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That’s right, numeralogy (not numerology). In my last column I described a mathematical art: the creation of mathematical structures, structures that dazzle, intrigue, excite, and/or amuse. There are many genres of this art, including algebras, geometries, games, puzzles, and tilings. This column is about one of the smaller genres: numeration systems.
I still remember the surprise I felt when my seventh-grade teacher (New Math, 1957) told us that a numeral was different from a number, that a numeral was a name for a number. What’s in a name? How is that important? I knew about Roman numerals, of course. They were just annoying. Surprise turned to delight as we explored base-6, binary, and other numeration systems. It was, perhaps, my first aesthetic mathematical experience.
Are numeration systems art?
Numeration systems indeed fit my definition of mathematical structure—they can be described completely and unambiguously. But the systems that cultures evolved over...