The best journeys can be those you don't know you need to take. The Phantom Tollbooth, one of those rare children's novels that both delights the adult reader and returns them to a child's perspective, begins in a fug of stasis and ennui. Milo is a bored and boring little boy, baffled by school and disengaged from the world - "there's nothing for me to do, nowhere I'd care to go, and hardly anything worth seeing" – until the day he finds a strange package in his room containing a flatpack tollbooth and an incomprehensible map. He duly assembles the tollbooth, gets into the electric car he's ignored for months, and sets off in desultory fashion for Dictionopolis – "I might as well go there as anywhere."

What he finds is a fantastical land where the abstract concepts that seem so irrelevant at school are made both concrete and surreal: words are bought and sold in the marketplace, and numbers mined out of rocks. Conclusions is an island that's easy to jump to but hard to escape, eating subtraction stew just makes you hungrier, and to reach the Kingdom of Wisdom you must scale the Mountains of Ignorance. Milo's quest is to reconcile the rulers of Dictionopolis and Digitopolis, who are warring over the importance of words versus numbers, and rescue the exiled princesses Rhyme and Reason: his journey, of course, is the road to enlightenment.

He is accompanied on the way by Tock, an earnest watchdog who helps him not to squander our most precious resource, time, and the Humbug, a pompous giant insect who provides light relief and an example of the dangers of lazy thinking. Their journey is punctuated by meetings with other extraordinary characters, such as the floating Alex Bings, who was born in the air and is growing down: he scoffs at the human system of growing upwards and not knowing where you'll stop until you get there ("Why, when you're 15 things won't look at all the way they did when you were 10, and at 20 everything will change again"). Or meet the Soundkeeper, who soliloquises on the many different kinds of silence:

"Have you ever heard the wonderful silence just before the dawn? Or the quiet and calm just as a storm ends? Or perhaps you know the silence when you haven't the answer to a question you've been asked, or the hush of a country road at night, or the expectant pause in a roomful of people when someone is just about to speak, or, most beautiful of all, the moment after the door closes and you're all alone in the whole house? Each one is different, you know, and all very beautiful, if you listen carefully."

It's typical of Juster's insistence on considering things from all angles that he follows this beautiful and stirring speech with Milo's wry thought: "For someone who loves silence, she certainly talks a great deal."

And then there's Chroma, who conducts the colours of the sunset; the Dynne, who loves noise; the Terrible Trivium - literally a "monster of habit" - who chillingly promises that "if you only do the easy and useless jobs, you'll never have to worry about the important ones which are so difficult," along with scores of others, all remarkable, witty and surprising.

Published in 1961, The Phantom Tollbooth is the closest thing we have to a modern Alice in Wonderland; like Carroll's classic, it preaches reason through oddity, exalting rationality while letting the imagination run riot. Both books are full of obsessives ("everybody is so terribly sensitive about the things they know best," sighs Milo), and ought to go over children's heads, but don't. Tollbooth was not expected to be a hit: "Everyone said this is not a children's book, the vocabulary is much too difficult, the wordplay and the punning they will never understand," Juster later remarked. In fact, the genius of his book is that at the end of the journey, the child reader is left like Milo - knowing that there's more to learn, and that they want to learn it.

Neither book talks down to children because both bubbled up from their author without commission or design. Juster wrote the book when he was "trying to avoid doing something else", and found himself thinking back about his relationship with learning as a child (at 10, like Milo, he "spent a large amount of time being uninterested"). The illustrations were similarly a happy accident: Jules Feiffer, who shared an apartment with Juster, came to investigate what all the pacing was about, and ended up contributing his strange, dark, "itchy-scratchy" drawings (as Maurice Sendak described them). Like the words, they are unlikely, but perfectly apt: funny, footloose and scary by turns.

There's one big difference between Carroll and Juster. The more you think about Alice in Wonderland, the more morbid and perverse it becomes. The Phantom Tollbooth's message is bracing but benign: it calls on us to rise to the challenge of the world by paying proper attention to its wonder and difficulty. Boredom and depression are far from merely childish demons, not least because an adult has to battle them for so much longer. When Milo thinks at the book's beginning that "it seemed a great wonder that the world, which was so large, could sometimes feel so small and empty", it must strike a chord with every reader, young or old.

"When a housefly flaps his wings, a breeze goes round the world," says Reason at the end of the book, in a neat riff on community, complexity and the butterfly effect. "Whenever you learn something new, the whole world becomes that much richer." Milo has to leave home to discover how fascinating it was all along.

Tomorrow: Simon Hoggart on Notes from Overground by Roger Green