More Than Neighbours: Albert E. Bosman & M.C. Escher

How to depict infinity on paper was something that fascinated both M.C. Escher and Albert E. Bosman. Albert Bosman (1891-1961) was an engineer and maths teacher who also became an artist. Mathematics lay at the core of his work. Bosman and Escher were neighbours in Baarn (NL), where they bonded over a mutual interest in mathematical shapes, ideas and principles. The two artists made abstract principles visually accessible to a wider audience. For the first time, their work is being shown side by side in M.C. Escher & Albert E. Bosman: A Mathematical Connection. Bosman’s best-known creation, the Pythagoras Tree, and the other drawings based on it are on show in this small but fascinating presentation from 21 February until 29 June 2025 at Escher in The Palace.

Albert E. Bosman and M.C. Escher both lived on Van Heemstralaan in Baarn from 1944 to 1961. They were regular visitors to each other’s home, where they discussed their love of maths and the music of Johann Sebastian Bach. They may have first met while studying in Delft, where they were members of the Delftsch Studenten Corps fraternity at the same time.* Bosman graduated from Delft with a degree in electrical engineering, and he worked as an engineer for many years. But his engineering career came to an end with the outbreak of the Second World War, marking the start of a period of creativity in which he explored the principle of the Pythagoras Tree in the many drawings he made over the years. It inspired him so much that he wrote a book, The Wonderful Field of Plane Geometry, on the subject, which was published in 1957. Bosman had started teaching maths in 1948, and he loved teaching and drawing in a playful way. He was keen to inspire his students and others who were interested in maths to research and enjoy the hidden secrets of geometry. As Bosman himself put it, “We experience geometry not as a clearly delineated, superimposed system of values, that does nothing to inspire, but as a fascinating interplay of lines and figures, whose conjectured relationships and secrets entice us. […] It is all about finding the source, on the basis of which one can make one’s own discoveries.”**

Neighbours and friends

Bosman lived in Baarn from 1935 until his death in 1961. It was there that Escher and Bosman became close friends, when Escher moved into the house opposite. In letters to his children, now in the collection of Kunstmuseum Den Haag, Escher wrote about his friendship with his neighbours opposite. On 6 July 1957, for example, he wrote to his son Arthur, “To give you an idea of our life in Baarn: we were just at the Bosmans’ house, where they were giving a party to celebrate Edda’s marriage to a Mr Land, whom I found not disagreeable. All the relatives we know were there, of course.”*** The families often visited each other, and the Bosman family still eagerly tell stories from this time. Bosman’s son Eckart, for example, has clear recollections of seeing Escher making blocks for woodcuts in his studio. Several members of the family also received a print from Escher as a gift for a special occasion, such as a wedding. 

Escher and Bosman went out together from time to time, to attend lectures by the local meteorological and astronomical society, for example. Escher’s fascination with the universe started in childhood, and is occasionally reflected in his prints. Both artists liked to decipher natural laws, which are often associated with mathematical structures. In his book, for example, Bosman explores the links between mathematical principles, shells, nature and the cosmos. Their shared fascinations contributed to their friendship.

Personal messages

In 1946 Escher made a bookplate for Bosman, which reflects the interests that connected them. The insect standing on an open book seems to refer to a bookworm. It is however a stylised caterpillar rising up from a page on which the phrase ‘neti-neti’ appears repeatedly. This is a Sanskrit expression meaning ‘not this, not that’, signifying that by identifying what is not true, it is possible to get closer to what is true (‘tat’). This word is written on the opposite page, towards which the caterpillar appears to be moving. Bosman refers to these words in the final chapter of his book, to indicate that, although the figures in the illustrations will not be able to solve all mathematical problems, they do offer a way forward. 

Escher not only made the bookplate for Bosman, he also gave prints with personal messages to members of his family. He gave Linde Bosman, Albert’s daughter, the wood engraving Double Planetoid (1949) for her wedding. It is an appropriate gift, depicting two worlds coming together. Escher described this print as “two immutably fused tetrahedrons”, with triangular structures and humanlike creatures on one, and rocks with plants, trees and animals including a Tyrannosaurus rex on the other. In this ingenious structure, Escher plays with perspective and gravity. He felt it was so important for viewers to have a sense of gravity that he made it possible for the print to be rotated, so there is no up or down. The original frame actually had four hooks on the back, so that it could be turned through 90 or 180 degrees. Each time the print is rotated through 90 degrees, a different inscription appears at the bottom. So without having to turn your head, you can read ‘For Linde and Hans’, his signature ‘M.C. Escher’, their wedding date ‘4 April 1952’ and ‘self-printed copy’ (evidence that Escher printed it himself). 

