Abstract Mathematics Is.....
The whole idea of Astounding Math Stories captured my attention and had this Rod Sterling effect....Astounding...Math...and Stories! Currently only about two stories are available, but they hopefully are a good taste of what will follow. The first story discusses an interesting numerical pattern that holds for the first 271,440 cases but breaks down for the 271,441st case. What a great example of why inferential proofs do not suffice. The second story deals with an apparent contradiction in that it is faster to determine if a number is prime than it is to find a factor....yet shouldn't the two be connected?
The "Astounding Math Stories" are part of a new web site still under construction, with bits and pieces showing up sporadically. Being put together by Charles Wells, Professor Emeritus of Mathematics at Case Western Reserve University, the website is organized around the theme of
abstract mathematics.
Created to help people (students or teachers) who intend to study some aspect of abstract mathematics, the web site offers:
 A definition of what is abstract mathematics?
 Overview of background issues and attitude
 Diagnostic examples of some difficulties people experience when studying and doing abstract mathematics
 Discussions of four key areas: the languages of mathematics, proofs, understanding mathematics, and doing mathematics
 Links to other web sites and lists of texts that focus on abstract mathematics
I find the web site refreshing, and it will be a resource that you can use to challenge your better mathematics students. Start with the "Astounding Math Stories" and then gently push them into the other areas.
I should note that Charles Wells, the web site's author, also is the author of the recently released text The Handbook of Mathematical Discourse. This book focuses on the mathematical words and phrases that create problems for students as they begin to study abstract mathematics. The book is interesting and may be reviewed at a later date.
