The author was an astronomer, best known today for coining the term "The Big Bang". (FWIW He intended this silly name to indicate what a dumb idea the thought it was. It is therefore ironic that it lives on today despite the theory's widespread acceptance.) Consequently, he has some of interesting things to say about science (and math), which he manages to squeeze into the book without distracting too much from the story.

The role of physics, biology, and engineering in this book is as great (if not greater) than that of mathematics. Still, there is enough math in this book for me to consider it an example of "mathematical fiction". Below I will summarize the mathematical highlights of the book, but it should be understood that there is a lot more to the book than this. (And, after that, I will provide a "spoiler" which explains the stunning -- but entirely non-mathematical -- conclusion of the book.)

Mathematical Highlights:

• The narrator introduces himself as follows:

  (quoted from Ossian's Ride) From my school in Ashburton, Devon, I won a Major Scholarship in Mathematics at Trinity College, Cambridge. I took my B.A. degree in June 1969, specialising in my final Tripos in Algebra, Functional Analysis, and Topology. This is relevant to what is to follow. By the early summer of 1970 I was well started in research, on a problem in the theory of infinite groups. I was just turning over in my mind what I would like to do during the summer vacation, when I received a curious letter from an address in Whitehall. The letter offered interesting employment for the months of July and August. The writer was wholly inexplicit, however, about the nature of the employment.

• The British agent who recruits him explains that a mathematician would be best suited for the job since his goal is to understand not the specific physics or biology of each individual discovery, but the logical question of how Ireland was able to make such stunning advancements on so many different fronts.
• Through a computation, the narrator discovers that the Irish scientists have developed an exceptionally strong steel beam:

  (quoted from Ossian's Ride) I made the best estimates I could of lengths, widths, and so on. Then in the evening I looked up the elementary theory of stress and strain--I am ashamed to say I had forgotten it--in Trinity Library. It took an hour or two to clarify my ideas and to seek out the appropriate physical constants I believe I used the old Smithsonian Tables. But the result was worth the trouble, for the eye had not been deceived. The metal arms in the Central Station were carrying a transverse stress roughly a hundred times greater than they should have done.

• While pretending to be an uneducated fisherman so as to observe the scientists at work, he overhears an argument between five men and one woman that hinges on a question of topology:

  (quoted from Ossian's Ride) The five were very sure of themselves. The solitary girl was equally sure. Whatever abstruse physical (or mathematical?) question was under discussion, she gave all the indications of knowing exactly what she was talking about. She had an odd appearance, a jolly-looking face, but a face that decidedly wasn't jolly. This jolly-girl-that-wasn't began to get very exasperated, as one might do in talking to a crowd of exceedingly dull, obstinate people. The five, with the confidence of the majority, kept firing all manner of objections at her. The scene was fast becoming acrimonious when the mental fog in which I had been immersed suddenly cleared away. I saw where the trouble lay. Perhaps I had better explain. In two dimensions a circle divides the plane into two parts, the 'inside' of the circle and the outside', both parts being simply connected. All this is obvious enough. The same result is true for any closed curve in two dimensions that can be put into a continuous one-to-one correspondence with a circle. So far, so good. Now the majority of five were generalising this theorem to higher dimensions in the course of their argument, and I knew this to be already wrong in three dimensions.

  Unable to control himself, he enters the argument and "blows his cover", revealing to them for the first time that he is a mathematician ("an embryo one"). Surprisingly, they seem to welcome him into their community.

• He reads a paper in an astrophysics journal on magnetic flux lines in the atmosphere and realizes that this is somehow related to the Irish fusion reactors.
• In a paragraph that I think was Hoyle revealing his own true thoughts about scientific seminars, the narrator explains how he was able to use them to boost his own reputation:

  (quoted from Ossian's Ride) I noticed a curiously contradictory feature of these weekly scientific meetings. Anyone who could ask intelligent questions of the lecturer of the day gained great prestige. And if the lecturer made an error that one could correct, then better still. In spite of the reputation that could be won in this fashion, nobody took the trouble to prepare himself in advance-apart from the lecturer, of course. Nor was it at all difficult to prepare oneself, because the subjects of the meetings were always announced at least a week beforehand. So in addition to my own work I deliberately began to read up carefully in advance on all manner of topics. Sometimes the subjects were fairly mathematical. These were not only the easiest for me to cope with but they were also the greatest prestige-winners.

• He helps out other researchers by using numerical analysis to produce approximate solutions to differential equations:

  (quoted from Ossian's Ride) One day I had a conversation with one of the older scientists. Would I undertake the solution of a set of equations that had proved very puzzling? They were of a non-linear partial type that could only be tackled numerically on a high-speed digital computer. I agreed to this proposal because I particularly wanted to gain some experience in the use of such a computer. The special difficulty of the equations was that derivatives with respect to each of the variables became so large in certain ranges of the variables that it seemed impossible to store a lattice with the usual property of small changes of the functions from one lattice point to the next.

  That leads to him working late at the computer lab, feeding his program into a computer on data cards. There he again meets the "girl" who earlier was arguing about topology. The program she wrote was far longer and more sophisticated than the narrator's.

• Over dinner after the encounter at the computer lab, she and the narrator discuss his new theory that electric charges can be understood as rotation. She seems to already know all there is to know about that, and promises to explain it to him later.

I'd like to say a bit more about the book, but it is not especially related to mathematics and it necessarily involves "spoiling" the surprise ending. So, if you intend to read this book for pleasure or only care about the mathematical content, then please stop reading now.

Yet, Ireland is shown to be the most technically advanced country in the world, and this one woman seems to have something to do with that. So, while I was reading it, I was wondering if maybe the conclusion would reveal that the author was not as prejudiced as I thought. Could the point of the book be that women and the people of Ireland had been misjudged by the world? Maybe, I thought, the realization the narrator would have at the end was that Ireland's secret was to support gender diversity in science? Okay, so that seems like a terribly "woke" ending for a book written in the 1950s, but I thought it was possible!

However, that is not the case. In the end, the narrator realizes that some of the people he has met in Ireland are not humans at all, but aliens from a planet which has become uninhabitable. They projected their minds into human bodies, leaving them far less intelligent than they had been in their own but still smarter and more knowledgeable than anyone else on Earth. And, I'm left with the impression that the reader is supposed to realize that this is the only sensible explanation: "Of course, women and Irish people could not be brilliant scientists. They must be alien body snatchers!" (So much for it being "woke", eh?) And that's not all. The narrator seems entirely unconcerned about the people who would have lived in those bodies had the aliens not taken them over. Moreover, he seems to completely buy in to the superiority of this technocratic society. In conclusion, a lot of the ideas in this book have not aged well.