Edward Scheinerman

A Guide to Infinity - Challenge Problem
January 22, 2026

Challenge Problem - A rectangle has 4 edges and a cube has 12 edges. How many edges does a four-dimensional hypercube have?

A Guide to Infinity - Solution to the challenge problem
January 23, 2026

A four-dimensional hypercube has 32 edges. Here’s why. Start with a simple line segment. It has only one edge...

A Guide to Infinity - In a nutshell
January 24, 2026

Infinity. Inconceivable! Agreed. Inscrutable! Nope. The infinite is hard to grasp. Does the universe extend without bound beyond what we can observe? Would we want to be immortal? Will this boring movie go on forever? Infinite time, space, wealth, love …

A Guide to Infinity - The wide angle
February 4, 2026

This tour of mathematical infinities was inspired by my granddaughter Shlomit who, some years ago, called me to ask: What is the number before infinity? A fantastic question!

A Guide to Infinity - A close-up
February 17, 2026

Mathematics is not a dreary sequence of equations and calculations. Many ideas are brought to life through pictures. I hope that a casual bookstore browser might open this Guide to Infinity

A Guide to Infinity - Challenge Problem

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?
January 22, 2026

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

Edward Scheinerman

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. 

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