Have you ever used an analogy in a conversation only to have the conversation derailed as the person with whom you’re speaking points out that the analogy is not quite perfect in some way? Of course it’s not perfect! If it were perfect, it wouldn’t be an analogy. It would just be the thing itself. Or maybe you’ve been the one nitpicking an imperfect analogy. I was that nitpicker in a recent Facebook conversation, and it reminded me of a blog post aptly titled Analogies are the Worst! from Jean Pierre Mutanguha’s blog Euler, Erdős. In it he uses analogies to explain why he doesn’t like analogies, or at least the way many people use analogies in arguments. He also writes about how his mathematical thinking influences the way he converses and thinks through arguments.
Mutanguha is a graduate student in mathematics at the University of Arkansas. I took a peek at his blog when he followed me on Twitter (you can follow him here), and I added it to my feed because I enjoy the way he writes about math with enthusiasm and humor. Math is clearly a joyful subject to him, and he wants to share his insights about his favorite topics rather than trying to impress you with how much he knows.
One of my favorite posts is the fanciful Annotated history of the reals. Math textbooks can give one the impression that math came to humans perfect and immutable, created by the hands of a divine being. Mutanguha takes that idea and runs with it: “In the beginning, there was nothing, 0=∅. Then we realized it was something, 1={∅}. Then we wondered, why not have another thing? 2. And another thing, 3. And another, 4, and another, 5, and another, 6, etc. Just like that, we had the natural numbers!”
“In the beginning…” Image: The Creation of the World and the Expulsion from Paradise, Giovanni di Paolo. Public domain, via the Metropolitan Museum of Art.
Mutanguha started his blog in 2013 because he felt like there weren’t enough math blogs for undergraduate-level math. Some of his early posts are explainers about topics from pentagonal numbers to ordinal numbers to the inclusion/exclusion principle. He’s tended to incorporate more of his own insight and voice over time. Recent offerings include Fermat and his missing proofs, mathematical crafts, and randomness. I’m always excited when I see a new post from him in my feed, and I think people who read this blog will enjoy adding it their internet mathematics diet. So why not surf over to Euler, Erdős and start reading?