“The universe (which others call the Library) is composed of an indefinite, perhaps infinite number of hexagonal galleries.” That’s how Jorge Luis Borges starts The Library of Babel, beloved by maths geeks and book nerds alike for the way it toys with the mathematical concept of infinity.

I liked the short story so much I nicked its main idea when I started my Libreria bookshop, blanketing the store’s insides with mirrors to trick you into thinking you are in a “perhaps infinite” space. (The mirrors require a near infinite amount of cleaning, but there we go.)

As for maths professor Sarah Hart, she’s so enthralled by the ways her academic field has enriched the work of poets and novelists that it is the subject of her ebullient debut book. “By seeing mathematics and literature as complementary parts of the same quest to understand human life and our place in the universe, we immeasurably enrich both fields,” she writes.

She’s not wrong. Some of Hart’s examples will be familiar to readers – such as the way numerology shapes the structure of Eleanor Catton’s Booker prize-winning The Luminaries, or how maths puzzles are dotted throughout Alice’s Adventures in Wonderland (written by a maths professor, of course).

Most, however, were new on me. I’ve read Moby-Dick, but the references to mathematical curves known as cycloids totally passed me by. Hart does a great job of showing how Melville’s epic work “abounds with ideas that a mathematically attuned eye can detect and explore” (which probably explains why I missed them), and these can “add an extra dimension to our appreciation”.

It’s the same with Middlemarch – I didn’t register that the mocking of Mr Brooke includes a clever little mathematical construct: “We all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”

As Hart rightly points out, “The world of mathematics is a glorious source of metaphors” – and “once you are on the lookout, you’ll see [maths] everywhere”.

Hart uses Melville and Eliot to make a broader argument about how “the perceived boundary” between maths and other creative arts “is a very recent idea”, and that “for most of history, mathematics was part of every educated person’s cultural awareness”. That’s why these writers felt comfortable using mathematical ideas – and they also knew their readers were similarly attuned.

Perhaps the most interesting part of the book looks at little-known works, such as the slim volume by French writer Raymond Queneau that was published in 1961 and somehow contains a 100 trillion poems. Queneau managed to squeeze in that many by printing 10 sonnets with each line capable of being combined with any from the nine others, creating a preposterously large number of possible poems.

As Hart suggests, it raises some interesting philosophical questions, such as whether can we say Queneau wrote all of these potential sonnets, or in what sense the different poems even exist at all. Small wonder Hart makes the bold claim that poetry is “simply the continuation of mathematics by other means”.

The book is not perfect – like a messy mathematical theorem, it could have done with being stripped back and made shorter, more elegant. But you can’t help but be won over by Hart’s playful exuberance – and she’s up there with Richard Dawkins or Marcus du Sautoy in having the rare gift of being able to explain thorny scientific ideas using canny cultural references.

At a time when the British education system is becoming suffocatingly narrow, with arts and music being dropped by schools, and our universities falling behind America in encouraging multidisciplinary studies, Once Upon a Prime is a joyous reminder of the way so much human creativity comes from joining the dots between seemingly disparate fields.

Hart helps bring to life what she calls “the enduring conversation between literature and mathematics” – encouraging us to read and roam more widely, whether it is scientists getting stuck into novels, or fiction-lovers throwing themselves at maths conundrums. I’ve no idea if you’ll end up happier if you follow her advice. But one thing’s for sure, as Hart herself warns: “You’re going to need a bigger bookcase.”

• Once Upon a Prime by Sarah Hart is published by Mudlark (£16.99). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply