Mathematicians think a lot about primes, and they think a lot about where they can find them. This leads down a crazy rabbit hole, involving the harmonic numbers (), complex numbers (), and so on, so I’ll spare you the details. Instead, let’s think about an easier, but still interesting problem: how do we find … More Prime-Free Polynomials
Once again, it’s Friday, and that can only mean one thing: another Wandering Mathematician post! Today, I’m going to begin by stating that . Feel free to play around with this equation for a while. You can even try to solve it if you want — you should get . (I did have to look … More Secret Quadratics
Hello once again! I now have a new favourite mathematical fact: the Sylvester-Gallai theorem. This says that, given any finite set of points in the plane — any finite set you can think of — either all the points lie in the same line or you can draw a line that passes through exactly two … More Time to Draw the Line
Hello! I recently read about a way to solve certain types of equations, and I’m so pleased with it I’m going to share it with you. The proof is dull — it’s basically just shuffling algebra — but the result is fantastic. A “Pell equation” is an equation of the form for some . For example, … More Continued Fractions and Pell Equations
I’m breaking my usual routine today to say Merry Christmas! Wandering Mathematician updates will continue over the holidays and into the new year. As a present to my wonderful readers, I’m giving you some interesting facts about the numbers , , and . is the fifth square number. It is two less than . Any … More 25
Very excitingly, this is the 52nd Wandering Mathematician post, meaning that I’ve been going for a whole year! A while back, my maths teacher handed his class the following problem, leading to blank stares all around, followed by panic as soon as he left the room: I have a spreadsheet, with the names of ten … More Repeatedly Pressing the Big Red Button
Hello everyone! I’m super excited right now, because in just a few short paragraphs we’ll be dividing by and, in the process, proving that is prime. Sadly, for the moment, you’ll have to wait, because first I’ve got to tell you about Wilson’s theorem. (If you don’t know what is, it’s . It’s pronounced “ … More Let’s divide big numbers!