3. Basic Concepts of Computation

Named after William Horner (1786–1837) although apparently the method was discovered centuries before by the Chinese mathematician, Zhu Shijie (~1260–~1320).

These notations were introduced by the German mathematician Edmund Georg Hermann Landau (1877–1938).

Neils Henrik Abel (1802–1829) was a handsome man and a brilliant mathematician from Norway. Despite his short life he made great contributions to mathematics. He lived in poverty and died of tuberculosis. His teacher Bernt Holmboe helped Abel gain financial support for his studies, as did the German mathematician August Leopold Crelle (1780–1855), who founded the first journal devoted exclusively to mathematics and who published many of Abel’s papers. Indeed Crelle secured a nice job for him, but it was too late. There is a sentence in the middle of one of Abel’s notebooks that I have found it haunting: “Our Father who art in Heaven, give me bread and beer. Listen for once.” The French mathematician Èveriste Galois (1811–1832) generalized Abel’s work on solvability of equations. Galois also had a tragic life. He was imprisoned for his political views and lost his life in a duel; it is not clear if it was over love or politics. The modern or abstract algebra is based on the work of Abel and Galois. A good source on both men (but with some amount of math included) is Peter Pesic’s Abel’s Proof (2003); see also Men of Mathematics (1937) by E. T. Bell.