Abstraction, not just mathematics, has its place in science as it does in art
Games in a Simplified World
Just as in abstract art, what emerges in science after things are taken apart ranges from Hermann Hesse’s The Glass Bead Game (where the rules are only alluded to) to real understanding. In chemistry, there are many examples of paring away to get at the essence of an idea (rather than a molecule). One can see this in stereochemistry, which intently explores all the ways in which a molecule can be distinguished from its mirror image.
As another example, consider the synthesis of the two interlocked rings of catenanes, or the three of Borromean rings (right). The structures are real, and models of the molecules do look like physical rope knots or the Olympic symbol. But within chemistry I think there is a beautiful feeling of abstraction to them.
In another way, the small theoretical industry spawned by the work Charles Wilcox, Roger Alder and I did on stabilizing square-planar carbon also has an abstract feel to it. That molecule’s geometry is about as far as possible from that of a normal carbon atom with four atoms bonded to it at the corners of a tetrahedron. Our transgressive whim could be seen as playing games with high-energy structures. However we, and others, immediately had therapeutic designs—for the molecules, not humans—to ameliorate the energetic suffering of such preposterous bonding configurations.