Steiner, Jakob (1796–1863)

Swiss mathematician, the founder of modern synthetic, or projective, geometry. He discovered the Steiner surface (also called the Roman surface), which has a double infinity of conic sections on it, and the Steiner theorem.

Steiner was born at Utzenstorf, near Bern, and did not learn to read and write until the age of 14. After training as a teacher in Germany, he was admitted to the University of Berlin in 1822. By 1825 he was teaching at the university and in 1834 a professorship of geometry was created for him, which he held for the rest of his life.

His first published paper, which appeared in 1826, contained his discovery of the geometrical transformation known as inversion geometry.

The Steiner theorem states that two pencils (collections of geometric objects) by which a conic is projected from two of its points are projectively related.

In the Steiner–Poncelet theorem, an extension of work done by French mathematician Jean Poncelet in 1822, Steiner proved that any Euclidean figure could be generated using only a straight rule if the plane of construction had a circle with its centre marked drawn on it already.

His most important work is Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von Einander (1832).