In the halls of the math department at my old university there’s a TV screen that loops through different event announcements. But there’s one screen on the loop that will stick with me forever. Paraphrasing:
“Pure mathematicians value the proof, applied mathematicians value the theorem.”
I forget who said this, or if it’s attributed to anyone at all, but I’ve been mulling over this for years at this point. What I take from this is there exists a duality to all theorems. There’s everything that needs to come together to prove it, and there’s everything the theorem implies. Different mathematicians look at different parts of this duality depending on what they are working on. LLM autoproofs are the death of the pre-theorem part of the duality. If we are able to prove things with a quick LLM query, then there’s nothing to wrestle with.
This thought makes me actually feel a deep sense of loss. I went through my whole math education without formal proof engines, just books and my brain for every proof I had to write over the ~5 years I actually was doing proofs. I think this is a dying way to do math, especially in the age of AI, and for some reason that hurts.
I think the act of actually grappling with a problem is far more important than knowing the solution, and I see this as a larger problem with AI that goes beyond just math. We are witnessing what may be the dying of the old way of learning. There’s a new option we all have. Before we had to solve our problems, now we are fast approaching a world where we can choose to solve our problems or outsource it to AI. This is terrifying to me, as knowing how to solve problems is probably the most important thing a human can learn.
The first few months I spent talking with LLMs were some of the most depressing in my life. It felt as if everything I loved about the act of knowledge gathering and application, was saying goodbye.
It only dies if we want it to die. There’s nothing stopping humans who actually value the act of gathering and applying knowledge from doing so. We just won’t get there first that way, and there won’t be countless lives and vast sums of money and glorious prestige tied up in it. But it might become like a sport, or poetry, or the kind of person that tries to recreate bronze age tech in his backyard using only tools he made himself. This seems like a meta-ethical or fun-theoretic problem.
The act of doing math the old way, will, in the future, become akin to cultures practicing ancient out-moded traditions. They still exist sure, but not in the same way or scale.
When I say the practice will ‘die’ I mean as a primary mode of action on a large scale. The same way cultural traditions die, so do academic traditions. This is what’s depressing to me and its in the same way as someone who watches their culture die.
In the halls of the math department at my old university there’s a TV screen that loops through different event announcements. But there’s one screen on the loop that will stick with me forever. Paraphrasing:
“Pure mathematicians value the proof, applied mathematicians value the theorem.”
I forget who said this, or if it’s attributed to anyone at all, but I’ve been mulling over this for years at this point. What I take from this is there exists a duality to all theorems. There’s everything that needs to come together to prove it, and there’s everything the theorem implies. Different mathematicians look at different parts of this duality depending on what they are working on. LLM autoproofs are the death of the pre-theorem part of the duality. If we are able to prove things with a quick LLM query, then there’s nothing to wrestle with.
This thought makes me actually feel a deep sense of loss. I went through my whole math education without formal proof engines, just books and my brain for every proof I had to write over the ~5 years I actually was doing proofs. I think this is a dying way to do math, especially in the age of AI, and for some reason that hurts.
I think the act of actually grappling with a problem is far more important than knowing the solution, and I see this as a larger problem with AI that goes beyond just math. We are witnessing what may be the dying of the old way of learning. There’s a new option we all have. Before we had to solve our problems, now we are fast approaching a world where we can choose to solve our problems or outsource it to AI. This is terrifying to me, as knowing how to solve problems is probably the most important thing a human can learn.
The first few months I spent talking with LLMs were some of the most depressing in my life. It felt as if everything I loved about the act of knowledge gathering and application, was saying goodbye.
It only dies if we want it to die. There’s nothing stopping humans who actually value the act of gathering and applying knowledge from doing so. We just won’t get there first that way, and there won’t be countless lives and vast sums of money and glorious prestige tied up in it. But it might become like a sport, or poetry, or the kind of person that tries to recreate bronze age tech in his backyard using only tools he made himself. This seems like a meta-ethical or fun-theoretic problem.
The act of doing math the old way, will, in the future, become akin to cultures practicing ancient out-moded traditions. They still exist sure, but not in the same way or scale.
When I say the practice will ‘die’ I mean as a primary mode of action on a large scale. The same way cultural traditions die, so do academic traditions. This is what’s depressing to me and its in the same way as someone who watches their culture die.
In that case, fair, I agree.