I have some math background so have a little insight here, although I don't have the specifics you might be looking for. This ended up long.
So, there's math software that's been in longterm development for proof verification, such as Coq and Lean. I did read pretty recently that multiple big results were announced proven and verified by one of these, but on human review the AI had exploited undiscovered bugs in the prover. Automating theorem-proving has been in development for a long while as well, and is (was?) often referred to as AI although is definitively not an LLM.
With that out of the way, whether by LLM or otherwise, legitimate computer-generated proofs are having a lot more success. The caveat is that they're not innovating and my understanding is they're not expected to anytime soon. I'll explain what I mean by that, although you might be able to guess.
Different disciplines and subdisciplines have different tools and strategies used as go-tos. If I'm doing categorical homotopy theory and I'm looking to find an appropriate model structure on some category, maybe my category has certain features that would suggest my first attempt start with a transferred model structure from a model category which admits an adjunction to mine. A computer with access to all existing math literature can make these connections, that this approach is used often in this situation.
Like any subject, math literature is absolutely enormous. There have been instances of teams of mathematicians, people who have devoted lifetimes to understanding existing literature for a single subdiscipline, working together to prove a result for a new paper, and after publication someone from an adjacent subdiscipline reads it and comes out of the woodwork to point out the journal where their result was first proven forty years back as a lemma used in getting another result. Computers can access all of this literature at once.
This leaves a ton of room for computers to play connect-the-dots in a much more exhaustive way than mathematicians with knowledge limitations can. We want to prove X, well Y technique is a common approach, we'll need to prove Z to get there, W technique would be where to start... but if Z was published in some obscure journal as a corollary to a little-known result from a seemingly unrelated discipline, a researcher won't know that, and won't know that this result somehow fell out of matroid theory instead of algebraic topology, which would have indicated who to collaborate with.
A computer can also go much much further down rabbit holes that look not worth digging into to a human solely based on inconveniencing people. If I need to ask a graph theorist and she says we need to understand more about finite group theory, and the group theorist takes time to think before saying more knowledge of K-theory would help, and all of this ultimately ends up going nowhere, I'm going to feel pretty silly for taking time from all these people and they might give me less time in the future when I might be more desperate. The computer doesn't take consideration of whether this is a hassle, it just explores.
The common tricks and tools of a trade weren't always there though. Someone has to be the first to realize that taking homology is extremely effective in the contexts I'm working in. Someone has to be the first to say the objects in the dual to the category of rings can be viewed as locally ringed spaces, let's try doing algebraic geometry by gluing rings together analogously to how open balls glue together into manifolds. Someone has to come up with the concept of a ring as a mathematical tool. I don't think computers are anywhere close to that.
Computers becoming good at connect-the-dots could still devastate mathematics as a profession though. A mathematician can make a living by knowing the literature of a hyperspecialized subdiscipline better than anyone else. That knowledge means he needs much less new knowledge to make easy "connect-the-dots" in his specialty. The more practice he gets doing that though, the deeper his understanding grows. Deep insights typically don't come from thinking better thoughts than everyone else, they come from an intimate understanding of what you're looking at. Removing all the low-hanging fruit removes a lot of the incentives for a professional to start understanding a discipline better. Grothendieck doesn't revolutionize algebraic geometry without spending a ton of time doing algebraic geometry first, and being able to publish while getting your feet wet doesn't hurt with that. If publishing math is my living, why am I going to spend years researching a discipline when people who spent lifetimes doing that couldn't crack the remaining problems? I'll need to accept that the time investment probably won't help me make a living. Being a grad student today must be a nightmare.
We've always understood all these different branches of math are all deeply connected, but I have to think limitations of how much one human can learn have prevented us from grasping just how deep. It's conceivable that a computer could string together a chain of thousands of very straightforward logical steps pulling from all corners of literature to solve a millennium prize. It would be the analogue of a computer solving an enormous maze by brute-forcing every possible path, while a human would never have the patience to spend that much time on an approach requiring zero intelligence. Evangelists lacking the background needed to comprehend the problem would declare human ingenuity obsolete against the sheer brilliance of the brute-forcing machine.
In a perfect society, math would be enjoyed as an art and could be pursued as an art without necessity to break new ground regularly to prove your worth. In a perfect society, math in academia would be driven by a desire to learn and do math. If being credited weren't important, mathematics would still thrive alongside advances in automated theorem-proving. Time investment is the requirement for deep breakthroughs, and there are definitely those of us who would love to invest time into learning without the pressure to be credited with successes. We don't live in a world where academia is about learning. It's hard to picture the profession staying the same as long as academia functions as an economic gatekeeper instead.
