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Mathematical curiosities have a strongly addictive quality for the would-be mathematician …

With all its grandiose vistas, appreciation of beauty, and vision of new realities, mathematics has an addictive property which is less obvious or healthy. It is perhaps akin to the action of some chemical drugs. The smallest puzzle, immediately recognizable as trivial or repetitive can exert such an addictive influence. One can get drawn in by starting to solve such puzzles. I remember when the Mathematical Monthly occasionally published problems sent in by a French geometer concerning banal arrangements of circles, lines and triangles on the plane. “Belanglos,” as the Germans say, but nevertheless these figures could draw you in once you started to think about how to solve them, even when realizing all the time that a solution could hardly lead to more exciting or more general topics. This is much in contrast to what I said about the history of Fermat’s theorem, which led to the creation of vast new algebraical concepts. The difference lies perhaps in that little problems can be solved with a moderate effort whereas Fermat’s is still unsolved and a continuing challenge. Nevertheless both types of mathematical curiosities have a strongly addictive quality for the would-be mathematician which exists on all levels from trivia to the most inspiring aspects.

— Stanislaw M Ulam (Polish born US mathematician, 1909 – 1984)

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