 Lange 2017 (section 3, chapters 7 to 9) brings together several investigations on mathematical explanation by the same author (see Lange 2010a, 2010b, 2014, 2015b, 2015c; in what follows, we mainly reference the book of 2017). Lange’s investigations are characterized by a rich and varied choice of examples, which lead him to argue that although mathematical explanations do not fall under a general pattern, there are interesting classes of explanations. In chapter 7 of Lange 2017, Lange emphasizes the importance of symmetry and simplicity in mathematical explanations. The idea is that faced with a result that displays a salient symmetry, the explanation will be the one that will be able to account for the symmetry of the result by exploiting a symmetry in the set-up of the problem. Lange gives many examples (drawn from probability, real analysis, number theory, complex numbers, geometry etc.) including one concerning d’Alembert’s theorem (an example of explanation by subsumption under a theorem) to the effect that in a polynomial equation of n-th degree in the variable x and having only real coefficients, the nonreal roots will always come in pairs (both a non-real root and its complex conjugate will satisfy the equation). What explains this symmetry? A non-explanatory proof can be given by algebraic manipulations but this does not reveal the reason for the result which, according to Lange, is the fact that the axioms of complex arithmetic are invariant under substitution of i for -i. Lange offers similar considerations, using further case studies from geometry and combinatorics, for simplicity: if the statement strikes us as simple then an and explanatory proof should be able to account for it using simple features of the set up.