Even if I’m studying Applied Mathematics, I always had a great interest in Number Theory, it was so “simple” and “fun” for me (at least in high school -but in general it’s not that simple at all).
Since I’m talking about Number Theory, I’m going to talk about the Prime Numbers, they are my favorites, they’re so “unique”.
When I was in the first grade of high school, I first learned about the above-mentioned theorem. I also used it a couple of times to solve/prove some problems, it was a useful one.
However, we all know that for the prime numbers, there’s no formula or function that will give you any p prime number by plugging in an i number (inN) and p will be the i-th prime number.
One day, I was thinking about that theorem, but in a quite different way ( in a wrong way). I didn’t remember exactly the theorem at the time and I had it in my head as that “any number of the form 6k+1 or 6k+5 is a prime number.”
So in my head “problem is solved”, “I can find any prime number by plugging in a number for k.”
It felt so perfect and easy to be true, I had that feeling that I usually have when I do something wrong or I have an incorrect assumption in Math.
It is easy to see that by plugging in some number for k will give you a non-prime number (for example k=15, it gives 91 and 95), I realized it the very following hour.
Then I was looking for that theorem, on a textbook, I had in my head and when I found out that I was totally off, I was like “yeah, you’re really smart.”
From that day, I pay more attention not to miss a single word in math and to remember every definition or theorem the exact way that is written in the textbook. In math, we don’t like to add words that are not important just to make it “sound” better. Everything is so precise, that’s the beauty of Math anyway.