Cambridge Festival Speaker Spotlight

Professor Sarah Hart is a British mathematician specialising in group theory and author. She is Professor Emerita of Mathematics and Fellow of Birkbeck College (University of London) and has recently been announced as the Mathematical Association President during 2026-27.

Sarah will be speaking at Life in Lilliput – The Mathematics of Fictional Realms hosted by the Isaac Newton Institute for Mathematical Sciences on Saturday 22 March, which will explore what mathematics reveals about extreme sizes—in fiction and real life.

What first got you interested in this topic?

I’ve always loved books and reading, since I was a small child. And I was especially drawn to tales of tiny people, like the Borrowers in Mary Norton’s wonderful books. I was delighted by the descriptions of their tiny dwellings under the floorboards of our human houses, with cotton reels for chairs, matchboxes for beds, and postage stamps for pictures on the tiny walls.

When I was older, and chose to become a mathematician, I continued, of course, to love literature, and I relished the occasions when the two subjects intertwined. This happens constantly – the mathematical structures in poetry, the symbolism of numbers like 3, 7, and 12 in fairy tales and folk tales, and mathematical ideas like the fourth dimension that have been used by everyone from Oscar Wilde to Marcel Proust. I got so into this that I wrote a book about these connections, called Once Upon a Prime. One chapter was devoted to what I’m going to talk about in my lecture – the fascinating mathematics of fantastical creatures, like giants, Lilliputians, flying horses, the enormous spiders haunting the Forbidden Forest at Hogwarts, and all the large and small denizens of fairyland.

If we could shrink down to the size of a Borrower, what’s one surprising thing that mathematics tells us about what life would be like?

There are loads of brilliant things about life for a Borrower or other Lilliputian types. Here’s just one of them – we are often told that fleas would be amazing Olympic high jumpers, because if they were the size of humans, they could jump over a house. The thing is that’s totally false. The height you can jump depends on the power of your muscles, but the amount of power needed depends on how much you weigh. Both of these things depend on your volume, so if you scale any creature up or down, if its volume doubles, its weight doubles and the power of its muscles doubles.

So, in fact, the maths tells us that a human-sized flea can jump to the same height that its normal flea-sized friends can. Now, why is this so great for Lilliputians? Because by the same token, a Lilliputian can jump to the same height as a normal-sized human: about one metre. They’ll be springing around all over the place! In the lecture, I’ll show you lots more of the pros and cons of being tiny – it’s not all plain sailing, and we’ll find out whether Lilliput could ever be real.

Who are your favourite fictional giants, and why?

We do seem fascinated by the idea of giants – they feature in folk tales, religious books (think Goliath), fairy tales, and countless works of fiction. And it’s not just books: many films and TV shows have featured giant people or giant animals, from King Kong onwards. My favourite half-giant, naturally, is Hagrid, and in children’s fiction I love the BFG. But I have to say, just for sheer exuberant silliness, you can’t go wrong with Pantagruel.

You might not have heard of him, but he’s the star of a book by Rabelais which has the full, and crazy, title of The Horrible and Terrifying Deeds and Words of the Very Renowned Pantagruel, King of The Dipsodes, Son of the Great Giant Gargantua. It is very, very silly. Gargantua (from whom we get the adjective ‘gargantuan’) is born by climbing out of his mother’s ear. As a baby, his milk was supplied by a herd of ‘seventeen thousand nine hundred and thirteen cows’; his shoes are made from five hundred yards of blue-crimson velvet, and he combs his hair with a nine-hundred-foot comb whose teeth are elephant tusks.

Can we really deduce things about fictional beings? Do we even have any information to go on?

What really helps is when a story gives us some details. Rabelais throws numbers about with complete abandon, so it’s pretty hard to work out what size his giants are. But other authors are much more helpful!

Jonathan Swift, in Gulliver’s Travels, is presenting the book as if written by Gulliver, giving a detailed traveller’s account of his adventures. To convince us that he’s really made this journey, he gives a lot of detail. When he goes to Lilliput, there’s even a passage where he says that the King of Lilliput ordered the Court Mathematicians to measure Gulliver and work out how much food he would need. These mathematicians (with the aid of a quadrant for measuring the vast distances of Gulliver’s body) find that he is exactly 12 times their size in all dimensions, and they conclude from this that he’d need 1,724 times the amount of food that a Lilliputian needs.

We’ll have more to say on this in the lecture, but I reckon that if Gulliver is going to invoke maths in his book, that means it’s fair game for us to have a look at whether that maths really stacks up! In other stories, the exact sizes of the giants or tiny people are not given, but they are described as being just like us, except smaller or larger. As we’ll see, even that gives us a great deal to go on.  

In The Chronicles of Narnia, creatures like the giant lion Aslan and tiny mice like Reepicheep have very different sizes. How does maths explain the challenges they’d face in such a varied world?

One of the things we see in the Narnia books, but also in the natural world, is that animals come in a huge range of shapes and sizes. I remember when I was a teenager seeing an old film from the 1950s called Them!  that featured giant ants terrorising the inhabitants of small-town America. It begins with a mysterious trail of destruction, smashed windows, a storeroom turned upside down, and curiously the only thing taken is sugar.

The purest hokum, of course, and very enjoyable. But even if you’d never seen an ant before, if you saw a picture of one with no indication of scale, you’d very likely just by instinct be able to guess its rough size. That’s because larger animals are not just small ones scaled up. There’s a natural upper limit on the size of an insect, as we’ll see in the lecture, and a really simple mathematical rule that helps us find it. This same rule can explain all sorts of other things about animals, like why elephants have such big ears, and why ducklings are so adorably fluffy.  

Does maths prove that giants and other creatures from books can’t really exist? Doesn’t that make it a bit of a buzzkill?

One of the great things about maths is that thinking mathematically really helps us understand things, and for me, understanding things makes them even more fun and enjoyable.

There really are mathematical laws about what happens when things shrink or grow, that have implications for what the world is like for large or small creatures. I find these fascinating, and they have genuine real-life importance, for example we absolutely have to understand the maths when we are thinking about how scale models of machines work compared to the full-size versions, or whether (say) a dome twice the size of one we have already built will stay up or fall down. These things are incredibly important!

One of the first people to work out some of the mathematics about being very big or very small was Galileo. In his book about it he actually used giants as an example! We’ll see in the lecture that life would be pretty tough for giants that were exactly like us but scaled up. But I like to think of it like this: if we meet a creature whose existence appears to violate the laws of physics as we understand them, then that PROVES that magic is real. So, we can all still delight in fairy tales. I know I do!