This is why I never succeeded at math. Like why does this shit work?? How can people just take a problem and be like, nah I’m going to just throw numbers all over the place and reassemble them in all sorts of ways and get an answer somehow…
I can’t just memorize arbitrary nonsense that “just is” I need to know how it works or it never sticks and all the math I’ve ever been taught was just “memorize this arbitrary nonsense and regurgitate a specific formula for a specific application that we’ve spent 0 time explaining other than telling you to memorize it. You want proofs and you can’t get proofs until advanced college courses” well guess I’ll just never understand mathematical manipulation then…
I feel like 50/50 school failed me and I failed at math.
The rules underpinning math are axioms in the end, but they’re not completely arbitrary, because if you change them in most cases it just fucks everything up.
The axioms that were chosen were chosen for good reason, and the rules they result in (such as summation and multiplication being commutative so 3x4=4x3 and 3+4=4+3) allow more complex rules to be created.
There’s a lot of philosophy of math at the core of all this , but it’s not really true that this is all arbitrary.
It’s not arbitrary. Really try to think about the problem at hand. The ‘why’ is quite apparent. Ask yourself why did they go with 99+1+98+2… in the first place? And why is that the same as 101+101…? What was the benefit of simplifying it to that? How did it save the student time?
You can deduce this yourself and literally no memorization is involved to figure this out. No formulas needed either.
Once you have the idea, seeing that it works if often easy. But coming up with ideas like that can be really hard, which is why gauss was the only one in his class who got it. There is no general method, you just have to think about stuff for a while, but you can get better with practice. And it feels really good when you prove something for yourself, even if it’s relatively straightforward. You can just try to prove some simple things yourself, if you want, the advanced college courses are just for proving really advanced stuff.
This is why I never succeeded at math. Like why does this shit work?? How can people just take a problem and be like, nah I’m going to just throw numbers all over the place and reassemble them in all sorts of ways and get an answer somehow…
I can’t just memorize arbitrary nonsense that “just is” I need to know how it works or it never sticks and all the math I’ve ever been taught was just “memorize this arbitrary nonsense and regurgitate a specific formula for a specific application that we’ve spent 0 time explaining other than telling you to memorize it. You want proofs and you can’t get proofs until advanced college courses” well guess I’ll just never understand mathematical manipulation then…
I feel like 50/50 school failed me and I failed at math.
You were failed by people who didn’t help you learn intuitions and instead caused you to focus on memorization.
The rules underpinning math are axioms in the end, but they’re not completely arbitrary, because if you change them in most cases it just fucks everything up.
The axioms that were chosen were chosen for good reason, and the rules they result in (such as summation and multiplication being commutative so 3x4=4x3 and 3+4=4+3) allow more complex rules to be created.
There’s a lot of philosophy of math at the core of all this , but it’s not really true that this is all arbitrary.
But commutation is not an axiom, is it?
It’s not arbitrary. Really try to think about the problem at hand. The ‘why’ is quite apparent. Ask yourself why did they go with 99+1+98+2… in the first place? And why is that the same as 101+101…? What was the benefit of simplifying it to that? How did it save the student time?
You can deduce this yourself and literally no memorization is involved to figure this out. No formulas needed either.
Once you have the idea, seeing that it works if often easy. But coming up with ideas like that can be really hard, which is why gauss was the only one in his class who got it. There is no general method, you just have to think about stuff for a while, but you can get better with practice. And it feels really good when you prove something for yourself, even if it’s relatively straightforward. You can just try to prove some simple things yourself, if you want, the advanced college courses are just for proving really advanced stuff.
Look up how to solve it by george polya