Mathematical Masterpieces: Teaching with Original Sources

Our upper-level university honors course, entitled Great Theorems: The Art of Mathematics, views mathematics as art and examines selected mathematical masterpieces from antiquity to the present. Following a common practice in the humanities, for example in Chicago’s Great Books program and St. John’s College curriculum, we have students read original texts without any modern writer or instructor as intermediary or interpreter. As with any unmediated learning experience, a special excitement comes from reading a first-hand account of a new discovery. Original texts can also enrich understanding of the roles played by cultural and mathematical surroundings in the invention of new mathematics. Through an appropriate selection and ordering of sources, students can appreciate immediate and long-term advances in the clarity, elegance, and sophistication of concepts, techniques, and notation, seeing progress impeded by fettered thinking or old paradigms until a major breakthrough helps usher in a new era. No other method shows so clearly the evolution of mathematical rigor and abstraction. The end result is a perception of mathematics dramatically different from the one students get from traditional courses. Mathematics is now seen as an evolving human endeavor, its theorems the result of genius struggling with the mysteries of the mathematical universe, rather than an unmotivated,