Makes maths research fun, using socratic dialogue.
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A few years ago John Horton Conway of the University of Cambridge hit on a remarkable new way to construct numbers ... Conway explained his new system to Donald E. Knuth, a computer scientist at Stanford University, when they happened to meet at lunch one day in 1972. Knuth was immediately fascinated by its possibilities and its revolutionary content. In 1973 during a week of relaxation in Oslo, Knuth wrote an introduction to Conway's method in the form of a novelette. ... I believe it is the only time a major mathematical discovery has been published first in a work of fiction. ... The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as ``to teach how one might go about developing such a theory.'' He continues: ``Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself.'' ... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other ``real'' value does. The system is truly ``surreal.'' [quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19]
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