His research area was the theory of equations and he proved in 1890 that when a cubic polynomial with rational coefficients has three real roots but it is irreducible in ( the so-called " casus irreducibilis " ), then the roots cannot be expressed from the coefficients using real radicals alone, that is, complex non-real numbers must be involved if one expresses the roots from the coefficients using radicals, probably unaware of the fact that Pierre Wantzel had already proved it in 1843.
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