A trip to Coimbra

World Heritage site

The University of Coimbra is the oldest in Portugal, having been founded in 1290 (younger than Oxford, older than St Andrews), but after bouncing back and forth between Coimbra and Lisboa for a while, it finally settled in Coimbra in 1537. Dom João III gave the University his royal palace at the top of the hill, and this is now the heart of the University, with an ancient library, chapel, meeting room, examination room, and so on. The wonderful University palace quadrangle and surrounding buildings are since 2013 a World Heritage site.

Rosemary and I spent two quite extraordinary days in and around Coimbra. I thought the purpose of the trip was for me to give a colloquium talk – I did that, speaking on “The Random Graph”, and drew an enthusiastic audience of over thirty, quite remarkable for this time of year – but it seems that the real purpose was for me to be shown some of the wonders of this part of Portugal, and to receive Portuguese hospitality from my hosts Jorge Picado and Maria Clementino.

Jorge met us at the station, gave us a tour of the University palace and courtyard, and then with Maria took us to lunch. After my talk, we were delivered to the hotel with instructions about where to find Coimbra fado that evening.

Mathematics and fado

Coimbra fado is different from the Lisboa variety, and its performance is jealously guarded. It seems to me that it gives the musicians much more interesting things to play. We heard a singer and two guitarists (one playing a Portuguese guitar, whose tuning pegs radiate out like a peacock’s tail, the other a regular Spanish guitar) at the Santa Cruz café. Fado, beer, and ham and cheese to pick at. After the fado, we walked through the park on the banks of the river Mondego, the largest river entirely within Portugal (the Tejo and Douro both rise in Spain), where we sat and watched swallows, kites, and wispy clouds.

The next day was all sightseeing, first to the Roman town of Conimbriga, and then to the forest of Bussaco.

The guidebook says that the name Conimbriga gave rise to Coimbra when it was transferred to the town formerly known as Aeminium, though according to Jorge, not all authorities agree. There was a sizeable settlement here from about 900BC, on a plateau at the edge of a steep river gorge. The town flourished in Roman times; only 15% of it has been excavated. Some of the most extensive houses were demolished to build a defensive wall against the barbarians at the end of the Roman empire. Much of the underfloor heating systems and many fine mosaic floors remain, and many artefacts of Roman life have been found.

Many of the mosaic patterns are geometric, including a couple of vertex-transitive tesselations (one with squares and octagons, one with triangles, squares and hexagons).


Bussaco has an alternative spelling Buçaco, sometimes in the same document. It was owned by a monastery of Carmelite friars, to whom its remoteness was a great benefit. They built a via sacra and hermitages as well as a monastery. In the Napoleonic Wars it was the scene of a fierce battle, when Portuguese and British forces inflicted the first defeat on Napoleon’s troops. Later a hotel was built overshadowing the old monastery, in a flamboyant neo-baroque style in which the stone almost seems to be a living and growing organism.

The monks left much of the forest in its natural state, but also planted a wide variety of trees, so that now everything from pines to tree-ferns flourishes there. Many trees were blown down in a severe storm in January 2013, but there are so many trees in the forest, and so much conservation work has been done already, that the scars are not too noticeable. We had a pleasant hike down the stream and back up beside an artificial cascade, and then on the via sacra leading to the Coimbra Gate giving fine views over the countryside below.


At the end of the day, a fast train took us back to Lisbon, in half an hour less than it had taken us getting there the day before.

About Peter Cameron

I count all the things that need to be counted.
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4 Responses to A trip to Coimbra

  1. I forgot to say that, if you look very carefully at the mural behind Jorge Picado and me, you will see the name of Pedro Nunes.

  2. Alex Fink says:

    Carlos Santos has been collecting instances of the various frieze and wallpaper groups in Lisbon; he has examples of all the former and all but five of the latter. He spoke on the project at http://davidson.weizmann.ac.il/en/lectures/recreational_math , mentioning a deck of cards he was producing for sale to show off his finds. Unfortunately I neglected to take note of the project website and can’t recover it now.

    • And who knows what patterns lie buried in the 85% of Conimbriga which hasn’t been excavated? (or many other Roman sites in the same condition, such as Uriconium).

  3. João Araújo has sent me a link to a Scientific American blog post on some mathematical azulejos in the museum in Lisbon:
    These are from the former Jesuit college in Coimbra, and are diagrams from Euclid. See an article by Henrique Leitão and Samuel Gessner, in Mathematische Semesterberichte 61 (2014).

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