From all I've read or heard about birth rate rise the measures that sociologists see as the most effective are: provide cheap housing and pay much more to families (i.e. mostly to women) with children to compensate for their loss of potential career. The latter has a twist that the payment should start (or significantly increase) with the birth of the second child (and continue to rise with the third etc). Paying for the first child does next to nothing to the birth rate. Some countries already do that, but the amount of money poured into this should increase by order(s) of magnitude to achieve the replacement level.
Or we can go full medieval - completely deprive women of education possibilities and financial independence, like Taliban does.
> the amount of money poured into this should increase by order(s) of magnitude to achieve the replacement level.
Exactly. And I found it being obvious after having thought about it, even while not having kids and I most likely will never have any.
Just from observing and talking to people with 0-2 kids (nobody I know has more...).
I know a couple with good income, living in Munich, which is one of the most costly cities in Germany, one Child. Avoidable pain points (finding daycare, you better start right after the baby was born, because they have multi-year waiting lists) and they feel the financial hit pretty hard.
Works of Shinichi Mochizuki immediately come to mind. He is not AI but provides very good examples of math that is useless because it is incomprehensible by (other) humans.
Do AIs produce answers whose work is incomprehensible to humans? It seems like you could just have the AI elaborate multiple times until you were satisfied with the explanation and documentation of what went into figuring out the answer. It’s not like the AI is one shotting the answer in a single opaque query anyways.
Like other commenters, I think you’re also underestimating the complexity of esoteric higher level math.
Consider the “Magnus Carlsen” of mathematics, who is more capable of understanding mathematics than any other human. But then also realize that that individual has probably devoted their entire career into a specific subdomain of mathematics. Within other deep recesses of mathematics, this Magnus equivalent will be less capable than their peers without years of rewiring their brain to understand the esoteric concepts and properties within that other subdomain.
LLMs will be able to dig deeper and broader than any human mathematician, and find results that are completely useless to humans because it would take more than an entire lifetime to “speak the language” of the concepts the LLMs have produced. The only way those results can become useful to humans is if then the LLM itself finds a way for it to be practical to humans once again.
So, no, I don’t think this represents the “democratization” of mathematics where mathematicians are no longer necessary because anyone can just prompt the LLM to explain it. The bar for entry level mathematics is lower, for sure, but research level mathematics will continue to be unapproachable for anyone who hasn’t devoted their career to it.
> “speak the language” of the concepts the LLMs have produced
LLMs don't produce concepts, they just predict next tokens; they can't invent new concepts, only synthesize what is in their probability distribution already. They can mix/fuse vast areas of math together that are inaccessible to individual mathematicians, but can't create new concepts not present in their probability distribution.
I don't get it. LLMs don't have ego, they don't have the ability to say "no, this should be obvious, I'm not going to explain further", they are just token predictors, and given context, they can generate more tokens. If you don't understand how the answer was derived? You just ask more questions and it isn't going to get bored or annoyed, it will just try to answer the questions.
No, it doesn’t sound like you get it. It has nothing to do with the properties of LLMs and everything to do with the complexity of mathematics.
Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly.
Without a human holding the reins, consider an LLM a rudderless superboat speeding erratically towards the horizon, finding and proving meaningless theorems that not even your most talented classmate could ever begin to understand.
My point is the human is a critical piece to the puzzle, but not just any human, a career mathematician.
> Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly.
> Without a human holding the reins, consider an LLM a rudderless superboat speeding erratically towards the horizon, finding and proving meaningless theorems that not even your most talented classmate could ever begin to understand.
This feels like a little bit of a jump to me. AIs arent actually alive so of course someone is going to have to pose the question. They arent going to just do stuff on their own. And of course mathmaticians are going to need to interpret the results if we are to glean anything beyong if the conjecture is true or false.
But you seem to be suggesting that mathematicians will have to micromanage every step. That seems like a bit of a jump which i dont see much evidence for.
Micromanagement wasn't the message I took from that. Rather the level of human involvement required which (it seems like) the two of you more or less agree on.
The meaning I took was how far it's possible to travel from the shore - ie the scope of the state space. The mathematics we're exposed to is all quite shallow compared to what will (presumably) be possible between digital formalization and massive ML models. But the latter probably can't ever be understood by regular biological humans.
> Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly.
I'm really interested in this anecdote. I have never experienced this but have a reasonable academic background (BSc, MSc, MD) - and I am certainly not the person you're describing. Could you elaborate? Is this something more exclusive to pure mathematics (my bsc/msc are CS).
For me it was a “Modern Algebra” course required for my mathematics major, where I managed to squeak by with a B, but it was definitely a filter course for research-level mathematics. It was very clear in the class of a few dozen students who the top 5 or so were based on their questions during lectures and office hours, as well as when they blessed us mere mortals with their presence at our study groups.
