M.C. Escher & Albert E. Bosman: A Mathematical Connection

How to depict infinity on paper? This was a question that exercised the minds of both M.C. Escher and Albert E. Bosman. Albert E. Bosman (1891-1961) was a multitalented engineer who was keen to make mathematics and geometry accessible. He was not only a maths teacher, but also an enthusiastic artist who drew inspiration from his area of expertise. Bosman and Escher were neighbours in Baarn (NL) from 1944 to 1961. They shared a deep fascination with mathematical concepts and both explored limits and the finite and infinite in their work. They 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 at Escher in The Palace. The presentation fills a whole room and has been integrated into the permanent exhibition featuring key works by M.C. Escher.

M.C. Escher managed in his work to seamlessly link mathematics and art, a gift which in the second half of his career brought him into contact with scholars from around the world. But he also had such contacts closer to home, including Albert E. Bosman, his neighbour in Baarn. Bosman was a multitalented engineer who was keen to make mathematics and geometry accessible. He was particularly interested in the visualisation of mathematical concepts, as reflected in his best-known creation, the Pythagoras Tree, seen on posters in classrooms throughout the Netherlands for many decades.

Friendship

Alongside Escher’s prints, ten mathematical drawings by Albert E. Bosman are on show, as well as special prints by Escher that belonged to his neighbour’s family. The two men not only shared a love of mathematics and the music of Johann Sebastian Bach, they also got along well on a personal level. They may have first met while studying in Delft, where they were members of the Delftsch Studenten Corps fraternity at the same time. As neighbours, Escher and Bosman were frequent visitors to each other’s home, including during the difficult years of the Second World War. Stories about Escher are therefore very much part of Bosman family lore. 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 on a special occasion, such as a wedding. Escher marked his friendship with Bosman in the form of a bookplate he designed for him in 1946.

Bosman and Escher were interested in the world around them. They attended lectures given by the local meteorology and astronomy society in Baarn. 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 1957 Bosman published a book on plane geometry, which explained the links between mathematical principles, shells, nature and the cosmos.

The Pythagoras Tree

The Pythagoras Tree, Bosman’s way of making an abstract mathematical concept accessible in a fun way, was his most important creation. 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 identifiable way. Several versions of his design are on show at Escher in The Palace.