In his famous 1970 paper [1], Nicholas Katz used the character 兄 for the Gauss-Manin connection. I have always been curious about the history behind this symbol.

Question: What motivated Katz to use this symbol?

My guess is that it is because, in the previous paper [2] with Oda, they used the letter Д for the Gauss-Manin connection (maybe because Manin is Russian?). Then maybe Oda feels that Д looks like 兄?


[1] Katz, Nicholas M. "Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin." Publications Mathématiques de l'IHÉS 39 (1970): 175-232.

[2] Katz, Nicholas M., and Tadao Oda. "On the differentiation of de Rham cohomology classes with respect to parameters." Journal of Mathematics of Kyoto University 8.2 (1968): 199-213.

  • 1
    $\begingroup$ The symbol looked like a Japanese character, and a tweet seems to say so in Japanese. The machine translation is (I do not know Japanese): "There are actually quite a few examples of using hiragana, katakana, and kanji in mathematical formulas, which is interesting. There are many foreign mathematics papers in which Yoneda embedding is denoted by yo'', Katz denoted Gauss-Manin connection by older brother'', Satake compactification is denoted by sa'' and sa'', and the Mumford compact There are also papers that use the character ``ma'' to denote chemistry." $\endgroup$
    – ACR
    Commented Jan 17, 2023 at 21:39
  • $\begingroup$ This is the Japanese tweet "twitter.com/keisankionwykip/status/1413426168619929601" $\endgroup$
    – ACR
    Commented Jan 17, 2023 at 21:40
  • $\begingroup$ Yes, that symbol is a Chinese character/Japanese Kanji, meaning "older brother." Thank you for the link. I am still wondering why that symbol is used. $\endgroup$
    – lzww
    Commented Jan 17, 2023 at 23:15
  • 2
    $\begingroup$ It appears that Katz could have done a postdoc in Japan and he was influenced by the newly learned language. Tadao Oda is a pure Japanese name. $\endgroup$
    – ACR
    Commented Jan 18, 2023 at 0:55


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