Here are some interesting books with a math/science emphasis. Some easy to read, some difficult. No novels.
The Planiverse by A.K. Dewdney
This is a wonderful book about a hypothetical 2-dimensional universe. It is much better than Flatland by Abbott, because it gives plausible and detailed explanations of 2-dimensional cosmology, physics, chemistry, geology, weather, biology, sociology, art, music, politics, machinery, computers, etc. Unlike flatland, in which the characters are polygons that float around on a plane, the planiverse characters are flesh and blood and live in underground houses on the circumference of a circular planet which orbits a circular sun. The pictures are fascinating.The Planiverse has a fun storyline with a 2-dimensional protagonist.
Infinity and the Mind by Rudy Rucker
This explains the different levels of infinity. It goes way beyond Cantor's levels of infinity, which is where most treatments of infinity stop.
From One to Zero by Georges Ifrah
This is an informative history of number systems from all the world's cultures. It has a lot of pictures and charts showing all the different written numerals and how the different systems worked.
The Recursive Universe by William Poundstone
This describes how to build elaborate systems in John Horton Conway's mathematical game called Life. For example, it shows how 13 "gliders" can collide to build a "glider gun" which will then start shooting out a stream of gliders. It goes on to give the basic plan for building a general purpose computer within the game of Life, using streams of gliders to represent streams of bits.
Gödel's Proof by Ernest Nagel and James R. Newman
The most astonishing proof in all of mathematics is Kurt Gödel's proof that any consistent system of arithmetic must be incomplete. In other words, there are true theorems that are unprovable. Nagle and Newman's little book walks you step-by-step through the proof. You can understand it. The proof isn't very difficult; it's just very clever.
Precalculus Mathematics in a Nutshell by George Simmons
This lovely little textbook contains everything you really need to know about mathematics (geometry, algebra, and trigonometry) before calculus. It clearly explains everything and has exercises for you to solve, and yet it is very small (119 pages). I love it.
Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler
These puzzles are really intriguing. All the puzzles are simply stated, but the answers are sometimes advanced. For example, "How many figure eights can be drawn on the plane?" The answer, of course, is infinity, but which infinity?
General Science Books
Powers of Ten by Philip and Phylis Morrison and the Office of Charles and Ray Eames
This is an ordered sequence of beautiful pictures and detailed descriptions of things in the universe at all different size scales. It starts with the very large scale in which galaxies appear as dots, and zooms in by factors of ten, zooming right through a picnic in the park, until it ends at the very small scale in which subatomic particles fill the page.
Asimov's Biographical Encyclopedia of Science and Technology by Isaac Asimov
This contains absorbing summaries of the lives and achievements of the 1000 greatest scientists of all time, in chronological order.
The Flying Circus of Physics by Jearl Walker
This is my favorite book. This is a fantastic collection of hundreds of physics puzzlers, many taken from everyday life. It is full of thought-provoking questions about: superballs, silly putty, tops, and yo-yos; boiling water, dripping faucets, and blowing bubbles; rain, rainbows, snow, lightning, and tornados; bicycles, cars, boats, airplanes, and spaceships; magnets, electricity, radio, and television. It has answers, but it is more fun if you try to figure it out for yourself, and resist looking at the answer right away. Some of these simple questions are so deep that scientists don't know the answers yet. Wonder-full.
Quantum Reality by Nick Herbert
Quantum physics is the most amazing thing in the universe. This is the best book I've seen about quantum physics for the layman. Herbert presents the facts and all the different major philosophical interpretations of the facts.
Building Blocks of the Universe by Isaac Asimov
The stories of every element on the periodic table. Of course it's fun to read — it's Asimov. After reading this, every element is your friend.
A Guide to the Elements by Albert Stwertka
Each element on the periodic table has a few pages describing the element's properties, its history, and its uses. Open to any page and browse or read it straight through. Perfect for a school library.
Giants of Land, Sea, & Air — Past & Present by David Peters
This has spectacular color illustrations of the largest animals of all kinds, both living and extinct. All the pictures in the book are drawn to the same scale. There are a lot of animals here which you probably have never seen before, such as Doedicurus, an extinct armadillo-like glyptodont with a 5.5-foot-high shell!
Strange Creatures by David Peters
This is full of amazing color illustrations of the strangest creatures in the world, both living and extinct. There are a lot of animals here which you probably have never seen before, and may not want to see again!
From the Beginning: The Story of Human Evolution by David Peters
You know we evolved from fish, but did you know which kind of fish? This has detailed drawings and descriptions of all the creatures which are the direct ancestors of humans (or the closest known relative of each ancestor). It traces our descent from single cells to worms, fish, amphibians, reptiles, mammals, primates, and homonids. Meet your great-great-great-great-grandpapa!
On the Origin of Species by Means of Natural Selection by Charles Darwin
Arguably the most significant book ever written. Unlike other watershed scientific works, this is very readable from cover to cover. Darwin clearly describes his theory of natural selection and presents the evidence in plain but precise language. The book is nicely structured, for example, he starts with Variation under Domestication, then moves on to Variation under Nature. He illustrates his points with many pertinent examples from agriculture and nature. He recapitulates the key ideas so you never get lost. It is so clearly written, you can see why Thomas Huxley said "How extremely stupid of me not to have thought of that".
