(Crossposted from my Facebook page)
I'm reading a book called "Mathematical Cranks". It's an anthology summarizing a sample of different people, ranging from the mildly eccentric to the downright insane, who have tried to put forward their bad ideas as legitimate mathematical research.
A couple examples: A guy who claims that the number 57 is intimately linked with every major event in US history; numerous people claiming to have found fault in existing theorems; and a bunch of people who claim to have a Grand Unified Theory of Mathematics, which will change the world and will solve every problem in existence, provided that you purchase their book for 29.99. A modern example would be the Time Cube guy, or roughly half the people listed in the Wikipedia article about Usenet celebrities.
I'm about 56 pages in, and so far, all the cranks mentioned in this book have been male. Further evidence that we need to do more to remove the stigma around women entering the field of fake mathematics.
I get the sense that the author is being as generous as possible to the people he talks about, which I like -- I was worried the book would just be a series of "Hey, let's all point and laugh at this idiot for being bad at math!" but that hasn't been the case.
For example, there's a chapter on the Dozenal Society, a group of people who want everyone to switch to a Base 12 number system instead of Base 10, with the reasoning that Base 12 makes a lot of calculations easier. The author admits that these people aren't *wrong*, per se, but it's still never gonna happen. There are other cases where the crank in question has found something mildly interesting, but it's in the middle of a series of grandiose claims.
Part of the reason I was interested in reading this book is because I'm always interested in figuring out ways I hadn't considered in which my thinking could be wrong. In my last Facebook post, I mentioned that my high school math teacher made a joke about how, if I didn't keep my thinking under control, I would end up like Howard Hughes. I'd like to avoid that fate, if I can (the part where his mental illness drove him to become a paranoid recluse, not the part about being a genius billionaire playboy philanthropist).
And of course, there are a lot of mathematicians who end up losing their sanity obsessing over something or other. The best example that comes to mind is Georg Cantor, who spent his later years alternating between staying in mental hospitals and obsessing over the theory that Francis Bacon is the actual author of all the Shakespeare plays. But the subject of mathematicians and mental illness is a topic for another day.
But a recurring theme I've noticed among the cranks is that the most grandiose claims seem to come from the people who do the least actual mathematics. They spend most of their time talking about how great and powerful their theory is, how it makes all other mathematics obsolete, but then their "theory" turns out to be a couple of equations that aren't really that impressive, without elaborating on how to use these findings.
In other cases, the crank will make a grandiose claim, but fail to actually prove it formally. This is kind of a no-no in mathematics -- not that every finding always requires a formal proof, but if you don't have a proof, at least have the decency to call your finding a "conjecture" rather than a "Grand Unifying Theory that will Change the World". I can't find the quote, but I remember a mathematics blogger saying "The worst kind of mathematics is no mathematics at all" and that seems to be the case here.