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Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges.
In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
Loci: Convergence
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Euler Squares
Introduction
With the recent popularization of Sudoku, interest in related mathematical games such as magic squares and Latin squares has also been revived. Sudoku puzzles are a special case of Latin squares; in fact any solution to a Sudoku puzzle is a Latin square. A Latin square is a square grid filled with symbols in such a way that each symbol occurs once and only once in each row or column. For example, a 3x3 Latin square would have nine cells in which three distinct symbols would be arranged in a way such that no symbol is repeated horizontally or vertically (see Figure 1).
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Figure 1: 3x3 Latin square
Latin squares were known by early Arabic numerologists. These mystical squares, known as wafq majazi, were found on 13th century Islamic amulets [1] and sketched in the margins of a 16th century Arabic medical text [2]. The famous Swiss mathematician Leonhard Euler wrote about Latin squares in his paper Recherches sur une nouvelle espece de Quarres Magiques in 1782. More recently, Arthur Cayley (1821-1892), Ronald A. Fisher (1890-1962), and others have applied Latin squares in the fields of agronomy, computer science, number theory, graph theory, coding theory, and the design and statistical analysis of scientific experiments [3] [4] [5].