Yes, of course they're using your code to train their models. That use is in their terms and their licensing.
It's irrelevant to your point but this is absolutely not true. As far as I know they don't have legal basis to violate software licenses of new projects added to github, but even if I'm mistaken on that an enormous number of projects were on github when microsoft purchased it, and almost all of them were at minimum licensed so that code usage required attribution. Microsoft has been very aware that no person or organization behind a project hosted on github has the financial resources to take them to court.
I'd rather take it at face value and assume modern medical science is finally allowing us to substitute pills for normal body usage.
For one thing, I'm tired of having to go to the bathroom on a regular basis. Can I get a piss pill to experience an empty bladder without the tedium of actually peeing?
The moment we stop believing in that potential is the moment that we stop supplying AI companies with bales of cash to shovel into their money-furnaces so that they can afford to sell hundred dollar bills for a dollar each to Elon Musk cultists who want to generate child porn and pictures of Sonic the Hedgehog with giant boobs.
I didn't get it until I read the transcript. I thought that the second panel was a jab with barbed wire (tetanus risk) and that the joke was basically "if your body is punctured, be sure to treat it by puncturing your body".
I actually think I find that reading more fun than the intended one.
It's very easy to believe that young people hate AI CEOs, but following the links it's clear to me that I'm either extremely out of touch or that poll is garbage. The same poll says 74% of respondents ages 18-34 placed a bet in a prediction market (Kalshi or Polymarket) in the past thirty days.
I just finished Anode Heart after a million hours over the past couple weeks. Spectacular game. It's an indie monster tamer, it doesn't have the graphics of Nexomon: Extinction or Cassette Beasts but I liked it better than either of those.
I've started a monster taming game called Anode Heart and it's good stuff so far. There's a lot of depth to the gameplay, somewhat nonlinear with a strong story anyway. It came out about three years ago. Comparing to other indie monster tamers I'd definitely put it above Cassette Beasts, not sure about Monster Sanctuary but it's much less well-known than either and deserves to be.
I think when someone who isn't careerist or corrupt slips through the cracks and gets elected to congress, the more they hold to their principles the harder it is to survive. Holding firm means making enemies of almost everyone you work with and losing office. Trying to play nice while holding your principles means fading into irrelevance until you pick a path. Legitimately trying to accomplish things means actually breathing through that ecosystem day-in-day-out until you've absorbed the rot without even knowing it.
I don't know Massie's reprehensible opinions, I'm sure they're there because he wouldn't be a republican otherwise, but I do get the sense he actually believes things so isn't a lost cause. I think Sanders went the irrelevance route for ages before starting to compromise, but in the past decade has lost more and more perspective through the horrors of the campaign trail. I've had the sense AOC has always been a careerist, but if she wasn't to begin with she is now regardless. All of this is personal vibes-based analysis which shouldn't be taken seriously, but commenting to validate that I get the same impression.
I am so bad at doing stuff on time / arriving at appointment's, that this will fail any therapy where I have to arrive physically
Weirdly enough I end up at the opposite end. Before I have a rapport with someone I will worry way too much about being late, so I'll set an alarm earlier than needed and feel internal pressure to be out the door at a time that can account for absurdly bad traffic and I'll usually end up awkwardly sitting in the waiting room for half an hour. Once I know someone will cut me some slack I will be more relaxed until I actually am late for one, at which point I worry about if I do it again soon after it might look like a habit and I'm temporarily back to super-careful. The most helpful thing a counselor ever did for me was forget to show up for one in our first couple weeks, from there out it felt like I get a mulligan if something goes wrong.
If all I have to do is sit in front of my computer then my brain won't let me feel pressed until a few minutes before, and then sometimes distractions happen.
A class of students doing that would be a million times more fun for the professors too. Acadamia would be so much better if education were its primary purpose.
That was my niche in grad school. I authored a paper proving that the CW-complexes in the category of small categories under the Joyal-Tierney model structure are exactly the groupoids. I never came up with a reason why anyone should care, but at least it was fun.
