How do you bring the history of mathematics to life through illustration? Kat Flint, illustrator of A Little History of Mathematics, chatted with author Snezana Lawrence to discuss.
A Little History of Mathematics is a lively, accessible history of mathematics throughout the ages and across the globe. All aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from?
What is your “relationship” with mathematics? Is it positive or negative, or anything in between?
I always did pretty well with maths at school, which was a continual mystery to me because I found it massively intimidating and never really understood the “Why?” of any of it… but I was good at learning formulae and got the answers right. It was a feat of memory rather than actual understanding, in part due to the way maths is taught in the UK – the fun stuff doesn’t get a look in until university level, and there’s very little time given to the history and reasoning behind it all which makes it pretty dry. When you start to think of it as a series of tools developed to solve specific human problems, it takes on a whole new meaning – it makes me a little sad that we don’t tell those stories to kids, because so many people don’t see the use of it beyond the basic calculations required for everyday life.
From Chapter 5 ‘The Greatest Mathematical Bestseller of All Time’
What challenges does mathematics pose for an illustrator?
I wanted to challenge the notion of maths as a purely serious subject, to reflect the playfulness of thought that goes hand in hand with being a genuinely innovative thinker, as the finest mathematicians clearly are. It’s in my nature to be playful in my work too, and I really enjoy puzzles, puns, nerdy visual jokes… there’s a dose of silliness in my illustrations as a result, with a focus on the “human-ness” of it all. The visual interest, for me, lies in humans doing things – even the most abstract concepts were developed for something.
Each chapter brought a new hurdle – mathematical thought just gets weirder and denser as time goes on. I was determined to do justice to each concept and time period, which required a lot of research, not least getting my head around the core maths in each chapter. I had to get up to speed with a whole lot of complex thought as I received each draft, most of which was completely new to me. It felt important to get it right though (or as right as I could…). I suspect mathematicians are quite particular about details, which makes for an intimidating audience… I’m sure I’ve made plenty of errors in spite of my best efforts!
On a more practical level, this project involved a lot of historical portraits where original source references were few and far between – trying to depict someone in a new way without leaning too heavily on the one known image of them was tricky, as was the fact that a lot of the big names through the ages are very similar-looking white, European blokes. The hair-dos, beards, glasses and moustaches are doing a lot of heavy lifting in my illustrations!!
Lastly, I found the carving of the blocks a real technical challenge due to the sheer number of fiddly diagrams and grid lines… I tried to avoid them as much as I could, favouring people over formulae, but in many cases there was no getting around it. Carving perfect lines for hours along the edge of a ruler rather sucks the joy out of it, so I went a little more rustic and freehand… trying to strike a balance between “made by a human hand” and “mathematically correct” was an interesting one to manage.
From Chapter 10 ‘A Mathematical Tapestry’
What was the most fun/interesting thing about mathematics you learnt about whilst doing illustrations for this book?
My top ten newly-acquired maths facts:
1. The Egyptians discovered Pythagorean triangles before Pythagoras…
2. There have been more maths-based cults and secret societies than you might imagine…
3. The are different sizes of infinity! (Some infinities are more infinite than others… WHAT?!)
4. Lewis Carroll (of Alice in Wonderland fame) was also an avid amateur mathematician, dabbling in logic problems…
5. Mathematical history is an interesting clash of ego and collaboration: most major discoveries seem to have arisen from people either arguing with each other or just plain showing off.
6. You can’t move for child prodigies in the maths world. (Honestly, if you’ve not secured a lecturing post by the age of 19 can you even call yourself a mathematician…?)
7. Everyone in the history of mathematics seems to have hung out with Paul Erdos at some point…
8. A long-thought-impossible shape that creates a never-repeating tiled pattern was discovered by accident, by a hobbyist called Dave. The fact he just called it “The Hat” makes me smile. (Oh – and he immediately discovered a second one).
9. A famous mathematician whose work continues to influence modern thinking was entirely made up by some students for a laugh…
10. Don’t stay at the Hilbert Hotel – it always has vacancies, but once you leave your room you’ll definitely never find it again.
From Chapter 15 ‘Harmony of the World’
What would you say to people about mathematics now as opposed to what you would have said six months ago? Have your views on mathematics changed at all?
