IS MATHEMATICS a matter of invention or discovery? It is an age-old question that probably has no resolution, but this week we report on a breakthrough that backs the latter camp.
A mathematician on a geometrical safari has stumbled upon 鈥渉yperstructures鈥� composed of interlocking rings that are themselves linked ring structures.
The discovery has set physicists hot on the trail of new states of matter (see 鈥淢ake way for mathematical matter鈥�). It is a further example of what Eugene Wigner once called 鈥渢he unreasonable effectiveness of mathematics鈥�. The most celebrated illustration is Paul Dirac鈥檚 prediction of the existence of antimatter, based on nothing more than his equations.
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There are wider lessons here. Critics of string theory should take note: strings provide another area where geometry seems to provide a connection 鈥� perhaps an unreasonably effective one 鈥� with the physical world of particles and forces. Funders should also pay heed. Playing with shapes and shadows in strange mathematical worlds might not have an easily predictable impact, but these are adventures of the mind that can turn our gaze to undiscovered wonders at our feet.