You don't welcome someone who is currently dangerous. My point is that a person who is facing an entire lifetime of self-loathing in silence is more likely to eventually become a threat years down the road. Most people feel a need to get things off their chest after a long enough time hurting quietly, and someone in that position will be much more likely to turn into a predator if the only people they feel safe opening up to are other pedophiles. You can call opening up to someone who can give them healthy perspectives "an outlet", but I think it would be less harmful than repression. I'd rather they try to get help and make other people aware of the issue in the process.
Realistically there's no magic wand to solve this, but I do believe that pushing people who are not predators underground is much more dangerous than looking at it as an illness that deserves support in mitigating.
I'd bet that the societal stigma actually makes it more difficult than heroin in spite of the raw addictiveness. Society does look down on drug addicts, but there's still a decent chunk of people who will be understanding and rooting for them sincerely when they're trying to overcome it. I have to imagine it would be infinitely harder to find just one person you feel safe asking for help, much less an entire community.
I have to think they'd be much less dangerous in a society more willing to differentiate between pedophilia and predation just because of how much of a difference community support can make. If they feel like the only people they can open up to are other pedophiles, that's probably not a recipe for hearing healthy perspectives.
On the other hand, it's probably easier for me to say this stuff from my armchair with no children of my own and not even interacting with any children on a regular basis.
I believe veganism is ethical but have failed repeatedly in attempts to give up comfort foods. A lot of tastes nauseate me, so I don't intend to give it another try until I can afford the costs (in time, finances, emotional health) of trial-and-error to find more meals that work for me.
intrinsic critical thinkers whose nature overcame their upbringing
I'm going to push back on this because I don't think it's true and also because I think it's harmful.
There are not people who are naturally inclined not to think critically. Just as much as upbringing can shape someone's worldview, environment can shape willingness and capacity for introspection. People don't think critically when they're naturally predisposed to do that, they think critically when they're either adequately distanced from the disincentives for reflection they've known forever or when the incentives for reflection create enough desperation to overwhelm.
I say harmful because is there anyone who sincerely doesn't picture themselves as an intrinsic critical thinker? Everyone is already there, so the "intrinsic critical thinker" worldview means assuming some people you meet will be worse at it. "I'm naturally better at critical thinking than this person" is a mindset that provides a shortcut to dismissing this person's viewpoints without actually evaluating them.
I have some math background so have a little insight here, although I don't have the specifics you might be looking for. This ended up long.
So, there's math software that's been in longterm development for proof verification, such as Coq and Lean. I did read pretty recently that multiple big results were announced proven and verified by one of these, but on human review the AI had exploited undiscovered bugs in the prover. Automating theorem-proving has been in development for a long while as well, and is (was?) often referred to as AI although is definitively not an LLM.
With that out of the way, whether by LLM or otherwise, legitimate computer-generated proofs are having a lot more success. The caveat is that they're not innovating and my understanding is they're not expected to anytime soon. I'll explain what I mean by that, although you might be able to guess.
Different disciplines and subdisciplines have different tools and strategies used as go-tos. If I'm doing categorical homotopy theory and I'm looking to find an appropriate model structure on some category, maybe my category has certain features that would suggest my first attempt start with a transferred model structure from a model category which admits an adjunction to mine. A computer with access to all existing math literature can make these connections, that this approach is used often in this situation.
Like any subject, math literature is absolutely enormous. There have been instances of teams of mathematicians, people who have devoted lifetimes to understanding existing literature for a single subdiscipline, working together to prove a result for a new paper, and after publication someone from an adjacent subdiscipline reads it and comes out of the woodwork to point out the journal where their result was first proven forty years back as a lemma used in getting another result. Computers can access all of this literature at once.
This leaves a ton of room for computers to play connect-the-dots in a much more exhaustive way than mathematicians with knowledge limitations can. We want to prove X, well Y technique is a common approach, we'll need to prove Z to get there, W technique would be where to start... but if Z was published in some obscure journal as a corollary to a little-known result from a seemingly unrelated discipline, a researcher won't know that, and won't know that this result somehow fell out of matroid theory instead of algebraic topology, which would have indicated who to collaborate with.
A computer can also go much much further down rabbit holes that look not worth digging into to a human solely based on inconveniencing people. If I need to ask a graph theorist and she says we need to understand more about finite group theory, and the group theorist takes time to think before saying more knowledge of K-theory would help, and all of this ultimately ends up going nowhere, I'm going to feel pretty silly for taking time from all these people and they might give me less time in the future when I might be more desperate. The computer doesn't take consideration of whether this is a hassle, it just explores.
