In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777-1855) was an epochal example. August Ferdinand M bius (1790-1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that...