The three parts are the pedestal, a frame made of stainless steel bars, and a bell-shaped plastic piece that is a surface of revolution of a tractrix.
The pedestal suggests the stepped development of the science, and also the six steps symbolize the first six days of the week. The seventh level (the seventh day) is the level of enlightenment, the level of scientific discovery. The tubular structure is a symbol of spacetime: the four triangles stand for four quarter-years (each consisting of three months) and the 12 squares stand for 12 months, (each consisting of four weeks). Also, the skeleton is equivalent to a shape that can be used to fill hyperbolic three-space. The shape was inspired partially by Jeff Weeks's Curved Spaces software.
The piece of a pseudosphere in the middle is the surface that Beltrami discovered was a model of hyperbolic plane geometry.
On an incision in a corner of the pedestal is engraved a quotation from János Bolyai: "From nothing I have created a new, different world”. This quotation is from a letter János Bolyai sent on November 3, 1823 to his father, Farkas Bolyai (also a mathematician), in which the young mathematician announced the discovery of the new geometry. With the help of two hidden mirrors, this inscription is illuminated by the Sun each year on November 3.
The following is written on the monument in Hungarian, Romanian, and English:
HOMAGE TO FREEDOM,
TO THE UNIVERSALITY OF TRUTH
AND TO THE SCIENCE OF SPACE.