Incomplete Nature: How Mind Emerged from Matter by Terrence Deacon
In this broad and deep book, Terrence Deacon presents a very plausible scientific explanation of how life and mind may have emerged from matter. It's a heavy read (550 pages, no equations). Deacon synthesizes the ideas from many disciplines and advances the field with original creative insight. Life and mind are hierarchical complex dissipative far-from-equilibrium dynamic systems (see Ilya Prigogine). Rather than starting with speculations about consciousness, Deacon builds on a solid foundation by starting at the bottom (atoms) and working upward (life and then mind). Lower level dynamic systems interact and constrain each other, thus creating higher-level dynamic systems with entirely new emergent properties. Constraints drive nature’s creativity. Deacon emphasizes three levels of emergent dynamic systems: Thermodynamics → Morphodynamics (form-creating systems) → Teleodynamics (end-directed, self-creating systems). The description is more physical than philosophical. Physical work must be done at the lower levels to create emergent properties at the higher levels. Entropy may decrease locally but must increase globally.
The core of the book is the very plausible description of how the first proto-life may have formed from non-life. In some primordial soup, two or more types of molecules happen to catalyze the production of each other in a cycle (autocatalysis). Furthermore, one of the molecules in this cycle also happens to self-assemble into a simple tube or capsule (containment). The capsule happens to capture some catalysts. When the capsule happens to break open the cycle begins again and it replicates, if the necessary substrate molecules are around. It's called an autogen or autocell. To visualize this, you can watch the excellent autogen demo animation (teleodynamics.flv uploaded by Jeremy Sherman). The autogen would be the first self-creating, self-maintaining system, the first teleodynamic system, the beginning of life. It only requires a few types of molecules and none very complicated (no RNA or DNA). Deacon carefully points out that autocatalysis by itself is self-undermining and containment by itself is self-undermining, but the combination of autocatalysis and containment would be self-sustaining. Furthermore, he points out that a simple impermeable but breakable capsule suffices; a semipermeable membrane is not required. This careful, realistic reasoning is what makes the argument credible. With this first self-replicating autogen, the evolution ratchet begins. Eventually, evolution will produce efficient living cells, with features like semipermeable cell membranes, energy molecules (ATP), and simple information molecules carrying signals about the environment. Later, complex information molecules (RNA or DNA) would evolve. The appearance of the first teleodynamic systems introduce many abstract attributes into the physical world. Autogens are the first nonsentient selves, so we can now say their parts have function, purpose, or value, with respect to these nonsentient selves. When autogens evolve to start using the first simple information signal molecules, we can now say the physical world contains contentful information, representation, and meaning.
Eventually, neurons and brains evolve. Higher levels of teleodynamic systems create emergent mental attributes like sentience, emotions, feelings, intention, and consciousness. Deacon does not solve the "hard problem" of consciousness (qualia), but he advances our understanding of sentience and consciousness, and he is able to answer to some deep questions. Animal brains are sentient because they are dynamically deep, self-creating systems (they have a real self), whereas even complex intelligent computers are not sentient because they are dynamically shallow and not self-creating (they have at most a simulated self). Mind is not based on quantum weirdness — mind emerges at dynamic levels much higher than the quantum level.
Social Science Books
Guns, Germs, and Steel: The Fates of Human Societies by Jared Diamond
This sweeping but easy-to-read book attempts to explain the fundamental causes for the overall pattern of the story of civilization. Specifically, it answers the question: What caused Europeans to dominate the world? Why did Africans, Asians, or Native Americans not colonize Europe, instead? This profoundly anti-racist book makes a convincing case that the root cause is the unique geography of the Mediterranean, which produced a natural environment that had more plant and animal species suitable for farming than any other region in the world.
The Righteous Mind: Why Good People are Divided by Politics and Religion by Jonathan Haidt
Every adult should read this book. Haidt describes how human beings actually make moral judgments. This book is descriptive, not prescriptive. It is based on evidence from years of social research studies on tens of thousands of people. For everyone, our emotions steer our reason (as Hume said). Haidt identifies six moral foundations used by people when they make moral judgments: (1) Care/harm, (2) Liberty/oppression, (3) Fairness/cheating, (4) Loyalty/betrayal, (5) Authority/subversion, and (6) Sanctity/degradation. Everyone uses all these foundations to some degree, but studies repeatedly reveal this key difference: conservatives use all six moral foundations about equally whereas liberals/progressives most often use the first three foundations, especially Care/harm. After understanding how the "other side" thinks, you will be less angry at them, and if you talk to them in their moral language, they will be less angry at you.
Practical Ethics by Peter Singer
Are you searching for a non-religious framework for ethical thinking? Are you searching for a moral system that encompasses both humans and animals in single continuum? What are the relative values of the lives of humans at different life stages: an embryo before it has a brain, an infant, a child, an adult, or a terminally ill old person in a coma on life-support? What are the relative values of the lives of animals of different levels: a human, a chimpanzee, a cow, a chicken, a fish, an ant, or an amoeba? What about plants? Does a group or a species have moral standing, or do only individuals have moral standing? Singer provides a framework for answering these questions. His short answer: We ought to give equal consideration to the interests of all individual sentient beings. An individual with more interests (like a child) is deserving of more consideration than an individual with fewer interests (like a dog).
Inversions by Scott Kim
Gorgeous and extremely ingenious symmetrical designs made with words or names which can be read both right-side-up and upside-down or mirror-reversed.