THREE MATHEMATICAL VIGNETTES; MILLENNIAL, PONTIFICAL, AND NYCTAGINACEOUS
Two first century (A.D.) manuscripts, the Introduction to Arithmetic, by Nicomachus of Gerasa and Mathematics Useful for Understanding Plato by Theon of Smyrna were the main sources of knowledge of formal Greek arithmetic in the Middle Ages. The books are philosophical in nature, contain few original results and no formal proofs. They abound, however, in intriguing number theoretic observations. We discuss and extend some of the results found in these ancient volumes. Secondly, we discuss the mathematics of Gerbert the Great, a tenth century educator. We end with the achievements and adventures of Louis Antoine de Bougainville, mathematician, explorer, and student of D'Alembert.
EPISODES IN THE EARLY HISTORY OF THE LUCASIAN CHAIR
In 1663, Henry Lucas, the long-time secretary to the Chancellor of the University of Cambridge, made a bequest, subsequently granted by Charles II, to endow a chair in mathematics. A number of conditions were attached to the Chair. Among the more prominent Lucasian professors were Newton, Babbage, Stokes, Dirac, and Hawking. We focus attention on the early Lucasians. Many of whom were very diligent in carrying out their Lucasian responsibilities but as history has shown such was not always the case. In the process, we uncover several untold stories and some interesting mathematics.