On Using AI to Learn Things
It started with a moment of doubt.
8pm, Sunday 27 Sep 2026. I dunno why I felt so depressed. I think it had something to do with going 0-3 at my first USCF tournament back in five years (Marshall Morning Action) yesterday. Even though that was what I expected, the emotional damage from the losses had somehow drifted into "I'm not good at anything that requires one to think," and that was doldrums.
Then I watched a video on YouTube about how Cambridge's math dept doesn't really teach so much as it creates the conditions for optimal suffering to occur, and it sort of reminded me of undergrad at Reed. Not because of the teachers (they tried to do this but usually the material was too easy for it, also Reed is fairly good at actual instruction), but because of what I did outside of classes, or rather, instead of them: I would skip lecture and hole up in the library reading whatever I wanted, which usually turned out to be the most formidable math book I was aware of at any given moment. I would not go in order. I would flip through until I found something interesting, and then with all my might, attempt to understand it cold.
I don't know how productive this was for my actual math understanding, but the type of person it turned me into is something I value. That type is: I learn things on my own terms. No one spoonfeeds me, no matter what. I don't care if I don't know a damn thing about what I'm trying to figure out, no one is robbing me of my own confusion.
So, back to me moping on a Sunday evening. Inspired by the video, I say, well, let's at least see if I understand Cauchy-Schwarz at all. I go over to the ping pong table that is currently my desk and try to recall/reconstruct one of the three proofs I'd seen before. I'm particularly fond of Brimnathwala's geometric argument, but then that stubbornness kicked in again. No. Do something else.
So I fumbled around with it for hours. I tried breaking up into real and imaginary parts (bad, gets the triangle inequality involved, and CS is usually how you prove the triangle inequality). I tried squeezing out the bound with nothing but random roots of unity applied to an identity that popped out (if you've ever tried this yourself, you know the one) and stared in abject disbelief at these tiny octagonal corners where the vector just barely squeezes out of my algebra's reach.
Nothing was working. I took a nap.
I wake up later with what I thought was the dumbest idea of the entire problem solving session. "Well, if lambda can be any complex number, isn't the phase you get from the inner product itself a complex number? No, it's not that simple, but what if it is? I guess we'll see."
And it worked.
I call up my friend Alles and tell him in a daze that "I might have found a nonstandard proof of Cauchy-Schwarz" and after some back and forth he says he'll look at what I write up. I throw it together in typst and email it to him.
The morning after (well, later in the morning), it hits me. This isn't big enough to publish, and if I bring it to an actual mathematician, they'll at best have a bit of a chuckle and at worst say "...well how else would you do it?" So, convinced that I have nothing to lose, I give Claude Opus 5.5 my PDF.
It found some typos (and one genuine inaccuracy), and it also suggested a real stylistic fix that I then accepted (using lambda equals the inner product instead of the normalized inner product), and it assured me that nothing I was doing was new at all. That was healthy.
And then the moment of realization that made this entire ordeal worth a blog post -- I thought to myself, "wait, have people not been interested in my stuff because they think that with the advent of strong LLMs, I'm basically dead in the water?"
It was a very believable claim. I decided I didn't really give a fuck about what people think of my writing, and reduced it to something more tangible: "if I am to rely on LLMs to forward my learning, what does that make me?"
And what I landed on was, "a denizen of 2026."
Look, Claude is good nowadays. It's so good that people are having existential crises about their own technical expertise and doomsaying that AI will turn us all into glue. I don't buy it, though. Because as low as the lows were, that emotional rollercoaster of getting to a solid proof of Cauchy-Schwarz independently was about as close as I can get to an answer as to why I feel like life is worth living at all.
I am a human, and I struggle.
Struggle is not the point of life, but it's so centrally thematic to the experience of anyone who tries things worth trying, that it warrants taking a step back at some point to ask, "does this actually edify me? am I really having fun?" and if the answer is yes, I believe it's fair to say that, even in an age of LLMs that can catch your typos and do the lit search for you and even suggest more tasteful angles to refine your own judgement, the fun has yet to be ruined.
Also, there's a point about humility I want to make. I am not God, nor will I ever be. The lambda change was genuinely good, and whether it was Claude's or something Claude ingested does not matter -- it wasn't mine, that's for damn sure. At a certain point it does make some sense to defer to the product of aggregate human knowledge in a can. Where you draw that line yourself, I am not here to say.
So, am I dead in the water? I kinda avoided the question earlier, but let's actually address it a little. I don't think so, and the reason why is not because AI is going to plateau (doubtful) or that people are gonna stop shifting to using it as a canonical reference (this shift has basically already happened, see the slang term "meat proxy" if you don't believe me). I believe I'm not dead in the water because for every person who uses AI the way I use it, there are maybe nine people who use it far more lazily and irresponsibly, to use generous numbers. After all, I could've just prompted it to generate a few proofs of Cauchy Schwarz and picked from the bounty of token-fueled output.
But that would've robbed me of my confusion. And no one does that to me, ever.
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