Charles Hermite
Life
A profoundly modest French mathematician who, despite a lifelong limp from a clubfoot, refused all academic limelight while quietly reshaping analysis. In 1858 he expressed the general quintic through elliptic modular functions, moving beyond the universal formula by arithmetic and radicals that Abel had proved impossible. In 1873 he proved e is transcendental, and Lindemann adapted the method nine years later to settle π and close the 2,000-year squaring-the-circle problem. His name persists in Hermitian matrices, Hermite polynomials, and Hermite forms. He taught Poincaré.
Decisive moments
Solving the quintic with elliptic functions
ParisHe expressed solutions of the general quintic through elliptic modular functions, going beyond the universal arithmetic-and-radicals formula Abel had ruled out. The roots were not absent; the permitted language changed.
Proving e is transcendental
ParisIn Sur la fonction exponentielle he proved that e is not the root of any polynomial with integer coefficients (transcendental). A new frontier was drawn in the kinds of numbers themselves.
His student Lindemann's π is transcendental
Adapting his method, Lindemann proved π is transcendental — settling the 2,000-year squaring-the-circle problem as impossible with compass and straightedge.
If this person hadn't existed
This is a thought experiment about influence, not a verified historical fact.
Without Hermite's 1873 proof that e is transcendental, Lindemann's 1882 proof for π — and thus the resolution of the 2,000-year squaring-the-circle problem — would have arrived later. Without Hermitian matrices, the standard mathematical language of quantum mechanics would have taken a different shape.
Beyond MathVoyage
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