Welcome to this week’s Math Munch!
Math can be confusing. Everyone knows that. And, actually, that’s what lots of people love about it. Some things in math are more confusing than others. One such thing, in my opinion, is a theorem developed by this kinda creepy-looking guy:
His name is Kurt Gödel, and he’s responsible for a theorem that basically says: You know how you thought we had rules for arithmetic that work, don’t contradict each other, and can answer all kinds of questions with numbers? Well, there are problems with numbers (really strange problems, granted) that our arithmetic cannot answer. And if you try to fix your system so that it can answer those problems, you’ll have issues with other problems. There’s no way to repair your system so that it stays complete and answers all problems.
If this sounds disturbing to you (math doesn’t work?!?!), you’re not alone. Lots of mathematicians were upset by this. They thought, as lots of us do, that math is supposed to be logical. It’s supposed to give us the answers we need. We’re supposed to be able to rely on it. Gödel arrived at this theorem by playing with paradoxes, or statements that self-contradict. (Such as, “Today is opposite day.”) The statement that he came up with really rocked the world of math.
If you’d like to learn more about Gödel and his disturbing theorem, listen to this podcast episode from Radiolab. It talks about Gödel’s life and what his theorem meant for math, with an appearance by everyone’s favorite mathematician, Steve Strogatz!
Gödel’s confusing theorem is only one in a long string of crazy, confusing math paradoxes. Another of my favorites is the Barber Paradox, which mathematician Bertrand Russell came up with. Here it is, in dry-humor video form:
If you like that paradox, you’ll probably also like the Pinocchio Paradox— which was developed by 11-year-old Veronique Eldridge-Smith:
This video comes from the YouTube channel, SpikedMathGames. I suggest you check it out!
Finally, I thought it would be nice to close off this loopy Math Munch post with a loop back to podcasts– and a link to a very large archive of math podcasts called Math Factor. Math Factor is a podcast produced out of the University of Arkansas about all kinds of interesting math. They even have an episode about the topic of this week’s Math Munch! Give it a listen.
Have a terrible opposite day, and bon appetit!