(Aside, this was one of the only undergrad courses where I felt I needed to attend study groups in order to not fail.)
The first exam was easy to pass based on intuition alone, as the topics were isomorphic to concepts I was familiar with like geometry or algebra. The midterm was a wake up call when it was made clear that just understanding the homework wasn’t sufficient, you were going to be asked to prove things that were much more difficult than what I’d ever encountered, and under time pressure (I had been doing math proofs since age 13 in geometry, and I was 22 at that point).
Maybe if you did discrete math, combinatorics, or linear algebra I would say it was 5x to 10x more abstract and difficult. Probably 2x more difficult and abstract than Theory of Calculus, if you had taken that or a similar course.
Edit: I also do endurance running and play soccer into my 30s. Seeing people run literally twice as fast as me (world record pace), and playing against former college athletes is equally as humbling. The time has passed for me to have anything near their ability haha.
Algebra is the class where I learned I shouldn’t try to figure out how to prove theorems named after people during tests.
And I think you’re underestimating the jump from discrete math and linear algebra to abstract algebra… I think I attended each of those classes and opened their textbooks a total of 3 times each and did fine - once for each exam. But fml abstract algebra and measure theory were rough.
For myself it was learning what a limit is in calculus, then learning about vector spaces, then learning about metric spaces and then learning about different topological spaces.
Then I had to relearn how a limit worked.
From a proof with epsilon delta inequalities.
To a proof with showing for some n dimensional metric spaces that has all the properties needed to converge does in-fact converge. Finally to a proof that for any space that is metric there is an isometric function into that metric space that also converges.
And that does touch measure theory, functional analysis or set theory. So there’s still so so much more for me to learn.
> Have you ever been exposed to concepts that are so complex that you feel like you could devote your entire lifetime to trying to understand it and still fall short? It’s a very humbling experience, especially if you have classmates who pick it up effortlessly.
I do have a PhD so I kind of know how that feels. I watched my entire field (PL) get eaten up by AI though, the problems that I thought were huge 10 years ago are just silly footnotes now.
> Without a human holding the reins, consider an LLM a rudderless superboat speeding erratically towards the horizon, finding and proving meaningless theorems that not even your most talented classmate could ever begin to understand.
I don't disagree with that. LLMs are a tool, a super fast pattern matcher, research, token predictor. I don't expect it to go out and define its own esoteric (or useful) problems to pursue without human interaction. That's for the humans to do.
I don't understand what that has to do with my original comment though. I wasn't addressing what problems the LLMs were answering, just how to review and dissect the answers that they would come up with.
Excluding supergeniuses, pure mathematics—even at a very basic, undergraduate level—simply can't be understood passively. Even with an infinitely patient AI teacher who could answer any question on-demand, it'd still require a massive amount of work to actually understand anything in research-level mathematics. Basically every single word in a mathematical definition is a term of art, and (IME) if one doesn't grok each of those words at a fairly deep level, the new definition never really makes too much sense. And this applies recursively: each of the words has some thoroughly inscrutable definition of their own.
Of course it'd be super helpful to have, say, a teacher who could tailor explanations to anyone's precise background (e.g. where possible, using examples that come from the student's field of study when explaining some abstract concept). Or, if some definition comes with some precondition that has no obvious purpose, perhaps an omniscient teacher could explain why it's there with concrete counterexamples.[0] But even granting all this, I think that mathematical intuition is necessarily based on a lot of hard work actually exploring definitions on one's own, with pencil-and-paper and a lot of thought. That is to say, even though the process could probably be sped up a lot with a nigh-omniscient teacher[1], I doubt that a student wouldn't still need years of training to even have a clue what's going on.
(I'm saying all this, by the way, as someone who is terrible at all this and has very little mathematical maturity[2]—I'm speaking from my own frustrating experience....)
[0] c.f. Lakatos' excellent book Proofs and Refutations
[1] without the "curse of knowledge," or else we're back to square one of "answers that are correct but useless"
It’s easy to imagine this being a problem both in quality and in volume. Verifiable work is less valuable than verified work. And noise is always costly.
In the RN for the latest release it states:
Breaking Changes
Use of jqwik >= 1.10 with coding agents is strongly discouraged. Jqwik’s output to stdout may confuse AI-based agents.
So to me it is malware as much as the "rm" command is malware - if used without understanding and reading docs it can wipe all your data.
Knowing swedish people's mindset I'm not surprised at all by the breach. What can be mildly surprising is that no major e-gov service has expressed concerns on their websites. Only on skatteverket.se, which is Swedish Tax Service website, there is a vague note on "maintenance work" planned for coming Saturday. Maybe totally unrelated though.
