[In this science fiction novel],
the crew of the first spaceship to ever visit a neutron star discover that the star is inhabited by a race - the Cheela - whose metabolism is based on nuclear reactions instead of chemical reactions. Thanks to this the Cheela live about one million times faster than terrestrial life, and in a few days (for the humans) they progress from prehistory to space age.
What may interest you is the rather detailed description of how the neutron star inhabitants, still in their stone age, discover arithmetics.
A clan of Cheela need to abandon their living place and move to a safer region that was discovered by a pack of hunters, so they're collecting pods to eat during the journey. One of the discoverers, a female Cheela called Great-Crack, wonders if they're collecting enough and has an idea (Forward's wonderlful sentence is "in a flash of inspiration, one of the greatest mathematical minds ever hatched in the past or future of the cheela made a great leap of abstract thought").
Great-Crack has conserved a seed from each pod she's eaten during the voyage. She puts the seeds in a row, then she takes some of the gathered pods and puts them in a row as well, one beside each seed: that' how many pods a Cheela needs to eat in travel. Making a row for each member of the clan, she runs out of pods before she's made a row for everybody, so she realizes there's not enough food.
The leader of the clan, trusting his intuitive notion of quantities, believes they're ready to go ("There must be enough there to feed all the clan, for I have never seen so many pods before") and is not able to abstract the concept of "number" from the seeds to the pods, refusing to believe that seeds can tell him if he'll survive the journey. Great-Crack has to challenge him to a fight, win and become the new leader in order to save the clan from starvation.
While the clan is gathering new food she also perfects her new discovery, inventing a base 12 numeration. It is thanks to her that the clan will make it to the new land.
I'm not certain this is enough to make a piece of mathematical fiction of Dragon's Egg, but certainly the book presents mathematics - even if it's just the act of counting - as something vitally useful, connects it with a dramatic journey and has a woman (although an alien) as the main mathematician. I could hardly imagine a more intriguing and stereotype-free way of presenting arithmetics.
In case you decide to include it in your site, my marks are:
Literary quality 4/5
Mathematical content 2/5 (the mathematics dealt with is not at all advanced, but it's presented in a way that makes you realize how it must have been difficult to discover what every first-grader today knows, and gives you a hint of how it could have been done).