Everything and More: A Compact History of Infinity

Author: David Foster Wallace
Published: 2004
Website: Amazon page

http://www.toxel.com/inspiration/2008/12/03/creative-and-unusual-sofa-designs/Everything and More is a thorough history of abstract mathematics and infinity for any reader with a basic level of mathematical knowledge. Wallace does a remarkable job of weaving together history, philosophy, logic, and short biographies to create a carefully researched summary of the last two-thousand years of mathematics. His snide footnotes and interesting quotations help the dry topic of long-term mathematical evolution and infighting/disagreement among famous mathematicians seem more like an everyday novel than a dusty historical tome, but there were several things about Wallace’s presentation on this amazing subject which quite simply got on my nerves (and which ruin some of his most interesting proofs and anecdotes).

Wallace admits that Everything and More is meant to be popular science, and he accomplishes his stated goal; but Wallace twice offers a beautiful summary of a proof and then adds an offhand remark about the immense difficulty of introductory college math classes and a short anecdote about how he never understood what he had just proved. Trusting an author is not necessarily something I have problems doing, but suspension of disbelief becomes difficult when the author himself tells you that what he has just said confuses him. My other main problem with Everything and More was Wallace’s overuse of abbreviations. In the prelude he offers the reader a list of 40 abbreviations with which he proceeds to indiscriminately sprinkle his paragraphs. Wallace seems to believes that using abbreviations and stylized section breaks makes his novel a mathematical treatise. I completely agree with his choice to abbreviate “Zermelo-Fraenkel-Skolem system of axioms for set theory” as ZFS, but why in the world would anyone want to abbreviate vicious circle as VC or the real line as RL when the point of the book is to turn complex mathematical symbols and concepts into words? Also, the use of twenty pages of “emergency glossary” right in the middle of three separate important thoughts. And my last (extremely minor?) quibble is with Wallace’s definition of induction, which I believe is incorrect. I’ll block quote it in the next paragraph because I think he completely forgot about the actual proof step (unless it’s hiding in his “particular circumstances”).

“The Principle of Induction states that if something x has happened in certain particular circumstances n times in the past, we are justified in believing that the same circumstances will produce x on the (n + 1)th occasion” (15).

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2 Comments to “Everything and More: A Compact History of Infinity”

  1. That definition of induction seems like scientific induction rather than mathematical, because of the lack of a proof step and the use of the words “justified in believing” which are more epistemological than mathematical. I’m not sure why he would do that, and I’m also fairly convinced that that’s a poor definition even for scientific induction. What was the context of the quote?
    – Chana

  2. I think you’re right and he might have been trying to explain scientific induction, but he transitions straight from scientific induction into an explanation of mathematical or philosophical infinity… hmmmmmmmm.

    -Ezra

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