Everything and More by David Foster Wallace

Given my strong preference for fiction over non-fiction, it's surprising that I haven't read any of David Foster Wallace's novels (although they are on my to-read list).  I have, however, read a lot of his non-fiction, and I adore it and him.  His erudition, wit, linguistic skills, mix of high art and popular culture, and copious footnotes form something I find irresistible.  I particularly recommend his essays on the Illinois State Fair, grammar, cruise ships, John Updike and other writers of his ilk ... you know what? It'll be faster if I recommend all of the works that I've read.

To which I can add Everything and More: a Compact History of Infinity, his "booklet" on the mathematical history and significance of infinity.  I recognize that this won't appeal to everyone, but I thoroughly enjoyed it (and the work-out my brain got).  Although I probably have more mathematical knowledge than the average person, it falls far short of Wallace's own (had he not turned to writing, he could have become a mathematician in his own right).  Wallace does his best to explain the concepts for a layperson, but this particular topic necessarily involves complex math and abstract concepts.  My half-remembered calculus took me far, but eventually I had to just trust Wallace's explanations (not a bad thing).  On the other hand, I think my mathematical knowledge might have actually hampered me on occasion -- it took three reads to really grok Dedekind's definition of real numbers, which included the first successful attempt to construct irrational numbers, I think because I (like everyone else today) take irrationals for granted.

Transfinite numbers involve concepts far removed from ordinary life, concepts that touch on the foundations of mathematics -- are we inventing math, or discovering it? Can it be completely divorced from our reality? Is math real, and what does it mean to say it is real? I find these questions intriguing, so I'd like to read another volume from the publisher's series: Rebecca Goldstein's Incompleteness, about Kurt Godel's work in this area.