The Fields Medal is to math people what the Nobel Prize is to other scientists. It can be a big deal. And no, I'm not going to get one.
But this morning I felt like a math guy. I was studying for my cumulative final exam, which I have to take in 5 weeks or so, when I came across the proof that there are an infinite number of prime numbers. It's a fairly simple proof to understand, but then it led me to a realization--aren't all consecutive whole numbers relatively prime?
Logically, it would make sense that they are. But then I thought I could prove it. A couple minutes later and I was done! Assuming I didn't make an error in my proof, I proved my assertion. QED.
Now, I'm not going to assert that I'm the first human ever to figure this out. For all I know, this "theorem" is so well known that it has a name! But I don't recall that I've ever in my life heard this--yet I came up with it on my own, and then proved it.
Given the rough time I've had in my current master's course, it feels good to have accomplished something mathematical lately!
aren't all consecutive whole numbers relatively prime? Logically, it would make sense that they are.
ReplyDeleteWell, sure. But this doesn't really come from any particular characteristic of integers per se, as much as it comes from how we have chosen to define "relatively prime."