You're reading: Irregulars

What does DALL·E ‘think’ mathematics and a mathematician looks like?

DALL·E is an Artificial Intelligence (AI) system that has been designed to generate new images given a text prompt. It’s very much like doing a Google image search with one very important difference: DALL·E doesn’t try to find existing images to match your query, but creates a handful of new ones that it hopes will fit the bill.

A little while ago Peter Rowlett tested a similar system, DALL·E mini, to see what it thought of mathematics. This tool has since been renamed craiyon at the request of DALL·E’s creators, but the original name hints at the relationship between the two: craiyon might be thought of as a cut-down version of DALL·E: it’s easier to store and cheaper to run, which are possibly some of the reasons why craiyon is open to all whereas DALL·E is, for the time being at least, invitation-only.

I received an invitation, so signed up and carefully chose my first submission: “Leonhard Euler with a ruler in a boiler“. Peter noticed and suggested I might do something a little more productive with my new found powers and replicate his craiyon experiment. If you’re at all interested in the development of AI you’ll be aware that they tend to pick up biases that exist within the training data sets, which is part of what prompted Peter’s explorations with craiyon. What would the meatier DALL·E make of the same inputs, given its larger set of training data?

There’s only really one way to find out…

“Mathematics” prompted a very different set from DALL·E than it did from craiyon: here, all four images depict handwritten pseudo-maths that looks very much like what you’d expect to see in a movie mathematician’s notebook – right down to the fact that it’s complete nonsense.

Next up is “data science”, which is…

… utterly disappointing, especially next to craiyon’s efforts which, if no more illustrative of the field, were at least interesting. So far, no people.

Peter’s next input was “doing mathematics”, so that was mine too:

Classrooms, as with craiyon’s output, featuring conspicuously white folk throughout. I feel that these students are older than those represented in craiyon’s images. Something I noticed here is that DALL·E’s people are a lot more realistic than the more abstract smudge-faced creations by craiyon (an issue which is discussed by craiyon’s creator in an article in Science Focus).

“Mathematics on blackboard” resulted, as with craiyon’s images, in some sort-of mathematical notation on a blackboard. Again, this brought to mind the kind of thing that turns up in the background in lazier movie depictions of mathematics at work. It feels, to me, a little more realistic than craiyon’s depictions, but it’s still nonsense.

Peter’s difficulties with getting craiyon to see mathematics as something that exists naturally in various contexts were also evident with DALL·E, but manifested themselves in different ways, as we will see later. The next thing Peter tried was “mathematics lecture”. DALL·E’s results seem a little less dry than craiyon’s, with stronger colours and a feeling that these lectures are a little more participatory:

Still entirely white, though, but less thoroughly masculine than our attempt to generate people “doing mathematics” earlier. Disappointingly, “darth vader presenting mathematics” didn’t replace the teacher in similar scenes with everyone’s favourite Sith Lord, as craiyon did:

I don’t know what it means, but “Maamatiec mate” is a phrase that was disappointingly absent from my own mathematics education.

DALL·E’s depiction of “iron man saving the world using mathematics” is less MCU and more comic book, and also introduces our first non-white character so far:

At this point, Peter started to try looking at some other disciplines that incorporate mathematical themes. Craiyon’s images for “mathematical physics” and “mathematical biology” were swirly. DALL·E’s were…

… equations. It seems physicists do them on blackboards whilst biologists are more paper-based. “Statistics” received similar treatment to “data science”, earlier, although there were some charts involved this time:

DALL·E’s response to “Mathematics in chemistry” lacked the brightly coloured liquids in glass flasks and replaced them with blackboard or paper-based pseudo-notation. “Engineering mathematics” is the first of these discipline crossovers to introduce people, but only in two of the four images (whereas all four have pseudo-notation). These two people look pretty serious: engineering is clearly not a subject to fool around with. Interestingly, they’re not obviously in a classroom, which contrasts with craiyon’s output.

Peter was curious about craiyon’s decision to represent social science with people writing on blackboards. DALL·E does away with the people entirely: it’s all about the pseudo-notation. I’m feeling that some pseudo-trig and pseudo-relativity is going on in a couple of these. DALL·E appears to be, if anything, even stronger than craiyon on the “mathematics as a collection of symbols being taught” front.

So what does DALL·E think a “mathematician” looks like? There’s certainly a lot more colour (all of craiyon’s responses to this input were in black & white), and a little diversity (though the older one is still white and still looks grumpy).

These all feel fairly modern, but I’m staying faithful to Peter’s quest, so a “modern mathematician”, according to DALL·E, looks like this:

And a “historical mathematician” looks like this:

These last three results all show more diversity than craiyon’s results, but I’m suspicious of the fact that in each case there is precisely one non-white character and precisely one feminine character in each set (sometimes these are the same character). The earlier images that involve representations of people do not seem to follow this trend, but none of those have specifically asked for a mathematician. Notably, the Iron Man images do appear to follow it when accounting for the fact that the input specifically asks for a “man”. Asking specifically for a “female mathematician” has similar results, with precisely one non-white character depicted:

And “black mathematician” includes precisely one character who does not appear overtly masculine.

I feel that “young mathematician” fits the trend as well:

As does “21st century mathematician, although one image doesn’t involve people at all:

So DALL·E’s results aren’t quite the same as craiyon’s: it doesn’t produce quite the density of “old white men with beards from a bygone age”. The results are still rather white and rather masculine, though less-so, but the “one non-white, one non-masculine” trend throughout these image sets does make me wonder whether this is the AI’s choice, or whether it’s a human-implemented adaptation to the input process, which is a possibility that has been suggested elsewhere.

May I end by wishing meath 2 teaith matmamty to you all.

One Response to “What does DALL·E ‘think’ mathematics and a mathematician looks like?”

Leave a Reply

  • (will not be published)

$\LaTeX$: You can use LaTeX in your comments. e.g. $ e^{\pi i} $ for inline maths; \[ e^{\pi i} \] for display-mode (on its own line) maths.

XHTML: You can use these tags: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>