【摘录自可轻松阅读的部分，省略了所有数学问题的推导细节】

Prologue

Calculus is the math study of change. Its essence is best captured by its original name, “fluxions,” coined by its inventor, Isaac Newton.

It’s a game they love playing together– so often the basis of friendship between men – a constant while all around them is in flux.

Continuity (1974-75)

He’d suggest a problem, very gently, not at all insistent, and then he’d step aside.

Mr. Joffray was an incredible cheerleader. He’d sometimes watch me and Ben, the tortoise and the hare, with a look of such admiration, almost awe, and happiness too.

He made me sound generous, and heroic.

Pursuit (1976)

The first hint that something was wrong with this gauzy vision came when I concocted a question of my own.

I spent months on it. It was frustrating, tantalizing, and delicious.

What I didn’t know yet was that some math problems are unsolvable.

Most differential equations are unsolvable in the same sense. Our library of formulas isn’t rich enough to encompass them. Which makes those few problems we can solve – the ones they give you in high school – seem all the more precious.

Relativity (1977)

What I couldn’t bring myself to admit was that my first math course in college had utterly deflated me and changed the way I viewed myself. It was a proof-oriented course on linear algebra, aimed at freshmen who had aspirations of being math majors……I read the book, did the homework, paid careful attention in lecture, and had no idea what was going on.

Sometimes, as in relativity theory, a frustrating problem becomes clearer when viewed in the right frame.

Irrationality (1978-79)

Some people never find their passion. But by denying mine, I found it and became sure of it.

Shifts (1980-89)

Would he have corrected me and told me life is not linear, that it’s more like the unpredictable currents of a whitewater kayak course?

Proof on a Place Mat (March 1989)

Years later, when Feynman was working on the Manhattan Poject, he was approached by a colleague whose team had been stuck on a problem for three months. “Why don’t you do it by differentiating under the integral sign?” asked Feynman. Half an hour later, the problem was solved.

In the years to come, he’d often show the place mat, like some sacred scroll, to his latest crop of advanced students.

The Monk and the Mountain (1989-90)

In the June 1961 Mathematical Games column in Scientific American, Martin Gardner posed a riddle that has become a favorite in courses on the psychology of creativity

Randomness (1990-91)

A few days later came an unexpected diversion, a rare moment when it seemed like the whole country was arguing over a math puzzle. It all started when Marilyn vos Savant, author of the “ask Marilyn” column for the Saunday ‘Parade’ magazine answered a brain teaser posed by one of her millions of readers.

Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors?

正好前几天 编程模拟了这个三门问题。