Illustrating this book has confirmed something I always suspected – that mathematicians are every bit as creative as artists. So much so, that mathematical history is littered with polymaths – writers, painters, soldiers, musicians, monks, philosophers all moonlighting as mathematicians. It takes an extraordinary leap of creative thought to dig into concepts so abstract that they can’t even exist within reality as we know it… and yet there are people whose minds take them there, not just to explore but to do some really hard calculations while they’re at it, figuring out relations and behaviours of imaginary things within imaginary frameworks in ways that somehow miraculously can be applied in the ‘real’ world. It all just blows my mind and makes me wish I was smarter.
From Chapter 4 ‘The Secrets of Pythagoreans of the World’
Do you have any advice for aspiring book illustrators?
I’m loathe to call myself a book illustrator as this is the first book I’ve worked on – usually I make larger scale prints plucked from the depths of my own brain, so take my advice with a pinch of salt. I would say, however, that it’s really important to develop a distinctive, original style that is identifiably yours – you want people to glance at a piece and think “Oh! I know that artist!”, and for clients to seek you out because they want your specific style.
It sounds basic, but really get to know the material you’re illustrating – for me, it’s important to understand and connect with the core points being made, whether it’s a concept, an emotion or a moment in a plot. It’s usually pretty obvious from the text, and you can’t effectively illustrate without reading (or I can’t, at least). Find the things that will be attention-grabbing even to someone who knows nothing of the subject matter.
Don’t be scared to ask clarifying questions of the client when you’re not sure what direction to go in – better that than wasting your time heading off in totally the wrong direction. Take feedback with good grace, but push back politely if you know it’s missing something important. Adapt images to better fit the brief when necessary – the client is the boss! – but make sure you still produce work you’re proud of. After all, your name will be on it forever…
Lastly: make sure you can competently draw faces in your own style. This doesn’t necessarily mean photo-real – they can be as stylised and quirky as you like as long as they’re recognisable. Portraiture is vital for so many illustration jobs, and it’s a valuable skill that you’ll most likely need at some point.
From Chapter 26 ‘The Quiet Birth of Chaos’
How did you come up with the concept for each illustration in A Little History of Mathematics?
Illustrating something so abstract (especially in the later chapters when you’re immersed in imaginary dimensions, competing concepts of infinity, logical paradoxes and all the rest…), I was constantly on the look-out visual ‘hooks’ to build meaningful images around. Rachel at Yale did an amazing job providing helpful start points for each chapter, but I still had a fair few moments where I texted my partner in a panic, saying things like “OMG, how do I linocut the mathematical concept of THE VOID…?!” or “What does the 26th dimension look like?!?”
The hooks weren’t always obvious or easy to find, and required careful reading paired with a pool of reference images that I gathered for each chapter: portraits, diagrams, historical documents, examples of maths being applied in the real world… I’m always searching for something to spark an “Aha!” moment – usually, something that makes me smile or that acts as an unexpected visual bridge between key ideas.
Once I had a hook or two, I started to sketch panel ideas in a very quick, rough fashion, playing with the composition and flow of the image until it felt balanced and interesting. I also did a few loose, preparatory sketches of any people involved, to render them in my own style before I worked them into the image – it’s very important to me not to just mimic an existing image, but to create something unique. I usually drew each panel three or four times (more if it was a hard one!), refining it a little more each time and fleshing out the details before working it up to scale. There are a lot of motifs and compositional elements that echo through the book’s 40 panels – I wanted to give a sense of continuity over time, as one idea sparks the next.
About Kat Flint
Kat is a printmaker, illustrator and designer
Website: www.katflint.com/
Instagram: @flintkat
Illustration from Chapter 4 ‘The Secrets of Pythaogoreans’
About Snezana Lawrence
Snezana Lawrence works as a senior lecturer at Middlesex University, London, and was the chair of the History and Pedagogy of Mathematics International Study Group between 2020 and 2024. She is the author of The New Year’s Present from a Mathematician and editor of Mathematicians and Their Gods.
X: @snezanalawrence and @mathshistory
Website: snezana-lawrence.com/
