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This paper is an overview of results that show the Brouwer fixed-pointtheorem (BFPT) to be essentially non-constructive and non-computable. The mainresults, the counter-examples of Orevkov and Baigger, imply that there is noprocedure for finding the fixed point in general by giving an example of acomputable function which does not fix any computable point. Research inreverse mathematics has shown the BFPT to be equivalent to the weak K\"oniglemma in RCA$_0$ (the system of recursive comprehension) and this result isillustrated by relating the weak K\"onig lemma directly to the Baigger example.

Computable counter-examples to the Brouwer fixed-point theorem