared the same employers and were apparently mates.
So, who was Kratzer and how did he and Holbein become mates? Here we find a common problem with minor scientific figures in the Renaissance, there are no biographies, no handy archives giving extensive details of his life. All we have are a few, often vague, sometimes contradictory, traces in the proverbial sands of time from which historians have attempted to reconstruct at least a bare outline of his existence.
Kratzer was born in 1487 in Munich, the son of a saw-smith and it is probably that he learnt his metal working skills, as an instrument maker, from his father. He matriculated at the University of Köln 18 November 1506 and graduated BA 14 June 1509. He moved onto the University of Wittenberg, famous as the university of Martin Luther. However, this was before the Reformation and Wittenberg, a young university first founded in 1502, was then still Catholic. We now lose track of Kratzer, who is presumed to have then worked as an instrument maker. Sometime in the next years, probably in 1517, he copied some astronomical manuscripts at the Carthusian monastery of Maurbach, near Vienna.
In January 1517, Pieter Gillis (1486–1533) wrote to his erstwhile teacher Erasmus (1466–1536) that the skilled mathematician Kratzer was on his way with astrolabes and spheres, and a Greek book.
This firmly places Kratzer in the circle of humanist scholars, most famously Erasmus and Thomas More (1478–1535) author of Utopia, who founded the English Renaissance on the court of Henry VIII (1491–1547). Holbein was also a member of this circle. Erasmus and Holbein had earlier both worked for the printer/publisher collective of Petri-Froben-Amerbach in Basel. Erasmus as a copyeditor and Holbein as an illustrator. Holbein produced the illustrations for Erasmus’ In Praise of Folly (written 1509, published by Froben 1511)
Kratzer entered England either at the end of 1517 or the beginning of 1518. His first identifiable employment was in the household of Thomas More as maths teacher for a tutorial group that included More’s children. It can be assumed that it was here that he got to know Holbein, who was also employed by More.
For his portraits, Holbein produced very accurate complete sketches on paper first, which he then transferred geometrically to his prepared wooden panels to paint them. Around 1527, Holbein painted a group portrait of the More family that is no longer extant, but the sketch is. The figures in the sketch are identified in writing and the handwriting has been identified as Kratzer’s.
Like Holbein, Kratzer moved from More’s household to the court of Henry VIII, where he listed in the court accounts as the king’s astronomer with an income of £5 a quarter in 1529 and 1531. It is not very clear when he entered the King’s service but in 1520 Cuthbert Tunstall (1474–1559), later Prince-Bishop of Durham, wrote in a letter:
Met at Antwerp with [Nicolas Kratzer], an Almayn [German], devisor of the King’s horologes, who said the King had given him leave to be absent for a time.
Both Tunstall and Kratzer were probably in Antwerp for the coronation of Charles V (1500–1558) as King of Germany, which took place in Aachen. There are hints that Kratzer was there to negotiate with members of the German court on Henry’s behalf. Albrecht Dürer (1471–1528) was also in the Netherlands; he was hoping that Charles would continue the pension granted to him by Maximilian I, who had died in 1519. Dürer and Kratzer met in the house of Erasmus and Kratzer was present as Dürer sketched a portrait of Erasmus. He also drew a silver point portrait of Kratzer, which no longer exists.
Back in England Kratzer spent some time lecturing on mathematical topics at Oxford University during the 1520s. Here once again the reports are confused and contradictory. Some sources say he was there at the behest of the King, others that he was there in the service of Cardinal Wolsey. There are later claims that Kratzer was appointed a fellow of Corpus Christi College, but the college records do not confirm this. However, it is from the Oxford records that we know of Kratzer’s studies in Köln and Wittenberg, as he was incepted in Oxford as BA and MA, on the strength of his qualifications from the German institutions, in the spring of 1523.
During his time in Oxford, he is known to have erected two standing sundials in the college grounds, one of which bore an anti-Lutheran inscription.
