No full reviews, but will just mention/recommend two books I'm reading now… one old, one newer.
I've always enjoyed anything I've read from math-writer David Wells and science-popularizer K.C. Cole, and that goes for these offerings as well. Am halfway through Wells' 2012 book, "Games and Mathematics: Subtle Connections," and that's enough for me to already feel comfortable recommending it to anyone interested in those topics; as one reviewer calls it, "a very approachable yet erudite book." (I will caution that it is not so much a Martin Gardner-style mathematical games book, as a more academic or scholastic approach.)
K.C. Cole usually writes lyrically about physics or general science, so I was pleasantly surprised to stumble across her 1998 volume, "The Universe and the Teacup," and discover it's a volume of essays focused around mathematical notions. A bit dated, and not at all technical, but an enjoyable, accessible, almost lilting compendium of math-related essays for the layperson.
I'll end with a few passages therefrom:
"Curiously, the human brain is a product of exponential amplification. According to Anthony Smith in his book "The Mind," the human brain contains 10 to 15 billion nerve cells -- three times as many as there are humans on the planet. If you add in the number of connections between nerve cells, the sum is more than the number of humans who ever lived. Fifteen billion is also more or less the number of stars in the galaxy.
"The brain built up all this marvelous gray matter by doubling. To get to 15 billion nerve cells takes only thirty-three doublings of the first cell; to get to half that number takes just thirty-two doublings -- which is about the size of the number of cells in the brain of an ape. Our brains are only one doubling away from our simian relatives."
"In "Strength In Numbers," mathematician Sherman Stein offers the case of the men's support group that wanted to demonstrate how badly women treat the male sex. As supporting evidence, the group pointed out that more than half of the women on death row had murdered their husbands, while only a third of the men on death row had murdered their wives. What the group neglected to mention, says Stein, was that there were a total of seven women on death row. And 2,400 men."
"In fact, probability permeates just about any attempt to pin down a scientific 'fact.' The fact itself might wiggle away from any precise attempt at measurement, or the measurement (or measurer) might be wobbly or overwhelmed with background static and interference.
"Take a straighforward 'fact' such as my height. Recently asked how tall I was in a doctor's office, I answered five feet five inches. Then I added: 'At least in the morning.'
"The sad truth is, by evening, I've shrunk at least an inch. And so, dear reader, have you. There's no mistaking that gravity gets us down -- everybody equally. Give it a full day to pull us toward the center of the Earth, and we compress like an accordion."
"Math has its own inherent logic, it's own internal truth. Its beauty lies in its ability to distill the essence of truth without the messy interference of the real world. It's clean, neat, above it all. It lives in an ideal universe built on the geometer's perfect circles and polygons, the number theorist's perfect sets. It matters not that these objects don't exist in the real world. They are articles of faith."