Ed Scheinerman is a professor in the Applied Mathematics & Statistics department of the Whiting School of Engineering at Johns Hopkins University where he also serves as a vice dean. Scheinerman studied mathematics as an undergraduate at Brown and as a graduate student at Princeton. His research focus is graph theory—the mathematics that models networks (roads, social, neurons, computers, and so forth). He has twice been honored with the Paul Halmos-Lester Ford award for mathematical writing. He is the author of a variety of books including The Mathematics Lover’s Companion which is also written for a general audience.
I had a not-so-hidden agenda in writing this book: to have readers see what mathematics really is about. Mathematics is not arithmetic any more than literature is spelling and grammar.
There are ideas that are unimaginable that can be well understood by mathematical reasoning. A rectangle extends into three dimensions to form a cube; this we can visualize. A cube extends into four dimensions to form a hypercube. Can we picture a hypercube in our minds? That doesn’t seem possible. But can we understand and deal with it mathematically? Absolutely. We finite humans may not be able to visualize the infinite; mathematics gives us a way to handle infinity precisely.
Challenge Problem - A rectangle has 4 edges and a cube has 12 edges. How many edges does a four-dimensional hypercube have?
Edward R. Scheinerman, A Guide to Infinity: Ten Mathematical Journeys, Yale University Press, 192 pages, 6 x 9 inches, 70 b-w illustrations, ISBN: 9780300284799
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