You're reading: Posts By Christian Lawson-Perfect

We want your best #proofinatoot on mathstodon.xyz

Mastodon is a new social network, heavily inspired by Twitter but with a few differences: tweets are called toots, it’s populated by tusksome mammals instead of little birds, and it’s designed to run in a decentralised manner – anyone can set up their own ‘instance’ and connect to everyone else using the GNU Social protocol.

Colin Wright and I both jumped on the bandwagon fairly early on, and realised it might be just the thing for mathematicians who want to be social: the 500 character limit leaves plenty of room for good thinkin’, and the open-source software means you can finally achieve the ultimate dream of maths on the web: LaTeX rendering!

Timetabling choreography with maths

Earlier this week my sister-in-law (“SIL” from now on) sent me an email asking for help. She’s a dance teacher, and her class need to rehearse their group pieces before their exam. She’d been trying to work out how to timetable the groups’ rehearsals, and couldn’t make it all fit together. So of course, she asked her friendly neighbourhood mathmo for help.

My initial reply was cheery and optimistic. It’s always good to let people think you know what you’re doing: much like one of Evel Knievel’s stunts, it makes you look even better on the occasions you succeed.

I’d half-remembered Katie’s friend’s Dad’s golf tournament problem and made a guess about the root of the difficulty she was having, but on closer inspection it wasn’t quite the same. I’m going to try to recount the process of coming up with an answer as it happened, with wrong turns and half-baked ideas included.

The 12th Polymath project has started: resolve Rota’s basis conjecture

Timothy Chow of MIT has proposed a new Polymath project: resolve Rota’s basis conjecture.

What’s that? It’s this:

… if $B_1$, $B_2$, $\ldots$, $B_n$ are $n$ bases of an $n$-dimensional vector space $V$ (not necessarily distinct or disjoint), then there exists an $n \times n$ grid of vectors ($v_{ij}$) such that

1. the $n$ vectors in row $i$ are the members of the $i$th basis $B_i$ (in some order), and

2. in each column of the matrix, the $n$ vectors in that column form a basis of $V$.

Easy to state, but apparently hard to prove!

Watch this bold decision-maker score 100 at the “is this prime?” game

Fan of the site Ravi Fernando has written in to tell us about his high score at the “is this prime?” game: a cool century!

I’ve been a fan of your “Is this prime?” game for a while, and after seeing your blog post from last May, I thought I’d say hi and send you some high scores.  Until recently, my record was 89 numbers (last March 12), which I think may be the dot in the top right of your “human scores” graph.  But I tried playing some more a couple weeks ago, and I found I can go a little faster using my computer’s y/n buttons instead of my phone’s touch screen.  It turns out 100 numbers is possible!

Watch in amazement:

But, to the delight of prime fans everywhere, he didn’t stop there:

Today I even got 107 – good to have a prime record again.

Well done, Ravi!

Now is a good time to point out that the data on every attempt ever made at the game is available to download, in case you want to do your own analysis: at time of writing, there have been over 625,000 attempts, and 51 is still the number that catches people out the most.