Last time on this series, I talked about the word manifold. Today, we’re going to add a modifier.

Today’s word is one that I use quite a bit: algebraic variety. The kanji is 代数多様体. The pronounciation is “daisutayoutai.” Really this works out as “algebraic manifold.”

In fact, 代数 appears to be a prefix that means algebraic, and is used in many other situations. Here, the two kanji are actually pretty straightforward in why they make something algebraic.

The first is 代, which here is pronounced dai, and has a great many other pronounciations. It also has a great many different shades of meaning. But the obviously relevant one here is “substitute” or “replace.”

The second kanji, 数, is pronounced ~~kazu~~ su here, again among many other things. The meanings are “number,” “law,” “figures,” and the like. (According to a commenter, only “number” and “to count” are common meanings, the others may be archaic)

So together, they mean something like “substituting numbers” or “laws of substitution,” which mean algebra. As last time, we discussed the word “tayoutai,” or manifold, this means that daisutayoutai translates as “algebraic manifold.”

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## About Charles Siegel

Charles Siegel is currently a postdoc at Kavli IPMU in Japan. He works on the geometry of the moduli space of curves.

hi, i’m a math student in Tokyo. the pronounciation is “daisutayoutai”, not “daikazutayoutai”. 数 is pronounced in two different ways, and in this case it should be pronounced “su”.

Hi,

I just thought of making a small correction. “代数” should be read as “die-sue” in this case. A generic (in the mathematical sense) kanji has two pronunciations, one originally from China and one invented in Japan, and the basic rule is to not mix the two kinds. (In the case of “代数,” we use the “Chinese” ones.) Also, “数” certainly means “number” or “to count,” but I’m not quite sure about “law” or “figures” which you mentioned above. At least they should be very rare that I never came across in my life.

One interesting/weird fact is that “mathematics” is “数学” in Japanese, whose direct translation is the “study of numbers,” whereas “number theory” is “数論,” which means the “theory of numbers.” I have no doubt that many mathematicians find this irritating :)

Thank you both very much for the corrections! As for meanings, I was going off of the website linked at the first appearance of the kanji in the second paragraph, so I’d guess that those meanings might be archaic.

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