Configurations: A case study in mathematical beauty (Q1057872)

Is there beauty in mathematics? This is the question the author wants to explore. Therefore he considers a small book of \textit{G. H. Hardy} with the title ``A mathematician's topology'' (1941; Zbl 0027.00403). Some of Hardy's ideas concerning beauty in mathematics are helpful so that the writer can use them as criteria of beauty in mathematics. As Hardy's examples of simple but important theorems with casy proofs which exhibit his criteria are too brief and limited the author wants to find a more suitable simple elementary mathematical topic rather than isolated theorems embodying some or all of Hardy's criteria that will be of interest to mathematicians in general and that can also be explained to the layenau in mathematics and that will give the reader some idea of what mathematical beauty can mean. The topic chosen, configurations deals with nothing more complicated than points, lines and tables of the integers 1,2,3,.... It is a topic in which new results are still being found and a subclass of configurations called projective planes is an area that has played an important part in modern algebra. These have led to block designs an area now considered an essential part of combinatorics. In order to show how beautiful mathematics may be the writer makes an extensive description of configurations written for the layman.