Vladimir Arnold was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, Russian mathematicians have a strong tradition of writing for, and even directly teaching, younger students interested in mathematics. The present volume contains some examples of Arnold’s contributions to the genre.
“Continued Fractions” takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision. While it exemplifies for the student the kind of generalization and abstraction that mathematicians routinely engage in, it does so in a com- pletely non-routine way. The essay also has a powerful lesson for all of us. The author claims to have set out to invent a completely useless (i.e., in- applicable) mathematical construct, yet found that people came to his door asking about it because it was just what they needed for a particular appli- cation. Mathematicians, it seems, do more than build a better mousetrap. They seem to invent new creatures to be trapped.
In “Geometry of Complex Numbers, Quaternions, and Spins” the con- text is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics.