Season 9 Episode 2

In this episode, Jack joins the club to show us a maths theorem from a TV show and explore how it works.

OOMC Season 9 Episode 2

Watch on YouTube

Further Reading

PROMYS Europe

PROMYS Europe is six weeks of challenging and stimulating mathematical exploration for mathematically ambitious school students aged 16+ from across Europe. It's hosted in Wadham College and the Andrew Wiles Building (the Maths department) in Oxford.

There’s also the original PROMYS in Boston and PROMYS India.

The application problem set is here. Ten maths questions, all of them interesting and difficult. Could be worth a look, even if you have no intention of applying.

 

Futurama Theorem

There’s a surprisingly detailed plot synopsis for the Futurama episode in question on Wikipedia.

This webpage has a bullet-point list of the swaps, which is easier to read, and also a plain English description of the solution (I’m using a web archive link because the original page appears to be down at the time of writing; if you find that the original page is up again, please let me know via the email address at the end of the page).

The theorem is due to Ken Keeler, who has a degree in applied mathematics and who wrote for The Simpsons and Futurama. I sometimes get asked about what you can do with a maths degree. I sometimes wonder what you can’t do with a maths degree.

 

Permutations

If you liked the charts that we drew to illustrate the swaps, then here’s a NRICH activity for you all about bellringing.

There’s a page on the UCL website for their MATH0007 course including notes on permutations, and it describes the other notation that Jack was using.

The Oxford equivalent is perhaps our course in the second term of first year called Groups and Group Actions, but that course contains a lot of other things too, such as...


Group theory

You could find out more about Group Theory from the Oxford notes above, but perhaps a nicer way to get some sense of what this topic is about would be to look at this NRICH page. Groups might be included in your Further Maths A-level, depending on exam board and which units you're doing. Here's a massive cheat sheet for A-level groups from PMT Physics and Maths Tutor, which might give you an idea of what you'll learn when it comes up.

Jonah discussed some symmetry theory and group theory in this past episode of OOMC; Groups, bosons, & monsters.

 

Derangements

If everyone’s mind is in the wrong body, then the permutation is called a derangement. You can find out more about derangements with this past episode of OOMC; Everything Wrong.

There is some cool notation for the number of possible derangements of $n$ objects; some people write !$n$ for the number of ways to put $n$ minds in $n$ bodies with none in the right body. The idea is that it's a bit like the number of permutations, so the number should have notation that's similar to $n$!. Some people write $n$¡, but as far as I know no-one writes ¡$n $. So we can use that for something else. I'll let you decide what that should mean!

 

If you want to get in touch with us about any of the mathematics in the video or the further reading, feel free to email us on oomc [at] maths.ox.ac.uk.

 

Last updated on 24 Jan 2025, 5:04pm. Please contact us with feedback and comments about this page.