A few months ago I wrote about some mystifying mathematical and geographic tiles I encountered at the National Tile Museum in Lisbon, Portugal.

Their accompanying label gave no clue to who had made them or why. Several readers subsequently wrote to tell me what they knew about these tiles. Thank you to everyone who did so! I will be sharing in particular the explanation provided to me by Carlota Simões from the Science Museum of the Coimbra University in Coimbra, Portugal, and also drawing on a paper about the tiles published just this year that she cited.

When the tiles were first brought to public attention in a newspaper in 1982, no one knew where they might have come from. The majority of surviving tiles -- 20 of 31 -- were located in a museum in Coimbra, suggesting that was their origin. In 2010, archaeologists excavating the former Jesuit college there discovered pieces of a few more, confirming this idea.

Meanwhile, scholars had pieced together the tiles' story, involving Jesuits; the Marquis of Pombal, the influential Portuguese secretary of state and de facto ruler of Portugal during the mid-18th century reign of King Joseph I; and political intrigue (of course). Pombal is most famously known for rebuilding Lisbon quickly and efficiently after the devastating 1755 earthquake and tsunami that shook both Portugal and the thinkers of Enlightenment Europe.

The story begins with the Jesuits, a Catholic religious order who have become known over the centuries for their work in education and science (among many, many other things). The current pope -- Francis -- is the first Jesuit to reach the Throne of St. Peter, and much was made of this at his election and of the fact that it had taken nearly 500 years for it to happen.

The Jesuits had established a college in the Portuguese city of Coimbra. In 1692, the society received an order from Tirso Gonzales, the General of their Society in Rome, to improve the teaching of mathematics. It regulated the number of hours for teaching mathematics, which topics to teach, what materials and instruments should be available, and specified that the textbook should be the Andre Tacquet version of the Elements of Euclid.

According to Simões, this order also specified that "a frame containing the main figures of [Tacquet's Elements] should be placed in a visible place". The Jesuits required their students to be able to learn and explain the propositions of the first six books of Euclid from memory, according to Henrique Leitão and Samuel Gessner, authors of a paper on the tiles published just this year in the journal Mathematische Semesterberichte. During class, students had to stand up and demonstrate their knowledge using a figure on a blackboard, and teaching involved lengthy and repetititve analyses of the figures. The hundreds of tiles would obviate the need to draw these figures again and again.

The Jesuits apparently took their orders seriously, and produced more than 200 tiles illustrating figures from the book. The display in the room of such amassed math must have been dazzling.

Though no one is certain what year they were manufactured, according to Leitão and Gessner, it was most likely the early to mid-18th century, around 1740 -- although that's nearly 50 years after the order was promulgated. The common blue and white tin-glazed earthenware used to make the tiles was standard for early-18th century Portuguese tiles. Suspiciously, a copy of Tacquet's version of Elements from 1672 still held by the General Library of the University of Coimbra lacks all the pages that contained the figures. Simões believes it is possible that it was this very book from which the images were taken to serve as models for the tiles.

The result must have been a classroom panelled with a display of mathematics imposing enough to strike fear into the heart of students and elation into the hearts of mathematicians. The copies are a bit loose by modern standards, but they must have been sufficient to get the job done.

I also saw a geographical tile that puzzled me because the place name on it "Cumberlandia" was something I could only link to a the name of a county in northwest England, which is nowhere near the North Pole.

This tile, it turns out, probably depicts a 17th century map of the world by Dutch cartographer Joan Blaeu, according to work by Francisco Roque de Oliveira of the University of Lisbon. This particular tile represents the pole of the western hemisphere and Baffin Island in the Canadian Arctic. "Cumberlandia" was another name for Baffin Island, apparently, and was also used on some maps by Mercator; indeed, when I checked the globe in my living room, I saw that Baffin Island had both a Cumberland Peninsula and Cumberland Sound. If so, the map must have contained at least 50 tiles.

There are also four extant astronomy tiles. Together, they hint at another 50-tile panel that displayed the constellations of the northern and southern hemispheres, comets, and at least two models of the solar system.

Yet there still remain two tiles whose origin, and in one case, subject, are still obscure. One seems to depict some sort of hydraulics demonstration. The other is a complete mystery.

Today, the Elements tiles are the only glazed tiles known to have ever been created for teaching mathematics, not decoration. Yet if the tiles were truly installed around 1740, as Leitão and Gessner suggest, they did not last long. They were likely ripped off the wall in 1759, a mere 19 years later. Of the original 200+ tiles, only 31 whole or fragmentary tiles survive today. What happened? Why would anyone destroy such a glorious temple of math? (I realize some of you are thinking back on your own math classroom experiences right now and saying "I can think of some reasons," but bear with me.)

The Marquis de Pombal (remember him?) had grown to resent the Jesuits and viewed their grip on math and science education as a drag to the spread of a secular Enlightenment in Portugal. He had many other grudges against them, so in 1759, he expelled the Jesuits from Portugal and "expropriated" their assets. In order to justify this persecution, he publicly accused them (among many other things) of being an obstacle to modernization and to the study of science in Portugal. The tiles were evidence to the contrary. Their testimony to the truth was probably the very reason they were destroyed.

References

http://dererummundi.blogspot.pt/2014/08/azulejos-que-ensinam-ciencias_9.html (in Portuguese, but with nice images of things mentioned but not depicted in this blog post -- she provided me an English translation)

Leitão H. and Gessner S. (2014). Euclid in tiles: the mathematical azulejos of the Jesuit college in Coimbra, Mathematische Semesterberichte, 61 (1) 1-5. DOI: http://dx.doi.org/10.1007/s00591-014-0130-8 (in English)