It had been retarded in Germany by its almost Siamese connection with philosophy. Through most of this period it was regarded as a part of philosophy, and was included in it, along with scholarship and historiography, under the term Wissenschaftslehre, the study of knowledge. This association with philosophy damaged science, for German philosophy was then an exercise in theoretical logic soaring proudly above research, or verification, by experiment.

Two men especially brought scientific honors to Germany in this age-Karl Friedrich Gauss (1777–1855) and Alexander von Humboldt (1769–1859). Gauss was born in a peasant cottage in Brunswick, to a gardener-bricklayer-canal-tender father who disapproved of education as a passport to hell.18 Karl’s mother, however, noticed his delight and skill in numbers, and scrimped and saved to send him to school and then to Gymnasium. There his swift progress in mathematics led his teacher to secure an audience for him with Duke Charles William Ferdinand of Brunswick; the Duke was impressed, and paid for the boy’s tuition for a three-year course in the Collegium Carolinum of Brunswick. Thence Karl Friedrich passed to the University of Göttingen (1795). After he had spent a year there his mother, quite unable to understand her son’s work and play with numbers and diagrams, asked a teacher whether her son gave promise of excellence. The answer was, “He will be the greatest mathematician in Europe.”19 Before the mother died she might have heard Laplace’s statement that Gauss had already verified that prediction. He is now ranked with Archimedes and Newton.20

We shall not pretend to understand, much less to expound, the discoveries —in number theory, imaginary numbers, quadratic residues, the method of least squares, the infinitesimal calculus—by which Gauss transformed mathematics from what it had been in Newton’s time into an almost new science, which became a tool of the scientific miracles of our time. He himself turned his mathematics to fruition in half a dozen fields. His observations of the orbit of Ceres (the first planetoid, discovered on January 1, 1801) led him to formulate a new and expeditious method of determining planetary orbits. He made researches which placed the theory of magnetism and electricity upon a mathematical basis. He was a burden and blessing to all scientists, who believe that nothing is science until it can be stated in mathematical terms.

He was as interesting as his work. While remaking a science, he remained a model of modesty. He was in no hurry to publish his discoveries, so that credit for them did not come to him till after his death. He brought his aged mother to live with him and his family; and in the last four of her ninety-seven years, when she was totally blind, he served as her nurse, and allowed no one else to wait on her.21

The other hero of German science in this age was Wilhelm von Humboldt’s younger brother Alexander. After graduating from Göttingen he entered the mining academy at Freiberg, and distinguished himself by his studies of subterranean vegetation. As director of mines at Bayreuth he discovered the effects of terrestrial magnetism on rock deposits, founded a school of mines, and improved the conditions of labor. He studied mountain formations with H.-B. de Saussure in Switzerland, and electrical phenomena with Alessandro Volta at Pavia. In 1796 he began, by accident, the long tour of scientific discovery (rivaling Darwin’s on the Beagle) whose results made him, according to a contemporary quip, “the most famous man in Europe next to Napoleon.”22

With his botanist friend Aimé Bonpland, he started from Marseilles hoping to join Napoleon in Egypt; circumstances deflected them to Madrid, where the unexpected patronage of the Prime Minister encouraged them to explore Spanish America. They sailed in 1799, and made a six-day stop at Tenerife, largest of the Canary Islands; there they climbed the Peak (12,192 feet), and witnessed a meteoric shower that led Humboldt to study the periodicity of such phenomena. In 1800, starting from Caracas in Venezuela, they spent four months studying the plant and animal life of the savannas and rain forests along the Orinoco, until they reached the common sources of both that river and the Amazon. In 1801 they forged their way through the Andes from Cartagena (a seaport of Colombia) to Bogotá and Quito, and climbed Mount Chimborazo (18,893 feet), setting a world record that held for the next thirty-six years. Traveling along the Pacific coast to Lima, Humboldt measured the temperature of the ocean current that now bears his name. He observed the transit of the planet Mercury. He made a chemical study of guano, saw its possibilities as fertilizer, and sent some of this sea-fowl excrement to Europe for further analysis; so began one of South America’s richest exports. The indefatigable researchers, having almost reached Chile, turned back north, spent a year in Mexico and a short time in the United States, and touched European soil in 1804. It was one of the most fruitful scientific tours in history.

Humboldt stayed for almost three years in Berlin, studying his masses of notes, and writing his Ansichten der Natur (1807). A year later he moved to Paris to be near scientific records and aides; he remained there for nineteen years, enjoying the friendship of France’s leading savants, and the life and literature of the salons; he was one of Nietzsche’s “good Europeans.” He witnessed with the calm of a geologist those superficial disturbances known as the rise and fall of states. He accompanied Frederick William III on the visit of the victorious kings to London in 1814, but mainly he was occupied in developing old sciences or creating new ones.

He discovered (1804) that the earth’s magnetic force decreases in intensity from the poles to the equator. He enriched geology with his studies of the igneous origin of certain rocks, the formation of mountains, the geographical distribution of volcanoes. He provided the earliest clues to the laws governing atmospheric disturbances, and thereby shed light on the origin and direction of tropical storms. He made classic studies of air and ocean currents. He was the first (1817) to establish for geography the isothermal lines uniting places with the same mean annual temperature despite their difference in latitude; cartographers were surprised to see, on Humboldt’s map, that London, though as far north as Labrador, had the same mean temperature as Cincinnati, which is as far south as Lisbon. His Essai sur la géographie des plantes began the science of biogeography—the study of plant distribution as affected by the physical conditions of the terrain. These and a hundred other contributions, modest in appearance but of wide and lasting influence, were published in thirty volumes from 1805 to 1834 as Voyages de Humboldt et Bonpland aux régions equinoxiales du nouveau continent.

Finally, having exhausted his fortune in his work, he accepted a salaried post as chamberlain at the Prussian court (1827). Soon after his redomestication he delivered in Berlin the public lectures which later formed the substance of his many-volumedKosmos(1845–62), which was among the most famous books in European ken. The preface spoke with the modesty of a mature mind:

In the later evening of an active life I offer to the German public a work whose undefined image has floated before my mind for about half a century. I have frequently looked upon its completion as impracticable; but as often I have been disposed to relinquish the undertaking, I have again—though perhaps imprudently—resumed the task…. The principal impulse by which I was directed was the earnest endeavor to comprehend the phenomena of physical objects in their general connection, and to represent Nature as one great whole, moved and animated by internal force.23

As translated into English in 1849, the book ran to almost two thousand pages, covering astronomy, geology, meteorology, and geography, and revealing a physical world vivid in surprises, yet governed by the laws of mathematics and the regularities of physics and chemistry. Nevertheless, the general picture is one of a vast scene generated not by an inanimate mechanism but by the inexhaustible vitality, expansion, and inventiveness of inherent life.

Humboldt’s own vitality was inspiring. Hardly had he settled in Berlin when he accepted a call from Czar Nicholas I to lead a scientific expedition into Central Asia (1829). It spent half a year gathering meteorological data and studying mountain formation, and, on the way, discovered diamond mines in the Urals. Back in Berlin, he used his position as chamberlain to improve the educational system, and to help artists and scientists. He was working on Volume V of Kosmos when death caught up with him in his ninetieth year. Prussia gave him a state funeral.

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