Back in the times before the Great Flood, I was a lowly undergraduate student in a public university. I started out as a chemistry major but credits back then were very cheap, almost free, so I ended up taking an enormous number of credits in mathematics too. When I reached my senior year, I had taken all the requisite chemistry courses for the BS degree but I also had discovered that I found the lab work extremely tedious. What was a nerd to do? Well, I took a few more math courses and got my degree in mathematics instead. Since I was planning on raising an expensive family with Camera Girl, I decided to get a job as an actuary at one of the many fine insurance companies in Manhattan. Imagine my embarrassment to find that compared to being an actuary a lab chemist was like being James Bond. These insurance actuaries were the most boring human beings that walked this green earth. With two strikes against me I had to be careful what I did next. I talked to some smart guys and they asked me what I thought of chemical engineering. I asked them, “What is chemical engineering?” Well, these wise men told me that it was the golden road to wealth, fame and happiness. Since I’ve always been gullible, I believed them. Where things went from there is a story for a long winter evening but suffice it to say that I abandoned science for the greener pastures of the engineering world. In other words, I sold my soul to the devil. But I earned enough to raise a family.
But I always hankered for the chance to take more math classes. While I was taking my engineering courses I had the chance to speak to an old math professor of mine and described my regret that I’d be too busy for the next thirty years or so to take anymore math classes and wondered whether he could recommend a self-study text that covered all the fields of mathematics that I might be interested in. I knew that this guy was something of a bibliophile and luckily for me he said he had the very thing. He told me it was a Soviet Russian three volume set published in translation by the MIT Press. It wasn’t too pricey so I bought it and stuck it in a corner of my bookshelf and there it sat mostly unread for thirty years.
About ten years ago I finally got my last kid out of college and paid off the house and I was looking at cleaning out all the junk I had accumulated over the years when I rediscovered this set of books. On a lark I started thumbing through it and opened up the section on topology. And quickly discovered that I still enjoyed mathematics. Now you may think that engineering was a field where mathematics abounds. But after almost thirty years in the field the mathematical content of what I did on a daily basis had degenerated from differential equations into spreadsheets to figure out equipment depreciation and maybe the odd pressure drop or heat transfer calculation. I had become a lapsed mathematician. So, it was with great pleasure that I scanned the various sections of the set. Non-Euclidean Geometry, Topology, Prime Numbers and other equally useless but interesting things. Now whenever I have time I delve into the books and lose myself for a few hours and enjoy the guilty pleasure of contemplating the whichness of what. Today I was reading what these long dead Russians had to say about the relevance of Non-Euclidean Geometry when considering the details of our actual universe. When a ray of light can be bent by gravity what exactly is the validity of the concept of the parallel postulate? With our current understanding of particle/wave duality what exactly can we consider empty space? These esteemed commies made a statement from what they call dialectic materialism and define space as the form of existence of matter. Now what the hell does that mean? From what I read they are saying that the concept of space only has meaning in the contest of matter. Well does that mean there is no such thing as empty space?
This is great stuff. It makes me feel young again and inspires me to want to write a science fiction story where everything in the universe is adjacent to everything else and therefore problems like faster than light travel are merely a matter of having the correct mental picture when attempting to go from your leather recliner to, let us say, a planet in the Andromeda galaxy.
Anyway, if you’re ever in need of a general reference on mathematics that might spark your gray matter, I highly recommend Mathematics, Its Contents, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov and M. A. Lavrent’ev.