The common tricks and tools of a trade weren't always there though. Someone has to be the first to realize that taking homology is extremely effective in the contexts I'm working in. Someone has to be the first to say the objects in the dual to the category of rings can be viewed as locally ringed spaces, let's try doing algebraic geometry by gluing rings together analogously to how open balls glue together into manifolds. Someone has to come up with the concept of a ring as a mathematical tool. I don't think computers are anywhere close to that.
Computers becoming good at connect-the-dots could still devastate mathematics as a profession though. A mathematician can make a living by knowing the literature of a hyperspecialized subdiscipline better than anyone else. That knowledge means he needs much less new knowledge to make easy "connect-the-dots" in his specialty. The more practice he gets doing that though, the deeper his understanding grows. Deep insights typically don't come from thinking better thoughts than everyone else, they come from an intimate understanding of what you're looking at. Removing all the low-hanging fruit removes a lot of the incentives for a professional to start understanding a discipline better. Grothendieck doesn't revolutionize algebraic geometry without spending a ton of time doing algebraic geometry first, and being able to publish while getting your feet wet doesn't hurt with that. If publishing math is my living, why am I going to spend years researching a discipline when people who spent lifetimes doing that couldn't crack the remaining problems? I'll need to accept that the time investment probably won't help me make a living. Being a grad student today must be a nightmare.
We've always understood all these different branches of math are all deeply connected, but I have to think limitations of how much one human can learn have prevented us from grasping just how deep. It's conceivable that a computer could string together a chain of thousands of very straightforward logical steps pulling from all corners of literature to solve a millennium prize. It would be the analogue of a computer solving an enormous maze by brute-forcing every possible path, while a human would never have the patience to spend that much time on an approach requiring zero intelligence. Evangelists lacking the background needed to comprehend the problem would declare human ingenuity obsolete against the sheer brilliance of the brute-forcing machine.
In a perfect society, math would be enjoyed as an art and could be pursued as an art without necessity to break new ground regularly to prove your worth. In a perfect society, math in academia would be driven by a desire to learn and do math. If being credited weren't important, mathematics would still thrive alongside advances in automated theorem-proving. Time investment is the requirement for deep breakthroughs, and there are definitely those of us who would love to invest time into learning without the pressure to be credited with successes. We don't live in a world where academia is about learning. It's hard to picture the profession staying the same as long as academia functions as an economic gatekeeper instead.
It's irrelevant to your point but this is absolutely not true. As far as I know they don't have legal basis to violate software licenses of new projects added to github, but even if I'm mistaken on that an enormous number of projects were on github when microsoft purchased it, and almost all of them were at minimum licensed so that code usage required attribution. Microsoft has been very aware that no person or organization behind a project hosted on github has the financial resources to take them to court.
I'd rather take it at face value and assume modern medical science is finally allowing us to substitute pills for normal body usage.
For one thing, I'm tired of having to go to the bathroom on a regular basis. Can I get a piss pill to experience an empty bladder without the tedium of actually peeing?
Doctorow really writes like a poet, doesn't he?
I didn't get it until I read the transcript. I thought that the second panel was a jab with barbed wire (tetanus risk) and that the joke was basically "if your body is punctured, be sure to treat it by puncturing your body".
I actually think I find that reading more fun than the intended one.
It's very easy to believe that young people hate AI CEOs, but following the links it's clear to me that I'm either extremely out of touch or that poll is garbage. The same poll says 74% of respondents ages 18-34 placed a bet in a prediction market (Kalshi or Polymarket) in the past thirty days.
There's no way 74% even have accounts, right?
I can't get this method to work for me, do you have a guide?
I just finished Anode Heart after a million hours over the past couple weeks. Spectacular game. It's an indie monster tamer, it doesn't have the graphics of Nexomon: Extinction or Cassette Beasts but I liked it better than either of those.
Yes, let's spread the blame across all of planet earth. All of us should be equally ashamed.
You could have acted. I could have acted. Nancy Pelosi could have acted. No one's innocent here.
I've started a monster taming game called Anode Heart and it's good stuff so far. There's a lot of depth to the gameplay, somewhat nonlinear with a strong story anyway. It came out about three years ago. Comparing to other indie monster tamers I'd definitely put it above Cassette Beasts, not sure about Monster Sanctuary but it's much less well-known than either and deserves to be.
Holy shit.