Neither dial exists any longer and the only dial of his still there is a portable brass dial in the Oxford History of Science Museum, which is engraved with a cardinal’s hat on both side, which suggests it was made for Wolsey.
On 24 October 1524 Kratzer wrote the following to Dürer in Nürnberg
Dear Master Albert, I pray you to draw for me a model of the instrument that you saw at Herr Pirckheimer’s by which distances can be measured, and of which you spoke to me at Andarf [Antwerp], or that you will ask Herr Pirckheimer to send me a description of the said instrument… Also I desire to know what you ask for copies of all your prints, and if there is anything new at Nuremberg in my craft. I hear that our Hans, the astronomer, is dead. I wish you to write and tell me what he has left behind him, and about Stabius, what has become of his instruments and his blocks. Greet in my name Herr Pirckheimer. I hope shortly to make a map of England which is a great country, and was not known to Ptolemy; Herr Pirckheimer will be glad to see it. All who have written of it hitherto have only seen a small part of England, no more… I beg of you to send me the likeness of Stabius, fashioned to represent St. Kolman, and cut in wood…
Herr Pirckheimer is Willibald Pirckheimer (1470–1530), who was a lawyer, soldier, politician, and Renaissance humanist, who produced a new translation of Ptolemaeus’ Geographia from Greek into Latin.
He was Dürer’s life-long friend, (they were born in the same house), patron and probably lover. He was at the centre of the so-called Pirckheimer circle, a group of mostly mathematical humanists that included “Hans the astronomer, who was Johannes Werner (1468–1522), mathematician, astronomer, astrologer, geographer,
and cartographer and Johannes “Stabius” (c.1468–1522) mathematician, astronomer, astrologer, and cartographer.
Werner was almost certainly Dürer’s maths teacher and Stabius worked together with Dürer on various projects including his star maps. The two are perhaps best known for the Werner-Stabius heart shaped map projection.
Dürer replied to Kratzer 5 December 1524 saying that Pirckheimer was having the required instrument made for Kratzer and that the papers and instruments of Werner and Stabius had been dispersed.
Here it should be noted that Dürer, in his maths book, Underweysung der Messung mit dem Zirkel und Richtscheyt (Instruction in Measurement with Compass and Straightedge), published the first printed instructions in German on how to construct and orientate sundials. The drawing of one sundial in the book bears a very strong resemblance to the polyhedral sundial that Kratzer made for Cardinal Wolsey and presumably Kratzer was the original source of this illustration.
Kratzer is certainly the source of the mathematical instruments displayed on the top shelf of Holbein’s most famous painting the Ambassadors, as several of them are also to be seen in Holbein’s portrait of Kratzer.
Renaissance Mathematicus friend and guest blogger, Karl Galle, recently made me aware of a possible/probable indirect connection between Kratzer and Nicolas Copernicus (1473–1543). Georg Joachim Rheticus (1514–1574) relates that Copernicus’ best friend Tiedemann Giese (1480–1550) possessed his own astronomical instruments including a portable sundial sent to him from England. This was almost certainly sent to him by his brother Georg Giese (1497–1562) a prominent Hanseatic merchant trader, who lived in the Steelyard, the Hansa League depot in London, during the 1520s and 30s.
He was one of a number of Hanseatic merchants, whose portraits were painted by Holbein, so it is more than likely that the sundial was one made by Kratzer.
Sometime after 1530, Kratzer fades into the background with only occasional references to his activities. After 1550, even these ceased, so it is assumed that he had died around this time. In the first half of the sixteenth century England lagged behind mainland Europe in the mathematical disciplines including instrument making, so it is a natural assumption that Kratzer with his continental knowledge was a welcome guest in the Renaissance humanist circles of the English court, as was his younger contemporary, the Flemish engraver and instrument maker, Thomas Gemini (1510–1562). Lacking homegrown skilled instrument makers, the English welcomed foreign talent and Kratzer was one who benefited from this.
The Renaissance Mathematicus 