Field
Numbers, probability, games and proofs.
3 Ideas · 1 Book · 14 questions
Mathematics is the study of numbers, shapes, chance and proof. You do not need formulas to see what it can do. Many of its best results answer practical questions. When should you stop searching? How do you combine estimates? How do you decide when the future is uncertain?
The pieces here explain such results in words first. Where a number matters, the text shows where it comes from. Where an idea is a habit of thinking rather than a theorem, the text says so.
Start with the secretary problem. It asks how long you should look at candidates before you choose one, and it has a surprising answer. You should look at about 37 percent of them first and then take the next one who is better than all of those. Then read about inversion, a way of solving problems by asking what would make them fail. The wisdom of the crowd shows why the average of many independent guesses is often close to the truth.
The best first reads in this field, in this order.
IdeaIntermediate
You see your options one by one, and each one you turn down is gone for good. If you stop too early, you miss something better, and if you wait too long, the best has already passed. You learn the rule mathematicians found for this, how to work it out with ten flats, and why nobody quite knows who solved it first.
7 min read≈ 1,520 words3 questions
IdeaIntro
Ask yourself how to succeed at something, and the answers are often vague. One change to the question makes the answers concrete and quick to find. You learn that change, how to use it step by step on a real plan, where a famous quote about it really comes from, and when the method stops helping.
6 min read≈ 1,350 words3 questions
IdeaIntro
About 800 people at an English livestock fair guessed the weight of an ox, and most of them were far off. You learn why the average of their guesses was still almost exactly right and which three conditions a group needs for this. You also learn why the same group can fail badly when people copy each other.
7 min read≈ 1,630 words3 questions
How a Nobel economist redesigned the markets for doctors, school places and kidneys, and what his book teaches about markets where price does not decide.
10 min read≈ 2,210 words5 questions
