The World Stage 
The Early Republic
The World Stage

From
the 1870s, Americans began to play a larger role in discovering new
mathematical principles. Some studied abroad, especially in Germany, and a
few American universities began to offer graduate degrees in mathematics.
Mathematicians purchased teaching equipment linked to recent advances in their discipline. They and others also introduced devices to help the rapidly growing number of high school students. 

From ancient times, mathematicians had studied regular solids like
the tetrahedron, the cube, and the octahedron. In the 1850s, the Swiss
mathematician Ludwig Schläfli described the six regular figures, or
polytopes, that can exist in fourdimensional space. 

College
students studied figures that could be generated by the motion of straight
lines. This model shows two
such surfaces, the cone on the inside and the hyperboloid on the outside.
Surfaces of this sort had been discovered by the Swiss mathematician
Leonhard Euler (17071783), and were useful in engineering
education.


Americans
also began to build geometric models that reflected recent discoveries.
Richard P.
Baker, an Englishborn mathematics professor, did advanced work at the
University of Chicago and then taught at the University of Iowa. He
designed and sold several models of surfaces discovered by the German
mathematician G. F. Bernhard Riemann and his students.


In 1900, Edgar J. Townsend returned from advanced studies in Germany and became director of the mathematics department at the University of Illinois. He promptly arranged for the university to extend its collection of German geometric models and introduced a graduate program in mathematics. 

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