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Freakonomics Radio

483. What’s Wrong With Shortcuts?

Freakonomics Radio

Freakonomics Radio + Stitcher

Documentary, Society & Culture

4.632K Ratings

🗓️ 18 November 2021

⏱️ 43 minutes

🧾️ Download transcript

Summary

You know the saying: “There are no shortcuts in life.” What if that saying is just wrong? In his new book "Thinking Better: The Art of the Shortcut in Math and Life," the mathematician Marcus du Sautoy argues that shortcuts can be applied to practically anything: music, psychotherapy, even politics. Our latest installment of the Freakonomics Radio Book Club.

Transcript

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0:00.0

This is a little fairy tale that we all get told as mathematicians.

0:07.0

That's Marcus DeSotoi, who is a mathematician at Oxford University in England.

0:12.0

As for this fairy tale, I don't know whether it's true or not, but who cares?

0:17.4

The story takes us back to Germany in the late 18th century and a schoolboy named Karl Friedrich

0:23.2

Gauss. The young Gauss sitting eight, nine years old in his class, the teacher wants to get a little

0:29.1

bit of rest to set them a problem, that it'll take them ages to actually do.

0:34.8

Young Karl Friedrich Gauss would become one of the most remarkable mathematicians in history.

0:40.8

There are more than 100 theorems, formulas, models, and other math terms named after him,

0:46.5

but that was later. At the time of our story, he's just a very bright young student,

0:51.3

and the teacher gives the class this problem to solve. As DeSotoi said, it's not a particularly

0:57.4

interesting problem, the teacher says you've got to add up the numbers from one to a hundred,

1:03.2

and most of the class sets off and they go one plus two plus three plus three six.

1:08.6

Go ahead, try it for yourself. Add up the numbers from one to a hundred. I'll give you a minute.

1:19.8

Are you done? If not, then you are quite a bit slower than young Gauss.

1:25.6

Karl Friedrich Gauss immediately writes down a number on his chalkboard, slams it down on the desk,

1:31.2

and says there it is, and the teacher thinks he's being impudent, but looks down, sees,

1:36.9

but that's the correct answer. How did you get that so quickly?

1:40.9

You may be thinking, well, Gauss is plainly a math prodigy, so he just added up the numbers in his head,

1:47.1

really fast. That's not what he did. According to the story, here's what Gauss told his teacher.

1:53.7

He said, look, the rest of the class, they're all starting at the beginning and just plotting on

1:58.6

through this journey. I combined the beginning and the end of the journey, so one plus a hundred is

2:04.5

a hundred and one. Two plus ninety nine is also a hundred and one, three plus ninety eight, a hundred and one.

...

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