Pierre Wantzel

Pierre Wantzel, born on June fifth, eighteen fourteen, was a French mathematician renowned for his groundbreaking contributions to geometry. In a pivotal paper published in eighteen thirty-seven, he established the impossibility of solving ancient geometric problems such as doubling the cube and trisecting the angle using only a compass and straightedge. Wantzel's work also included a comprehensive analysis of constructible regular polygons, revealing that a polygon is constructible if and only if the number of its sides is the product of a power of two and any number of distinct Fermat primes.

Despite the significance of his findings, Wantzel's contributions were largely overlooked during his lifetime. His work remained virtually uncelebrated for decades, with only a single mention in a doctoral thesis by Julius Petersen in eighteen seventy-one. It wasn't until more than eighty years later, following an article by Florian Cajori, that Wantzel's name began to gain recognition among mathematicians.

In eighteen forty-three, Wantzel further distinguished himself by proving that the roots of a cubic polynomial with rational coefficients, which has three real roots but is irreducible in Q[x], cannot be expressed using real radicals alone. This theorem, known as the casus irreducibilis, would later be rediscovered and sometimes misattributed to Vincenzo Mollame and Otto Hölder.

Wantzel's personal life was marked by a rigorous and often unhealthy routine. He typically worked late into the night, relying on coffee and opium to sustain his energy, which ultimately contributed to his premature death at the young age of thirty-three. His untimely passing left a void in the mathematical community, as he was often overlooked for his significant contributions, leading to confusion regarding the authorship of the impossibility theorems he had established.