Does anybody know the paper where the Brouwer fixed point theorem first appeared?

Wikipedia and other articles available online have no reference. Schauder's paper about his fixed point theorem is available online at


but, even if I don't speak a word of German, it seems to me that there is no reference.

In Brouwer's wikipage


there are some references to Brouwer's papers, but only focused on his contribution to philosophy and philosophy of math.

Thanks in advance,


  • $\begingroup$ Sorry did misread the question;) $\endgroup$
    – Marc Palm
    Mar 6, 2012 at 11:00
  • $\begingroup$ You might have had better luck at the wikipage en.wikipedia.org/wiki/Brouwer_fixed-point_theorem -- which was the top hit when I googled on "brouwer fixed point theorem." (It's odd there was no link to it from the Brouwer bio wikipage.) $\endgroup$ Mar 6, 2012 at 18:12

1 Answer 1


The general theorem was first given in:

Brouwer, L. E. J. Über Abbildung von Mannigfaltigkeiten. Math. Ann. 71, 97-115. Berichtigung ebd. S. 598 (1912).

  • 1
    $\begingroup$ See in particular p. 114, Folgerungen 1,2,3 $\endgroup$ Mar 6, 2012 at 10:55
  • $\begingroup$ Thank you. What is the difference between the three Folgerungen? Sorry but I don't know a word of German and it's also impossible to copy the text and try a google a translation. $\endgroup$ Mar 6, 2012 at 11:05
  • 1
    $\begingroup$ The usual fixed point theorem is actually in the very last sentence: "Satz 4: Eine eindeutige und stetige Transformation eines n-dimensionalen Elementes in sich besitzt sicher einen Fixpunkt." Translation: "Theorem 4: A continuous transformation of an n-dimensional element in itself has certainly a fixed point." A n-dimensional element is a homeomorphic copy of a n-dimensional simplex. $\endgroup$ Mar 6, 2012 at 11:16

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