This is a classic Heinlein story, focusing on his constant theme of totally competent and complete individual. The title character, one Andrew Jackson Libby, has reprise appearances in at least two later novels, "Methusalah's Children" and "Time Enough for Love". Libby is portrayed as being one of those rare, but valuable, mathematical geniuses. The difference from the usual portrayal, is that he may be a tad focused, but is still perfectly able to function in the world. In other words, he is not the typical one-dimensional mad scientist.
Of course, the details of Libby's thought processes are not explained (how could they be?). The other mathematically interesting thing here is a fairly good exposition of basic celestial mechanics (I believe they are calling it astrodynamics, these days) and some other engineering mathematics. When you consider that the story was published in 1939, when space travel was widely derided as utter bunk, this is quite an accomplishment.
I stumbled across this story in an anthology in the mid-60's, as I was just entering high school. I'd always done well in math (and in other subjects), but this story actually whetted my interest in mathematics, in terms of its being useful for something besides passing a required course. In fact, I now make my living as a mathematician and engineering/scientific programmer.