Where things are and what they look like -- "I vote for Euclid" -- How many holes does a straw have? -- Giving the same name to different things -- A fragment of the sphinx -- "His style was invincibility" -- The mysterious power of trial and error -- Artificial Intelligence as mountaineering -- You are your own negative-first cousin, and other maps -- Three years of Sundays -- What happened today will happen tomorrow -- The terrible law of increase -- The smoke in the leaf -- A rumple in space -- How math broke democracy (and might still save it) -- I prove a theorem and the house expands

"Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. Geometry doesn't just measure the world-it explains it. Shape shows us how"--