Okay, like, every single. Okay, basically every single person who, you know, who is, like, better or good at maths, um, or good at maths, um, and it just spends way more time doing maths than you. Like, you can think about this kind of like a, a model or like a neural network. Or like a neural network. So we can say your brain is like a neural network, and when you're born, the weights are initialised at random. So simply by the random allocation of weights, of course, you're gonna have, like, some people who, um, some people who, um, are just naturally better at maths, you know, like, the sort of concepts you need, and also, like, the sort of mental models you need to do, uh, to understand, like, certain operations and stuff like that. And then I guess, like, at a deeper level, maybe stuff like the, uh, like, parameters required for easy learning rate, like, parameters required for easy learning rate, stuff like that. But these are all initialised at random. So in a way, like, yes, like, when you first start out, some people will be better. But if you think about how you train a model, like, if you just put in sufficiently, like, it doesn't have to be wildly different amounts of training data. Like, even with the same amount of training data, most models end up convergence at similar, like, loss. Um, actually, I don't know if that's true so much, but you get the point. Like, most people who you think are just naturally good at maths are not actually, like, naturally that good at maths. Like, they just spend way more time doing maths than you. And you can argue. Yeah, like, okay, the fact you like maths is in some ways, like, randomly or genetically determined. Um, like, the barrier to most people becoming good, and not just maths, but, like, anything, is simply having enough motivation to do that thing for as long as, like, someone else who's good at it. Right. Like, it's. It's always a motivation problem, not really a problem of grasping the concepts. Um, so, yeah, I guess, like, this is the thing. Like, people often asking, how do you get good at maths? Like, the answer is literally, just do more maths. Like, just. Just do more maths and you'll be fine. And this is also another thing, like, people say, okay, you need to focus on the foundations, uh, and then you can go on to higher, higher stuff. And to an extent, that is kind of true, but it's also not like, let's take doing A level maths as an example. Um, and let's say you, for some reason, you didn't know how to add. Like, you didn't know how the addition operator works. So you're doing A level maths questions and you're just go, you're going through them, like, you're not. You're not gonna be able to survive without knowing how addition works, right? Like, you're gonna event, you're gonna run into so many random inconsistencies, uh, based on your flawed perception of what addition is, that you're gonna be forced to understand how addition actually works. And this, this, like, this demo or whatever, like, works for complex, like, concepts which are way more complicated than addition. Like, if you were to, say, I don't know, vector calculus in uni, and you didn't know how simple vector operations like a dot product or a cross product works, you would be forced to understand how they worked in order to, like, understand a high level content. So it's not so much true that you need to focus on the basics and then move on to the high level stuff. Like, you can't just go straight for the high level stuff that you want, and you'll just be forced to learn the basics as you go along. Um, yeah, like, those are my thoughts and, um, yeah, like, those are my thoughts and, I don't really have much else to say. If you wanna get better at maths, just. Just do more maths.
