Here we're with another personal blog post ... I swear that I'll write more technical stuff. I'll separate personal from technical blog posts too. For now, let me update you about my decisions.

In the last post I was confused about what should I do. Well, now I'm more determined, because I thought more about how I got to where I am. I really didn't know if I started to like mathematics because artificial intelligence or the other way around ... But that it's irrelevant. Why, you ask? Well, I've been studying and practicing AI for 3 years, and I still like it, I'm fascinated with computer vision ... BUT, like programming, it's not enough to satisfy my thirst for knowledge. I need something more fundamental, something that can explain why things are like they are ... I need to learn more about mathematics.

No, I don't want to do calculations or use method X or Y to find a piece of information. I want to understand why those methods work, how people formulate them and where all the intuition came first. Then, after all that, yes, let me solve some problems and, if needed, apply those methods.

The magic behind mathematics and science, in general, is that we don't need to memorize anything. We only need to learn how to think, how to decompose a problem in smaller problems, how to take the most basic axioms (not before understand them) and build a logic sequence of premises whose create theorems and with all those truths we have tools to solve all the small problems and, in the end, after a lot of work and some luck (A.K.A random variables aligned with our objetives), we solve the problem.

I know, learning how to think can be a life time challenge, but it's important to get some progress on that. We need to think more, we need to learn about solving problems and we need to learn how to prove that something is true.

Obviously, AI is part of science, and it has all this beauty, but in a more higher level. Don't get me wrong, math have more higher level, abstract problems too. However, we can reach that abstraction from the bottom to the top, it's all math. In AI the bottom is math and the top is AI itself. I could be wrong but it's the way I feel.

Not much, but after all this thinking I realize that I want to study more math, pure math. So I started planning what to do and I found a master's degree in mathematics. It's hard to me, an undergrad computer engineering student, ending a degree and going to a master's degree in math. But it's the only way I have to get deep into these field, I want to learn the language of the universe (I know, physics gets a big piece of that language, but for me, now, it's only math)!

Since I've 1 more year and summer holidays (those are ending now ...) I thought: "Why not study some fundamental topics on my own to prepare for my new course?". Then I started with my favourite math field: Linear Algebra. I got the wonderful book "Linear Algebra Done Right" by Sheldon Axler and start reading it. I'll tell you my progress and experience with it in a moment, but let me tell you my self study plan first.

My plan was finishing this Linear Algebra book in the summer of 2023. In September I should start reading the book "Understanding analysis" by Stephen Abbott and in parallel I should do some calculus I and II courses of Khan Academy just to make sure I remember some concepts. After that I would be lost, but a dear friend of mine, shown me this video and I planned to follow the order and use the content recommended on it.

In the meantime, I got in touch with an AI graphics researcher that I admire a lot, Hallison Paz, I recommend you to watch the youtube channel, Programação Dinâmica, where he and his wife post videos about AI, Data Science, math and research. When I asked him if all this books would be a good preparation for the course and after I showed the master's degree classes and the books suggested on the other video, he said I should replace Algebraic Topology and Differential Geometry which are more advanced topics, with Measure Theory and Differential Equations. So I did that and my plan was prepared!

Ok, it's not realistic to say I will study all those things in 1 year ... But I will try! It's important to me and for my future. Now, you ask: "How's going those studies?". They're more challenging than I thought!

I said that summer holidays are ending, right? So linear algebra is studied, right? Yeah, I have a bad new and a good new.

The bad new is I'm not even in the middle of the book. The good new is I'm not even in the middle of the book. I'll explain.

Self studying mathematics isn't easy and I thought that's only for me, but it's not. Like you can see in here and here, people struggle a lot with this book and more experienced people (I hope they're) say it's normal, because the exercises are challenging and self study mathematics is not easy.

But it's a good new too, I could be in the last 100-50 pages of the book right now, but then I would realize that I didn't understand 1/2 of the book and that's not the point here. I prefer to solve all exercises and make sure I understand the concepts, the proofs and learn how to think and write them rather than just speed run the book. What I realize is that, I think, I understand the theory and, normally, the idea of the proof is right, but I need to improve a lot my proofs!

Well I definitely need more time but it'll be worth it. I pretend to post all my solutions in my blog ;)

The most important part here is that I'm learning and having fun (with some frustrations in the middle, of course).

For now, I'll finish 1-2 chapters and I'll start reading "Understanding analysis" in parallel since the topics are different. I want to, at least, start learning more about group theory and topology, but being realistic, probably I'll not reach that level. But I'll definitely try!

To help me on this, I'm leaving social media (for now, just using instagram to see some tech and math memes) and I'm planning to teach other people about some of the linear algebra concepts that I'm learning. I really enjoy to teach even with my impatience (that's somehting I need to improve) :D I hope they learn and enjoy linear algebra as much as I do.

Let me finish with an awesome answer of Albert Einstein to the question "What is the speed of sound?": "I don't carry such information in my mind since it is readily available in books. The value of a college education is not the learning of many facts but the training of the mind to think" (Source: Wikiquote)