This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) axioms in algebra; (2) the foundations of algebra; and (3) noncommutative algebra. (MP)

The author discusses the impact of mathematical developments around the turn of the century, and historical concerns and development of mathematics education. This article is a continuation of SE 515 504. (SD)