The German Genius

now that fossil content rose in importance as a more specific indicator of age and sequence. Like others, Werner recognized that fossils became more varied and complex in later (higher) geological levels. 8 From 1799 he identified paleontology as a discipline of the future and offered a course in it.
    This more sophisticated understanding of the meaning of stratigraphy was Werner’s main lasting contribution. Rachel Laudan of the University of Hawaii has now identified what she terms the “Wernerian radiation,” in which she says that Werner gave rise to a “movement” in geology, a “coherent lineage,” one strand of which accepted, developed, and modified his idea of rock “formations,” building on his ideas about fossils as the clearest way to understanding the past. The second branch of the Wernerian radiation was the causal school. This branch retained its interest in mineralogy but as an indication of causal processes, according an increasing role to heat in the earth’s economy and in the process amalgamating Werner’s and Hutton’s theories. 9
    Laudan traces the Wernerian radiation, beginning in Freiberg but then, via the people who studied there, spreading to Britain, Ireland, Scandinavia, France, the United States, and Mexico. She traces Wernerian textbooks and societies to France, Scotland, and Cornwall, Wernerian academic journals, Wernerian students as teachers in the École des Mines in France, the mining school in Mexico, and Wernerian courses at Oxford and in Edinburgh. There was also a Wernerian radiation away from geology. Goethe, for example, subscribed to Wernerian theory till the end of his life, as did many of the Romantics, some of whom—Novalis among them—even attended his courses. 10
    T HE F IRST M ATHEMATICIAN OF E UROPE
     
    Everyone knows the name of Isaac Newton. There are few prizes in the modern world for coming second in anything, but Carl Friedrich Gauss, according to John Theodore Merz in his History of European Thought in the Nineteenth Century , was, with Newton, one of the two greatest mathematicians of modern times, though that other German-speaker, the Swiss Leonhard Euler, runs them close. Laplace called Gauss the first mathematician of Europe. Many think modern mathematics begins not with Newton but with Gauss. He in turn was much influenced by Kant, whose arguments implied that mathematics was an aspect of the imagination and, therefore, a form of freedom.
    Carl Friedrich Gauss (1777–1855) was born into a laborer’s family in Brunswick and he was as precocious as Mozart. He made simple calculations before he could talk; at the age of three he was correcting his father’s arithmetic; and when he was nineteen he identified the formula that underlay the geometric construction of a 17-sided shape. 11 The Greeks had shown how, with a compass and straight edge, a perfect pentagon could be constructed, but no one between the Greeks and 1796 had been able to show how to use these simple tools to construct other “regular polygons” with a prime number of sides. Gauss was so excited by his discovery that, there and then, he decided to become a professional mathematician, and for eighteen years he would compile a mathematical diary. His family kept this diary in their possession for a century, until 1898, and it comprises one of the most important documents in the history of mathematics. Among other things, it confirms that Gauss proved—but often failed to publish—many results that other mathematicians did not discover until much later.
    Gauss was, perhaps, much more than anyone else, the embodiment of the mathematical imagination . Understanding the behavior of numbers is as much an aesthetic matter as a utilitarian one. Number patterns don’t have to be useful. The rest of us don’t always see the point of why prime numbers are so fascinating or why it is so important to understand their behavior. Partly because of this, mathematicians are perhaps destined to inhabit their own private, solitary worlds, and that was certainly true in Gauss’s case. He rarely collaborated, and worked alone for most of his life. His relationships with his wife and sons were less than ideal and he dissuaded his boys from a career in mathematics, it was said, so that there was no risk of the Gauss name being associated with inferior work. His wife died soon after bearing their third child, who also died, so Gauss spent much of his personal life stultified by despair and