Oh boy. This is the absolute worst. The Britta of my school career. And I'm using Britta correctly. It's means a small mistake. But I digress.

Today I was at a maths tuition class. Not because I need help or anything. I just really like to talk about maths. No one really wants to talk about maths, outside maths class. You know what we need? A maths bar. Just a bar where fellow math lovers can just talk about maths. This is a million dollar idea. Shotgun. Anyway, we were doing partial fractions.

Now, don't get me wrong, I love partial fractions and I love doing them. Really algebraic. Love that stuff. But something struck me.

Now here's the first type of partial fraction.

v/(x-a)(x-c) = A/(x-a) + B/(x-c).

Which makes sense. If you times coefficients together, A(x-c) + B(x-a) = v. Great. Lovely. Your on the ball fella.

But then this hit me in the face. Not the arm. not even the crotch. Right in the money maker. Okay, it doesn't make the money, but it might. I could be a late bloomer.

v/(x-a)^2 = A/(x-a) + B/(x-a)^2

And I don't get it. I mean, I can apply it sure. 1,2,3 done. It's nothing. But I where I have a problem is that they don't show how they came to this (if you know how, please leave a message in the comments). I mean, shouldn't it be

v/(x-a)^2 = A/(x-a) + B/(x-a)

I mean, that's how it would look had it been in the previous equation. I just don't get it. So naturally, I asked my teacher "Hey. Could you ummm, tell me how that works? I don't mean how to apply it, just can you prove it?"

And then he gives me an example and works it out. He just gave an example

And this ladies and gentlemen, is not proof. This is evidence. Now, I know some of you science nerds might say "You can't prove anything! Everything is subjective! You can only ever have very good evidence! Give the man a break!". And I'll agree. I'm with ya on that one. But see, the thing is. That's in the real world. This is maths. You can prove stuff here. You know, without doubt that 1 + 1 = 2. There's no denying it. It's true. You can say 1 = 2 and 2 = 1. but you're just giving a different name to a thing that already exists. Like calling a dog a cat. It's a dog. It's not a cat. You may call it a cat, but we all know that it's a dog.

And you know what? Evidence is fantastic, it's great. Nothing better than evidence. Except proof. And maths is the only place where you must have proof. It's the only place where you can have proof. You can't say "Well, I can't tell you how I got there, but let me tell you, I applied this method, and got pretty darn close to the correct answer." It's just not right. You gotta prove it. Otherwise, you aren't a mathematician. It's like saying all numbers add to two because 1 + 1 = 2. It's like saying Aristotle was right, just because you can drop a pen and a feather, and the pen falls down the fastest.

Back to the story.

I say "this isn't proof! This is evidence! This isn't right. I want mathematical proof of this!" And he just kept of giving me examples and I just kept on complaining. And then he realized what I was saying. I sighed a sigh of relief. Finally, I was going to get me answer. And here's the kicker. He didn't know. Come on! How can you teach this stuff, when you don't know it! That can't be right. I mean, how do you know it's right, yourself? You could be ruining a whole generation, giving them the wrong information. And you don't even know it!

Don't get me wrong, I love this teacher. Great teacher. Fantastic teacher. And love the book. Amazing book. Really gets you excited about maths. Always gives me explanations. But not this time. Not. This.Time.

Either way, to summarize ( just realized to summarize is TL;DR. So, if you couldn't read "to summarize", TL;DR:TL;DR), success is not proof. It's evidence. Great in real life, not so good in maths.

Either way, I'd love for someone to help me out here. I know there's gotta be a maths nerd among the 40 or so viewers of this blog.