Everything and more

About the book

Everything and more takes up the long effort to make mathematical infinity precise. Wallace moves through the ideas and the people who shaped them, from early puzzlement about the infinite toward the formal treatments that gave the concept a working definition. The book belongs to a series of short scientific and mathematical introductions, though Wallace writes with his own voice and his own sense of what deserves emphasis.

The central problem is deceptively simple. Infinity resists ordinary arithmetic: treat it like a number and contradictions pile up. Wallace traces how mathematicians learned to handle that resistance, building definitions and proofs that could survive scrutiny. He is interested in the machinery of those arguments and in the intellectual habits that produced them. Abstraction, in his account, is a practical tool.

Wallace addresses the reader directly, explains why certain ideas are hard, and returns to points he thinks were rushed. The book carries a reputation for difficulty, and that reputation is partly earned. The mathematics is real, and the prose sometimes circles a problem before landing. The circling is deliberate, an attempt to show how understanding gets built.

How to read it

Read the foreword. Wallace says up front that it is part of the argument and that the main text contains structural oddities, so skipping it will make later passages harder to follow. Keep a pencil nearby and expect to reread short stretches.

Track the distinction between informal intuition and formal definition. Wallace often shows why a casual picture of infinity fails before offering the rigorous version. When a proof appears, work through the steps rather than accepting the conclusion. The examples are there to be tested, and the book's argument depends on the reader doing some of that testing.

Who it suits

Readers who want a serious, voice-driven introduction to mathematical infinity will find one here. It suits people with some tolerance for notation and proof who prefer an author who explains his reasoning to one who simply states results. Readers interested in Wallace's nonfiction prose will also find his attention to difficulty and his habit of addressing the reader as a participant.

Reading considerations

This is not a light popular-science tour, and readers without comfort in formal mathematics may find stretches demanding. The book's structural quirks, flagged in the foreword, can make navigation awkward. Wallace's historical asides are his account rather than a neutral survey, and the mathematical claims are worth testing against a standard text when precision matters.