At this point I feel ashamed admitting I find this astonishing. Everyone come point and laugh because I'm somehow still not jaded enough.
I think when someone who isn't careerist or corrupt slips through the cracks and gets elected to congress, the more they hold to their principles the harder it is to survive. Holding firm means making enemies of almost everyone you work with and losing office. Trying to play nice while holding your principles means fading into irrelevance until you pick a path. Legitimately trying to accomplish things means actually breathing through that ecosystem day-in-day-out until you've absorbed the rot without even knowing it.
I don't know Massie's reprehensible opinions, I'm sure they're there because he wouldn't be a republican otherwise, but I do get the sense he actually believes things so isn't a lost cause. I think Sanders went the irrelevance route for ages before starting to compromise, but in the past decade has lost more and more perspective through the horrors of the campaign trail. I've had the sense AOC has always been a careerist, but if she wasn't to begin with she is now regardless. All of this is personal vibes-based analysis which shouldn't be taken seriously, but commenting to validate that I get the same impression.
Weirdly enough I end up at the opposite end. Before I have a rapport with someone I will worry way too much about being late, so I'll set an alarm earlier than needed and feel internal pressure to be out the door at a time that can account for absurdly bad traffic and I'll usually end up awkwardly sitting in the waiting room for half an hour. Once I know someone will cut me some slack I will be more relaxed until I actually am late for one, at which point I worry about if I do it again soon after it might look like a habit and I'm temporarily back to super-careful. The most helpful thing a counselor ever did for me was forget to show up for one in our first couple weeks, from there out it felt like I get a mulligan if something goes wrong.
If all I have to do is sit in front of my computer then my brain won't let me feel pressed until a few minutes before, and then sometimes distractions happen.
A class of students doing that would be a million times more fun for the professors too. Acadamia would be so much better if education were its primary purpose.
That was my niche in grad school. I authored a paper proving that the CW-complexes in the category of small categories under the Joyal-Tierney model structure are exactly the groupoids. I never came up with a reason why anyone should care, but at least it was fun.
I'm sure looking closely at their annual audits over the past decade will give us valuable insight into how this could be happening.
You don't welcome someone who is currently dangerous. My point is that a person who is facing an entire lifetime of self-loathing in silence is more likely to eventually become a threat years down the road. Most people feel a need to get things off their chest after a long enough time hurting quietly, and someone in that position will be much more likely to turn into a predator if the only people they feel safe opening up to are other pedophiles. You can call opening up to someone who can give them healthy perspectives "an outlet", but I think it would be less harmful than repression. I'd rather they try to get help and make other people aware of the issue in the process.
Realistically there's no magic wand to solve this, but I do believe that pushing people who are not predators underground is much more dangerous than looking at it as an illness that deserves support in mitigating.
I'd bet that the societal stigma actually makes it more difficult than heroin in spite of the raw addictiveness. Society does look down on drug addicts, but there's still a decent chunk of people who will be understanding and rooting for them sincerely when they're trying to overcome it. I have to imagine it would be infinitely harder to find just one person you feel safe asking for help, much less an entire community.
I have to think they'd be much less dangerous in a society more willing to differentiate between pedophilia and predation just because of how much of a difference community support can make. If they feel like the only people they can open up to are other pedophiles, that's probably not a recipe for hearing healthy perspectives.
On the other hand, it's probably easier for me to say this stuff from my armchair with no children of my own and not even interacting with any children on a regular basis.
I believe veganism is ethical but have failed repeatedly in attempts to give up comfort foods. A lot of tastes nauseate me, so I don't intend to give it another try until I can afford the costs (in time, finances, emotional health) of trial-and-error to find more meals that work for me.
I'm going to push back on this because I don't think it's true and also because I think it's harmful.
There are not people who are naturally inclined not to think critically. Just as much as upbringing can shape someone's worldview, environment can shape willingness and capacity for introspection. People don't think critically when they're naturally predisposed to do that, they think critically when they're either adequately distanced from the disincentives for reflection they've known forever or when the incentives for reflection create enough desperation to overwhelm.
I say harmful because is there anyone who sincerely doesn't picture themselves as an intrinsic critical thinker? Everyone is already there, so the "intrinsic critical thinker" worldview means assuming some people you meet will be worse at it. "I'm naturally better at critical thinking than this person" is a mindset that provides a shortcut to dismissing this person's viewpoints without actually evaluating them.