Escher experimented on several occasions with Double Planetoid, once making a version with a rotating mount. He believed that rotation was an ideal way of properly perceiving the entire image. A fascination that had Escher firmly in its grasp: “The moving element has me in its grip here, too, it seems”. He also added colours. The version in Kunstmuseum Den Haag’s collection, with several shades of green and blue, has a clearer orientation, as Escher signed it in only one place. The print belonging to the Bosman family is not only unique for its inscriptions, but also for the fact that Escher paid more attention to the rotating aspect of the work. 

Concentration and a steady hand

Both Bosman and Escher made abstract principles visually accessible to a wider audience. The two artists were different, however. Bosman had a background in theory, and he made drawings on the basis of mathematical principles, using his knowledge and understanding of the subject to depict mathematical concepts. He was more analytical than Escher, who used ideas of this kind more indirectly (and sometimes unconsciously) as a means of depicting infinity. In Escher’s work, the image comes first, then the mathematical structure behind it. However, they both needed supreme concentration and a steady hand to create such images. 

Bosman opted to use compasses, rulers, Indian ink and a ruling pen – an old drawing instrument that allowed lines to be drawn very accurately in ink. Used mainly in technical drawing, it works with a drop of ink held between the two halves of a metal nib. This forced Bosman to work very meticulously and he must have had a great deal of patience when making his drawings. In Radiation of Points on a Circumference of a Circle [6] (year unknown), a single mistake would mean he had to start all over again. This is similar to Escher, who made lots of woodcuts, carving directly into blocks of wood. Once a piece has been cut out, it is irreversible. Precision was also vital in Escher’s coloured prints, for which he would use several wooden blocks to print parts of the image over one another. In his print Smaller and Smaller (1956) he used four different blocks to transfer the image to paper. If the colours were not positioned properly, the work would lose its impact. The two artists therefore had to work with the utmost precision when creating their prints and drawings. 

The Pythagoras Tree

While Escher became world-famous for his work, Bosman remained relatively unknown. One of his images – the Pythagoras Tree – might however be familiar to Dutch people, as it has appeared on posters in classrooms throughout the Netherlands for several decades. The Pythagoras Tree was Bosman’s way of making an abstract mathematical concept accessible in a fun way. He enjoyed some success with it in his lifetime, having developed it to illustrate the consistent repetition of Pythagoras’ theorem. The Pythagoras Tree is a fractal, a geometric figure that consists of elements that are all a smaller version of the shape of the overall figure. Bosman based his tree on a square with an isosceles right triangle positioned against one side, with a base the same length as the side. Further squares abut the adjacent sides of the right angle, against which triangles are in turn positioned, in an endless repetition. This succession of shapes forms a tree structure that represents the mathematical proposition in an artistic and relatable way.

In his book on plane geometry, Bosman explained his Pythagoras Tree as follows: “The area of the largest square [in the centre] is equal to the sum of the two next smallest, and four of the next smallest etc. The number of squares with a joint equal area grows exponentially: 1, 2, 4, 8, 16, 32, 64, 128, [256], 512, 1024, 2048, ………… into the amazing structure of the Pythagorean tree with sharply defined limit lines and subtle edges.” The endless repetition also means that the area of the tree is infinite. Yet the size of the figure is finite, since after a number of repetitions parts of the tree begin to curl in on themselves.

It was precisely this contradictory element of the finite and the infinite that fascinated Bosman, and Escher too never tired of depicting the finite and infinite on paper. Despite the fact that these two friends and neighbours produced very different prints and drawings, their work continued to act as a bond between them. Both artists had an impact in their own way, too. While reproductions of Escher’s work often hang in doctors’ or dentists’ waiting rooms, Bosman’s mathematical figure has been hanging on the walls of classrooms throughout the Netherlands for decades. The influence of both these artists has remained tangible.