# You're reading: Blackboard Bold

### Open Season: Prime Numbers (part 2)

In this short series of articles, I’m writing about mathematical questions we don’t know the answer to – which haven’t yet been proven or disproven. This is the third article in the series, and across two parts will discuss various open conjectures relating to prime numbers. This follows on from Open Season: Prime numbers (part 1).

So, we have a pretty good handle on how prime numbers are defined, how many of them there are, and how to check whether a number is prime. But what don’t we know? It turns out, quite a lot.

### Open Season: Prime Numbers (Part 1)

In this short series of articles, I’m writing about mathematical questions we don’t know the answer to – which haven’t yet been proven or disproven. This is the third article in the series, and across two parts will discuss various open conjectures relating to prime numbers.

I don’t think it’s too much of an overstatement to say that prime numbers are the building blocks of numbers. They’re the atoms of maths. They are the beginning of all number theory. I’ll stop there, before I turn into Marcus Du Sautoy, but I do think they’re pretty cool numbers. They crop up in a lot of places in maths, they’re used for all kinds of cool spy-type things including RSA encryption, and even cicadas have got in on the act (depending on who you believe).

### Maths at the Fringe

Starting next week, the historic city of Edinburgh will be taken over by entertainers of all types, performing comedy, dance, theatre and music, entertaining visitors to their massive world-famous festival fringe. Since discerning mathematicians sometimes also enjoy being entertained, I thought I’d write a roundup of the shows maths has non-empty intersection with.

First up, since we haven’t mentioned him in a while, it’s Alan Turing! No, his reanimated corpse isn’t performing edgy stand-up, but theatre company Idle Motion is performing a visual theatre piece entitled That Is All You Need To Know, celebrating the work of Bletchley Park codebreakers. Alan Turing Alan Turing Alan Turing.

### How to Win at Pointless

For the benefit of overseas readers, or British readers in full-time employment, I should briefly explain the concept of daytime TV quiz phenomenon Pointless. The pinnacle of British public service broadcasting, it’s shown at 5.15pm every weekday on BBC One and is hosted by Alexander Armstrong of comedy double-act Armstrong & Miller, and Richard Osman of comedy double-act Armstrong & Osman. We shall investigate how we can use maths to analyse the show, improve our chances of winning it, and ultimately perhaps improve the show itself.

The aim of the game is in each round to give the most obscure correct answer to a given question. Each question ($Q$) has a large set of valid answers $A_Q$, questions perhaps asking contestants to name “Films starring Bruce Willis” or “Countries without an O in their name”. All the questions have been asked to 100 members of the public prior to the quiz (call this set $P$), and they each have 100 seconds to name as many examples as they can (giving rise to a set $A_p\subseteq A_Q$ for each $p\in P$. The contestant gets a point for every one of the 100 people who named their answer $a$:

$\mbox{score}(a) = \begin{cases} | \{p\in P : a\in A_p \} | & \mbox{if}\ a\in A_Q \\ 100 & \mbox{if}\ a\not\in A_Q. \end{cases}$

So an obvious answer like Die Hard or France will score a lot of points, and an obscure answer like Striking Distance or Central African Republic will score fewer points. Points are bad (hence the title) so it’s better to dredge up an obscure answer than stick with something safe. However an incorrect answer like Avatar or Mexico scores the maximum 100 points. At the end of the round the contestant with the most points is eliminated.

### 2² number theory tricks

Here are some nice number facts and tricks you can try out on your friends. They will work without understanding how, but with a little investigation you should be able to figure out how each one works.

### Here’s How Little I See Your Point

You may have seen an article linked to last week, written by Jordan Weissmann at The Atlantic. The article was titled ‘Here’s How Little Math Americans Actually Use At Work‘, although mysteriously this journalist makes use of some mathematical analysis of survey data, and not only that, the data appears to show that 94% of Americans claim to use mathematics as part of their daily job.

The article discusses people’s misconceptions about the future utility of what they were learning, as well as the divide between using ‘any math’ and ‘advanced math’, which includes calculus, algebra and statistics. The number of Americans who admitted to using this type of maths appears to drop off once you get to anything more complicated than fractions, and also presented is an analysis of this divide by job type.

A very well-written and thoughtful response to this has already been posted at mathematics professor Bret Benesh’s blog, which gives four reasons why the article annoyed him (and probably several other people too).

### Seeking election-themed graph blunders

Since we’d like to write a funny post about it, if you’ve been sent any literature for the upcoming local elections in the UK (or indeed, from the past or from other elections around the world) which contains a graph or chart of questionable rigor, we want to know about it.

As an example, Colin Beveridge sent us this classic from his doormat:

We’ll be awarding bonus points for inaccurate pie charts, exaggerated/meaningless bar sizes, the complete absence of axis label or scale, the use of ‘Can’t win here!’ and any other sneaky/incompetent features. Email your submissions to root@aperiodical.com, and watch out for a roundup post if we collect a sizeable pile.