= Pierre Wantzel
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{title2=1814–1848}
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<Pierre Wantzel> proved impossibility results for <straightedge and compass constructions>, including general <angle trisection> and <doubling the cube>. His 1837 work translated geometric constructions into restrictions on <algebraic numbers>.
Each permitted construction extends the coordinate field by at most a <square root>. Constructing a number of irreducible degree three over the rationals therefore cannot be achieved by such a tower of <quadratic extensions>. This explains why failure to find a construction can have a structural mathematical cause rather than merely reflecting lack of ingenuity.https://mathshistory.st-andrews.ac.uk/Biographies/Wantzel/[Biography, 1837 construction paper and impossibility results]{ref}
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