## Don’t trust the small numbers

In mathematics, the Pólya conjecture is true for every natural number up to 906,150,256… and then it’s not.

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# Category: Mathematics & statistics

## Don’t trust the small numbers

## Abnormal normal dice

## Experimental pi

## Will Rogers paradox

## The Yale blackboard rebellion

## Da Vinci’s fractal trees

## Cosmic ladder (Part 2)

## Cosmic ladder (Part 1)

## Ghost leg

## Mathematical collective

## Math homework

## Mathematical coincidence

## The birthday paradox

## Prehistoric mathematics

## Infinity and beyond

## First vanishing point

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In mathematics, the Pólya conjecture is true for every natural number up to 906,150,256… and then it’s not.

A pair of Sicherman dice have numbers ranging from 1 to 8 on their faces, but roll two of them together and they produce the same totals as a pair of normal dice.

If you have a piece of striped paper and some sticks, you can estimate the value of pi through a simple experiment.

Someone (not Will Rogers) once joked that “When the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states.” This quirk of statistics has some surprising implications for cancer survival rates.

In 1830, nearly half of the mathematics class at Yale was expelled for refusing to use a blackboard in their exams.

Leonardo da Vinci observed that tree branches together are always as thick as the trunk beneath them. This is true, and there are some good ideas why.

To measure distances in deep space, you need to look for candles in the darkness. [2 of 2]

It’s a lot more difficult to measure distances in space than you might think. [1 of 2]

Ghost leg is a technique to randomly match up two groups – assigning a list of chores to a list of people, for example. And all you need is a drawing of a ladder.

Since 1939 an author named Nicolas Bourbaki has published a series of volumes on pure mathematics. But Bourbaki does not exist.

In 1939 a student at UC Berkeley copied down two homework problems from the class blackboard. He solved them in a few days… and then discovered that they were two of the thorniest unsolved theorems in statistics.

A billionth of a century is approximately pi seconds. The diameter of the Earth is roughly half a billion inches.

Put 70 people in a room and there’s a 99.9% chance that two of them share a birthday. Why?

The Ishango bone, found in what is today part of the Democratic Republic of the Congo and dating back 20,000 years, may contain some of the earliest evidence of mathematical thought.

The set of natural numbers is infinite: 1, 2, 3…. The set of real numbers is also infinite: 0.1, 0.11, 0.12, 0.2… but it’s larger than the infinity of natural numbers. Georg Cantor devised an elegant argument to prove these different infinities.

Masaccio’s Holy Trinity is possibly the earliest surviving work of art to use a single vanishing point. His work and that of Brunelleschi triggered a Renaissance explosion of mathematical perspective in art.