This semester I’ve been teaching a module that covers a couple of different maths topics, and have been setting little puzzles for my students to complement what they’re learning – and some of them have been quite fun to write and play with. I thought I’d share some of them here, so you can enjoy them too.
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Carnival of Mathematics 206
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of June and hosted by Stormy, is now online at Storm Bear World.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
What does craiyon/DALL·E mini ‘think’ mathematics and mathematicians look like?
You may have seen DALL·E mini posts appearing on social media for a little while now – it’s been viral for a couple of weeks, according to Know Your Meme. It’s an artificial intelligence model for producing images, operating as an open-source project mimicking the DALL·E system from company OpenAI but trained on a smaller dataset. Actually, since I had a play with this yesterday it’s renamed itself at the request of OpenAI and is now called craiyon. Since the requests all take between 1-3 mins to generate, I’m not going to re-generate all the images in this post using craiyon so that’s why they have the old ‘DALL·E mini’ branding.
AI image generation is a massively impressive technical achievement, of course. craiyon doesn’t create as stunning images as DALL·E 2, but still it can create some ‘wow’s.
What’s interesting, sometimes, is how it interprets a prompt. The data craiyon is trained on is “unfiltered data from the Internet, limited to pictures with English descriptions” according to the project’s statement on bias, and this can lead to problems including that the images may “reinforce or exacerbate societal biases”.
To see that in action, we can take a look at how the model manifests cultural expression around mathematics. When I gave it the simple prompt ‘mathematics’, it produced this.
Carnival of Mathematics 205
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of May and hosted by Rob, is now online at Rob Eby’s Math Blog.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
Prime Run
Here’s a game I’ve been trying to make for a while.
For a while I’ve had a hunch that there’s fun to be had in moving between numbers by using something related to the prime numbers.
Over the years I’ve tried out a few different ideas, but none of them ever worked out – they were either too easy, too hard, or just not interesting. This time, I think I’ve found something close enough to the sweet spot that I’m happy to publish it.
Prime Run is a game about adding and subtracting prime numbers. You start at a random number, with a random target. Your goal is to reach the target, by adding or removing any prime factor of your current number.
Didn’t Graduate Texts in Mathematics
Every now and then a phrase pops into my head and won’t leave until I write it down or tell it to someone else.
One day the little voice in my head suggested putting “Didn’t” before the classic series of maths textbooks, Graduate Texts in Mathematics.
So I found a cover of a GTIM book, stuck “Didn’t” on the front and changed the title to an in-joke about not understanding category theory, and was happy with my life.
But then I thought that it would make sense to make a whole series of these, so I spent a couple of hours making a meme generator.
What we call mathematics
I notice in the news is an issue of whether we should have a different name for early maths. It’s actually quite interesting – and quite a problem – the different things we call ‘mathematics’.