### With humor and charm, mathematician Eduardo Sáenz de Cabezón answers a question that’s wracked the brains of bored students the world over: What is math for? He shows the beauty of math as the backbone of science — and shows that theorems, not diamonds, are forever. *In Spanish, with English subtitles.*

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### Watch

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### Glossary

**defend**– resist an attack made on (someone or something); protect from harm or danger**permeate**– spread throughout (something); pervade**pitfall**– a hidden or unsuspected danger or difficulty**hypotenuse**– the longest side of a right-angled triangle, opposite the right angle**conjecture**– an opinion or conclusion formed on the basis of incomplete information**theorem**– a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths

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### Think about it

*Answer the questions below. Pause at times indicated in brackets.*

- What do people really mean when they’re asking what maths is for? (1:05)
- How do mathematicians tend to react when asked what maths is for? What two main categories do they fall into? (2:42)
- How does the third category differ from the others? What example does Eduardo give to illustrate this? (4:27)
- Why does Eduardo refer to Pythagorean theory? (5:26)
- What idea about space did Lord Kelvin come up with? (7:30)
- Was Kelvin’s idea right? Why? Why not? (9:09)
- In what way is a theorem better than a diamond when it comes to love?

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### Practice makes perfect

Fill in the gaps with the missing words. Use ONE word per blank space.

Well, we mathematicians devote ourselves to come ________ with theorems. Eternal truths. But it isn’t always easy to know ________ difference between an eternal truth, or theorem, and a mere conjecture. You need proof. For example, let’s ________ I have a big, enormous, infinite field. I want to cover it ________ equal pieces, without leaving any gaps. I could use squares, right? I could use triangles. Not circles, those leave little gaps. Which is ________ best shape to use? One that covers the same surface, but ________ a smaller border. In the year 300, Pappus of Alexandria said the best is to use hexagons, just like bees ________ . But he didn’t prove it. The guy said, “Hexagons, great! Let’s go with hexagons!” He didn’t prove it, it remained a conjecture.“Hexagons!” And the world, as you know, split ________ Pappists and anti-Pappists, until 1700 years later when in 1999, Thomas Hales proved that Pappus and the bees ________ right — the best shape to use was the hexagon. And that became a theorem, the honeycomb theorem, that will be true forever and ever, for longer ________ any diamond you may have.

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