Editing Thue–Morse sequence (section)

== History ==
The Thue–Morse sequence was first studied by {{ill|Eugène Prouhet|fr}} in 1851,<ref>[https://cs.uwaterloo.ca/~shallit/Papers/ubiq15.pdf The ubiquitous Prouhet-Thue-Morse sequence by Jean-Paul Allouche and Jeffrey Shallit]</ref> who applied it to [[number theory]].
However, Prouhet did not mention the sequence explicitly; this was left to [[Axel Thue]] in 1906, who used it to found the study of [[combinatorics on words]].
The sequence was only brought to worldwide attention with the work of [[Marston Morse]] in 1921, when he applied it to [[differential geometry]].
The sequence has been [[Multiple discovery|discovered independently]] many times, not always by professional research mathematicians; for example, [[Max Euwe]], a [[Grandmaster (chess)|chess grandmaster]] and mathematics [[teacher]], discovered it in 1929 in an application to [[chess]]: by using its cube-free property (see above), he showed how to circumvent the [[threefold repetition]] rule aimed at preventing infinitely protracted games by declaring repetition of moves a draw.  At the time, consecutive identical board states were required to trigger the rule; the rule was later amended to the same board position reoccurring three times at any point, as the sequence shows that the consecutive criterion can be evaded forever.