Just another annoying advice seeker
This is a quite long read, but I hope you will take your time and share your critique and wisdom. I also know it's quite a common topic these days and might be annoying by now, but still. I want discussion, your actual thoughts. If this interests you at all...
I am currently a first-year pure mathematics student. How did you change your approach to doing math when AI came, now that it can "understand" the vast majority of problems? No matter what math problem I throw at it, it solves it. I know this is because it's in its training data; we can assume it has no creative, original insights, and we can argue and debate about how these things operate. But the fact is: it solves the problem, it outputs the proof, it gives the answer. And it's just a matter of time before hallucinations are reduced to zero.
I understand that I am naive and may have a limited understanding of the world and of "real world" problems, not just textbook ones or olympiad ones. And I honestly started to hate it when people say that math is a human endeavor and that it's just so fun solving and exploring problems together. Like, yeah, it's fun, but that immediately reduces the significance of math to something like chess. What I mean by that is this: before AI, when you solved some kind of problem, it felt magical, meaningful, something that would let you solve harder problems and contribute to the world. Thinking about the problem, that was the fun part. But most importantly, not only that: it signified some kind of intellectual superiority, bonded tightly to one's identity; for some, the whole world could be looked at through a mathematical prism. Then, when you didn't understand what to do, maybe you asked your peers, or professors, or experts, and you always knew there would be someone smarter than you. And that's okay, totally okay: you would learn from them, you would get inspired, and you wouldn't really care whether you'd manage to get a Fields Medal or whatever. But you knew you would be needed. Just a small fraction of the population is actually good at math, and an even tinier fraction actually puts in the work to become even greater. Now it just feels... meh, to be honest.
Then some will say: if calculators were invented, why do we still teach basic arithmetic? Well, I agree with that. It is, of course, to develop thinking skills, basic skills, something all of us globally should know. But when it comes to dedicating your prime years to learning advanced mathematics... well, you know what I mean.
Still, the reason I chose a pure math degree is that I am good at math (well, based on what grades and standardized test results tell me) and, most importantly, I do like math and actually view it as the universal language and something beyond... I believe no one has yet invented a better way to train the mind than mathematics, and I have yet to meet anyone complaining of having too much general aptitude. Learning mathematics helps develop the ability to think logically, analytically, and critically, to structure and organize, to process information, and it also trains the problem-solving skills that help us explore and understand the world. "Mathematics should be learned if only because it sets the mind in order," as the Russian polymath Mikhail Lomonosov said.
I mean, it's quite paradoxical at this point. I remember when I was in middle school, I really liked word problems. I would solve dozens of them, searching for ever harder and harder problems; that's how I really ingrained my first glimpses of learning in my mind, of how applicable math can be. When solving problems, I would do most algebraic manipulations with a CAS calculator, because I already knew how to do those, and I often thought: what if there were a system that could actually understand word problems? And here, bang! We have LLMs that can now solve the vast majority of them. I would have loved to have that at that age. How much more I could have learned and accelerated! But now I find it very hard to find the same motivation. Maybe because it's the real world now: how will I make money?!!!!!! Maybe I just should have gone into medicine, the field least affected by AI in the long term. But I don't like medicine. Never did.
So yeah, math is sublime, powerful, a universal language, and applicable. In the same way, AI is just math and nothing else: a huge, complex mathematical structure, a function. And then: we are all going to die, aren't we? So the last day on Earth won't really matter that much. Then I think: why learn anything at all? If AI can do anything, why should we learn? Why should we exist at all, maybe just end our existence? What's the point of it all? So, of course: we learn, we get better at what we do, and we simply know that we can't avoid taking risks, and so on.
So, my question after this monologue. I am not asking you whether it's worth learning mathematics; I do have a plan: pure math as the equivalent of a hardcore brain gym, then maybe a master's in machine learning/AI, and then work on AI, improving it. But the thing is, I often find it hard to believe what I want to believe. Do I believe it, or what? Also, I will most certainly not take the fully academic path, like a math PhD; I am more interested in application, and the only reason I am taking a pure math degree is that it is purely abstraction-loaded, believing it will train me, and I enjoy it. But how do I keep learning? How do I stop just thinking and thinking and posting questions on forums, and actually just do things? Maybe I am going insane, or maybe I am just so f**king stupid.
So please, share your wisdom.