What is This Blog?

Welcome! My name is Will Craig. As of this writing, I am a PhD student in mathematics at the University of Virginia. My current aim is to be a university professor. I greatly love both teaching people about various kinds of mathematics as well as working on modern research topics in number theory. I also enjoy reading and learning about pretty much anything, but especially philosophy, theology and religion, and the various sciences.

The title I’ve started off with for my blog is “Mathematical Apologetics”. To unpack what this means, we first must understand the word apologetics. This word has little to do with the English word apologize; rather, it derives from the Greek word apologia, which is a term which means “to give a defense.” This English term apologetics is a noun form of apologia, and an apologist is a person who does apologetics. It is used to denote someone defending a position or belief using some kind of reasons and evidence. This term is most commonly used in the context of defending a belief related to philosophy or religion; so you may have Christian apologists, atheist apologists, Muslim apologists, and so on.

The reason I’ve given the blog this name is two-fold. Firstly, I have loved math for nearly my whole life. And I don’t mean “math is my favorite subject” kind of love, I mean in the same way that a singer loves music or a painter loves a masterpiece. It is one step short of obsession. Math can be breath-taking, subtle, deep, and remarkably beautiful if you know where to look. Most professional mathematicians think of their mathematics as something comparable to an art form, but this idea has been portrayed most famously and poignantly in the great twentieth century mathematician G.H. Hardy’s classic essay entitled A Mathematician’s Apology. In this essay, Hardy takes the role of an apologist for the discipline of pure mathematics (that is, math that does not necessarily apply to the real world). While I do not fully agree with everything in the book, I highly recommend it to anyone who wants to know what it is like to be a mathematician.

I will say I agree with the core of his essay, which views mathematics as primarily a form of creative art, and since I also consider myself an apologist for this idea, I gave the blog this title as a way of paying homage to that great essay. It has been very frustrating that this side of mathematics is never seen, with all emphasis placed on “application to the real world.” It takes the fun out of it. Imagine if in art class you just learned how to paint walls one solid color, or perhaps you learn how to paint a stop sign. How much would everyone hate art class if that’s all you did? Sadly, math class today is a lot like that. One of my goals here is to present as best I can the beautiful, interesting, fun side of mathematics.

The second reason for this name is that I hope to discuss issues important to me outside mathematics in the manner of an apologist, using my background as a mathematician. Just as I believe most people misunderstand what mathematics is truly about, I think most of what is important to me is also greatly misunderstood. Modern “debate and discussion” is not only mostly unproductive, but harmful both intellectually and emotionally. And quite often, it seems like people have never tried to carefully understand those they disagree with, or to really understand deeply what they believe. There are plenty of exceptions to this, of course, but that we have any public figures at all engaging in such nonsense is saddening.

I hope to take the skills I’ve been developing that are important to mathematical thought and carry them into other areas in which I am interested. This will focus on areas outside of math about which I am most interested, and which matter the most to me. I plan on including issues of emotional/mental health, religious and philosophical topics, and some of the hard and soft sciences, as these are all important and interesting to me. I hope by taking the approach of a mathematician, I can try to calmly understand both sides of important issues, and to avoid common misconceptions. I hope that taking the perspective of a mathematician will bring a point of view that is not often seen or considered.

As a closing note, I also hope to have a Q&A aspect to the blog in addition to talking about what interests me. I have set up an email address for the blog, mathematicalapologist@gmail.com so anyone who wants to know more about the blog, about what I do as a mathematician, or has general suggestions or questions can contact me from the “About the Blog” page and I’ll reply as quickly as I am able to. Hope everyone enjoys the blog, and hopefully learns something.

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