I am a mathematician and artist creating mathematical art. In 2005, I received my Ph.D. in mathematics from the Johannes Gutenberg University Mainz (Germany) in a field called algebraic geometry which combines the two areas – algebra and geometry.
Many of the math objects I make are based on this – bridging two apparently separate branches of mathematics and at the same time bridging mathematics and visual arts.
Most of my math objects are not only vaguely related to mathematics, but represent a carefully chosen mathematical concept, result, or equation. Often, the abstract shapes on which my pieces of math arts are based are even defined by a single formula.
Inner mathematical beauty and outer visual beauty
Many of the mathematical sculptures I create have a fascinating inner beauty. Sometimes, this abstract beauty comes from a related mathematical concept or result which has an elegance in itself, e.g. because of its simplicity or generality.
Another aspect of the beauty of an object is the often hundreds or thousands of years of math and science history constituting the background behind the mathematical shape.
In some cases, at least parts of the inner abstract beauty are also visible in the final real world object. One such feature is the symmetry of an object. Abstractly, each kind of symmetry has a whole abstract building in the back, built by generations of math researchers trying to understand the big picture behind symmetry itself.
Luckily, we may appreciate many kinds of symmetry even in our apparently three-dimensional world. Symmetric 3d sculptures form a major part of my works. For shapes defined by a formula, symmetry often results in a much shorter and nicer equation. So, in this sense, outer beauty and simplicity is directly related to inner mathematical beauty and mathematical simplicity. One such example is my own world record surface (a so-called septic with 99 singularities) for which I constructed the equation from purely mathematical motivations; but it happens to be symmetric as well!
But symmetry is not all of beauty. Indeed, often it is the asymmetry which makes the beauty of an object. Some of our math objects do not use symmetry, others do.
I believe that some kind of simplicity and restriction is an essential ingredient of beauty. This applies in particular to my mathematical sculptures. If you – the reader – are interested in more details, I will be very happy to elaborate on this in a personal communication.
The creative process towards my math sculptures
In a first creative process during which I find interesting equations and concrete descriptions yielding fascinating shapes, I also decide which material and production method best fits the object I have in mind. E.g., laser-in-glass is a method for bringing extremely fragile abstract math shapes to real life.
After this heavily creative part, between artistic, visual, and mathematical creativity, I adapt my own software for the particular math object I wish to create. Depending on the materiality of the final object, the data I need will be quite different sometimes.
This software – developed by myself over the last some 20 years – then creates the data for the object I have in mind, and then a machine produces it in perfect quality.
Math sculptures in glass by Oliver Labs at the Bos Fine Art gallery
At the Bos Fine Art gallery, I present objects in glass, produced using the laser-in-glass method. As indicated above, this allows me to show abstract mathematical objects in an almost perfect way:
In the abstract world of mathematics, many mathematical shapes have a thickness of zero, e.g. a plane given by the equation z=0. But an object which is visible in our real world, has to have a certain thickness. With the laser-in-glass method, the thickness of the mathematical shapes I create is almost indistinguishable for our eyes from zero.
Another advantage of the laser-in-glass technique is the fact that there are essentially no stability restrictions… in the glass, I can even show several balls floating at a specifically chosen position in space. In this sense, my mathematical laser-in-glass sculptures come very close to the best possible visual representation of abstract mathematical shapes.
Currently available at the Bos Fine Art gallery are some numbered math objects from small series and some unnumbered ones.
The most recend math objects additions to the gallery, each based on a single mathematical equation, created by me especially for these glass objects (with the symmetry of the dodecahedron), are the following three:
– Dodecahedron Bloom 01 (2019, a series of 5 identical objects),
– Dodecahedron Bloom 02 (2019, a series of 5 identical objects),
– Dodecahedron Bloom 03 (2019, a series of 5 identical objects).
Reproducability of math-in-glass sculptures
All my laser-in-glass sculptures are produced using a machine based on the 3d data I created in a creative process between mathematics and visual arts and using my own software as described above.
Thus, reproducability is built into the process. However, apart of my classics such as the Barth world record sectic and some other cases, I restrict the number of copies of my larger math objects to a some small value such as 5 or 10 copies. Each of these objects is numbered, e.g. copy number 1 of 5 (such as the Dodecahedron Blooms mentioned above).
Only tiny versions of these works, such as 5cm glass cube mini sculptures or – even smaller – 3cm glass cube key chain objects, are unnumbered and may be produced in an unlimited number of copies in the future.
Exhibitions of math sculptures by Oliver Labs
As part of the so-called Imaginary exhibition, some of my works of math art – some images of world record surfaces and some 3d printed objects – have been exhibited in more than 100 cities worldwide since 2008.
Other works – such as my cubic surface math sculptures and my laser-in-glass sculptures are part of several famous collections of mathematical sculptures, such as the one at
– the Institut Henri Poincaré at Paris (France), or
– the Deutsche Museum at Munich (Germany),
– the University of Lisbon (Portugal), or
– and numerous other museums, math departments, and private collections, in Europe and the world.