"I share the view of Pythagoras that the world is number. The ultimate substrate of the universe is math. There's no way to test that - it's pure metaphysical speculation."
- Bart Kosko

A smaller-scale version of the same idea was used in Asteroid of Fear by Raymond Z. Gallun. In that story, it is assumed that the asteroid Vesta is an intact surface fragment of an ancient planet.

The next task prescribed by the Homesteaders' School was to secure a supply of air and water in quantity. Again, following the instructions they had received, the Endlichs uncrated and set up an atom-driven drill. In an hour it had bored to a depth of five-hundred feet. Hauling up the drill, Endlich lowered an electric heating unit on a cable from an atomic power-cell, and then capped the casing pipe.

Yes, strangely enough there was still sufficient water beneath the surface of Vesta. Its parent planet, like the Earth, had had water in its crust, that could be tapped by means of wells. And so suddenly had Vesta been chilled in the cold of space at the time of the parent body's explosion, that this water had not had a chance to dissipate itself as vapor into the void, but had been frozen solid. The drying soil above it had formed a tough shell, which had protected the ice beneath from disappearance through sublimation...

Drill down to it, melt it with heat, and it was water again, ready to be pumped and put to use.

And water, by electrolysis, was also an easy source of oxygen to breathe.... The soil, once thawed over a few acres, would also yield considerable nitrogen and carbon dioxide—the makings of many cubic meters of atmosphere. The A.H.O. survey expeditions, here on Vesta and on other similar asteroids which were crustal chips of the original planet, had done their work well, pathfinding a means of survival here.

You might want to compare this idea with the more dramatic Romulan flame drill used in the new Star Trek movie series (and the real-life flame jet drill deveolped for drilling into solid rock).

Also, here's a neat illustration of drilling into an airless moon or asteroid from The Radium World (1932) by Frank K. Kelly:

(Mining claim stake-markers from The Radium World by Frank K. Kelly)