Bourbaki dangerous bend symbol

The dangerous bend or caution symbol (U+2621 CAUTION SIGN) was created by the Nicolas Bourbaki group of mathematicians and appears in the margins of mathematics books written by the group. It resembles a road sign that indicates a "dangerous bend" in the road ahead, and is used to mark passages tricky on a first reading or with an especially difficult argument.[1]

French "virages dangereux" road sign, before 1949

Certains passages sont destinés à prémunir le lecteur contre des erreurs graves, où il risquerait de tomber; ces passages sont signalés en marge par le signe ☡ (« tournant dangereux »)

Some passages are designed to forewarn the reader against serious errors, where he risks falling; these passages are indicated in the margin with the sign ☡ ("dangerous bend")

Nicolas Bourbaki's description of the symbol in several textbooks[2]



Others have used variations of the symbol in their books. The computer scientist Donald Knuth introduced an American-style road sign depiction in his Metafont and TeX systems, with a pair of adjacent signs indicating doubly dangerous passages.[3][4][5][6]


Knuth's "Dangerous Bend" sign, with yellow color added.

In the LaTeX typesetting system, Knuth's dangerous bend symbol can be produced by first loading the font manfnt (a font with extra symbols used in Knuth's TeX manual) with \usepackage{manfnt} and then typing \dbend

There are several variations given by \lhdbend, \reversedvideodbend, \textdbend, \textlhdbend, and \textreversedvideodbend.


The Twenty One Pilots song "Overcompensate", makes direct reference to the symbol. Since 2018, the Nicolas Bourbaki group has also been referenced in the conceptual narrative of the band.[7][8]

See also



  1. ^ Steven G. Krantz (2011), The Proof Is in the Pudding: The Changing Nature of Mathematical Proof, Springer, ISBN 0-387-48908-8, p. 92.
  2. ^ See, for example, Théorie des ensembles, p. I-8.
  3. ^ Donald Ervin Knuth (1986), The METAFONTbook, Addison-Wesley, ISBN 0-201-13445-4.
  4. ^ Donald Ervin Knuth (1984), The TeXbook, Addison-Wesley, ISBN 0-201-13448-9.
  5. ^ George J. Tourlakis (2003), Lectures in Logic and Set Theory, Volume 2: Set Theory, Cambridge University Press, ISBN 0-521-75374-0, p. xiv.
  6. ^ Gerard P. Michon (2012), Dangerous Bend Symbol, doubled and tripled, Numericana.
  7. ^ Kaufman, Gil (February 29, 2024). "Twenty One Pilots Announce 'Clancy' Album, Drop Video For Booming 'Overcompensate' Single". Billboard. Retrieved March 1, 2024.
  8. ^ "Map of Dema". Retrieved October 7, 2018.