I do this, or in other words, I had to do this to go on. I think everyone comes up with some philosophy to keep on going. Even a street bum might have come up with philosophy on par with some of the greats that keeps them going...
In fact, for this particular idea, I am so over the edge that I sometimes feel pity for those conventionally lucky people who seemingly have it all and don't have a struggle on their on. I mean, what is the point of their life? But I find consolation in the possibility that they might have hidden struggles...
Only a precious few are so lucky that they don't have secret miseries. So you didn't get lucky -- I didn't either. Gotta take your licks and move on.
Besides, there is a way to transcend that unhappiness. I've seen people meditate their way out of it, but it takes years of study and discipline. The only reason why every psychiatrist doesn't tell you to start doing it is you can't just tell someone to work hard at something, they have to want to do it themselves.
1. I didn't say "the best we have." I said the best we could possibly have. There is no form of evidence generation, real or hypothetical, greater than the randomized controlled trial.
2. That doesn't necessarily make it always "sufficiently good evidence", but the beauty of statistics is we actually can know – quite precisely – whether a given evidence generation method gives us sufficient certainty. When an RCT is used as evidence for approval, it is not "well you did an RCT so I suppose it's fine." Approvals actually are not dependent whatsoever on the evidence generation method. The only thing that matters is whether you prove – to sufficient statistical certainty – the claims you are making. It's very hard to do this without RCTs (again being the greatest evidence generation form that could exist), which is why they tend to be the default. But you can run an RCT that fails to produce certainty, and your drug application will be denied. You can also get approval based on a non-RCT (but again it's hard to do because statistics).
We've had this discussion before and the crux of the issue is that you do not understand statistics while the people who design, run, and evaluate clinical trials do. I highly recommend taking a statistics course or four.
>There is no form of evidence generation, real or hypothetical, greater than the randomized controlled trial.
Wrong. You are lying by omission.
Randomization and controlling are essential. But the version of RCT that we currently employ have problems with control and evaluation. If you have a flaw in control or evaluation, then the whole thing becomes flawed.
So the idea of RCT is good, but we are limited by our ability to control and evaluate.So there can be a better version of RCTs that we currently employ, but with precise control and evaluation.
> but the beauty of statistics is we actually can know
The beauty of statistics is also that it is quite easy to hide falsehoods behind statistics.
There Are Three Kinds of Lies: Lies, Damned Lies, and Statistics
(I am not even going into the fraud problem, which is what we have discussed before, which turned out to be quite useless)
>So I wouldn't really say that this result is using or creating some fundamentally new techniques in convex geometry or optimization theory. What this means from my perspective is that if a result is attainable with existing techniques, modern AI methods will be able to solve those problems. I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed.
While they’ll never have the same subjective experience as humans, what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?
They are prediction machines, and so are we in a way. We can give them nearly limitless resources to scale their predictive capabilities. We have billions of years of training baked in. They distill directly from our knowledge and can walk down paths that no human has before.
It’s silly to say they’ll never do anything novel.
At their current capabilities, it sounds like they are already capable of being a specific type is research assistant. What will that look like in 10-20 years?
They also have ability to go deep and wide in a way that humans just can't. We have limits, get tired, distracted and biased where AI does not. I think there a lot of problem where all the information needed to solve them is there, but we just can't put the pieces together. Like no matter how many people you throw at some problems, you hit human limits and more people won't help, but AI will because it is just relentless.
Not really the kind of biased I meant though. There was a recent article about a AI disproving I think an Erdos conjecture by doing similar things humans have tried, but it was much messier and less "beautiful". I think it is a common bias in science and math that things should be "beautiful" but there is no real reason to think that.
>what stops an LLM from applying similar lines of thought* in a manner that results in a novel conjecture?
One thing is that an LLM can never assume, or find out, an inconsistency in its training data. Novel ideas often require correction of existing assumptions. As far as I understand, it is impossible, by design, for LLMs to contradict what is in its training data.
For example, an LLM trained on the data from an internet comprised of people who believe in the earth centric hypothesis can never say "Hey, that cannot be correct", or come up with the heliocentric alternative
Ok, I guess never is a real long time and eventually when we merge our consciousness with the machines we may have the same subjective experience.
I can confidently state that GPT-5.6 Sol is not experiencing the same reality as me. They _might_ be "experiencing" and I personally think they are, but their reality and experience is not the same as ours.
Well, sure. I'm not experiencing the same reality as you, either. I guess I assumed you were implying something more - a lesser experience or something. No?
Famously, all of maths is axioms and tautologies, so I'm not sure this will assuage any professional mathematicians currently having an existential crisis.
Maths was already infinite, it's still infinite, but who wants to spend all their lives changing rooms inside Hilbert's Hotel?
The author explains he's an expert in the domain and that he had worked sporadically on the problem for about a year, also with the help of previous LLMs. So whatever he means by "I wouldn't really say that this result is using or creating some fundamentally new techniques" it doesn't mean that the result was trivial. Also, says it might not make sense to work on low or even medium hanging fruits in the future- and I bet that's by far the largest share of work for most mathematicians.
Sure, it's not a breakthrough that opens new roads in mathematics- is this where the goalpost has moved now?
>because of AI, I've completely lost interest in this kind of stuff.
Where did the joy for doing it came from, before LLMs?
I mean, did people stop playing with LEGOs because we now have 3D printers?
Either you didn't really "enjoy" making stuff before, and were only doing it as a means to an end. Or you are just misguided for a bit, and will come back to it a while later..
In fact, for this particular idea, I am so over the edge that I sometimes feel pity for those conventionally lucky people who seemingly have it all and don't have a struggle on their on. I mean, what is the point of their life? But I find consolation in the possibility that they might have hidden struggles...
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