Some other comments mention BankID private keys . That would be the biggest disaster as that’s what everyone uses to identify themselves “securely” on all government services.
Well doesn’t Relying Parties using the BankID API for signatures and authentication have private keys to start the flows for users scanning QR codes etc?
Could you, having the right private keys, impersonate some company soliciting a BankID signature?
I’m not sure what you can do with that though. You cannot steal some other ongoing signature I guess.
You can start a signing process saying you are who ever owned that certificate. E.g. if you call someone. You can not use those signatures to gain access, and it is rather in phishing.
Yes, nothing and the facts that these are government services, they use BankID and they updated their websites with "maintenance work" announcements for tomorrow, Saturday. For kronofogden.se there was no maintenance planned just half an hour ago. Knowing swedish tendency to plan things months ahead I would _guess_ that this maintenance work has been rushed due to some circumstances.
It's quite possible that the maintenance is related, but I can nearly 100% assure you this has absolutely nothing to do with BankID. I don't know who suggested that but they are either poorly informed or actively trying to sow FUD.
Any situation when mobile internet cannot be used. That is not only protests, but also legal gatherings, i.e. street concerts, or places where mobile coverage is poor in general.
That depends on where your live (and when), but: Protest is the cornerstone of democracy and in general you shouldn't need permission to organize a demonstration.
I prefer voting. I find protests annoying. They're a good way for people to let off steam, hang out with friends, get photos for the international press etc. but they're not the right mechanism for finding out what the people want.
They're definitely effective when most of the country wants the government out, but by that point a vote would certainly do just as well, and with fewer flying bricks.
Protests can serve as an implied threat if the government is gaming the election process. They're certainly preferable to a riot or a coup attempt in that scenario.
They also serve to draw attention to issues that aren't showing up on the ballot for whatever reason. The system doesn't always work in an ideal way. To that end protests are supposed to be annoying to those who don't care.
Everyone prefers voting.. But to be able to vote, a vote must be happening. Protests are sometimes the only way to make a vote happen in the first place.
They are also a good communication tool for the world to see what the people are struggling with.
Name three currently existing democracies. USA is out (protests illegal), Europe is out (protests require registration which is denied for anything that has a risk of effecting change), the Middle East and Asia are out for obvious reasons. Maybe there's a democracy somewhere in Africa?
but the internet is for talking to people across the globe. and the app presents itself as an alternative for internet based apps. the reality is however that in any place where i can't use the internet, this app does not really solve that problem. it is only useful in situations where in most cases the alternative is talking face to face. it's not any situation where the internet can't be used, but just some of them. there certainly are good use cases for local communication, cases where face to face is just out of reach and many of these use cases are currently served with internet based apps too. but it's not an alternative to internet based apps per se.
The Internet is _not_ for talking to people across the globe. The Internet allows that, but not only that - one can have a Whatsapp chat with someone in the same bus, this is both legal and technically possible.
The bitchat app serves the niche where talking face to face is not an option and talking across the globe is not needed. And the app explicitly states "infrastructure independence" as one of its design goals: "the network remains functional during internet outages", which cannot be served by internet-based apps by design.
The Internet is _not_ for talking to people across the globe. The Internet allows that, but not only that - one can have a Whatsapp chat with someone in the same bus, this is both legal and technically possible.
technically possible but rather redundant and in most cases pointless. (yes, there are exceptions)
so i rather strongly disagree. 99% of my use of the internet is to talk to people across the globe. it's its primary use case. the example you mention is a fringe application, useful to a tiny minority.
"the network remains functional during internet outages"
that strongly implies that i can use this app to replace other apps that use the internet. but i can't, because it does not allow long distance communication the way internet based apps do.
so for 99% of my needs this app is not helping me. it does not make me independent of the internet. i have been in places where the internet was cut off due to political turmoil. and i have friends who have that happen to them. in all cases the main challenge was the lack of long distance communication. local communication was barely affected.
sms and phone still worked, and in fact the app that would have helped is one that can route data connections via sms and phone calls. like old acoustic modems.
infrastructure independence at a local level is nice, but much less serious or critical than independence for long distance communication. and long distance already starts at a few km.
I believe bitchat can also use the wider internet to exchange messages. So it is an app that can use either the internet or various other more local options. That seems like a desirable improvement to me.
What is conceptually different between prompts and code? Code is also not always what the computer will do, declarative programming languages are an example here. The only difference I see is that special precaution should be taken to get deterministic output from AI, but that's doable.
A prompt is for the AI to follow. C is for the computer to follow. I don't want to play games with definitions anymore, so I am no longer going to reply if you continue to drill down and nitpick about exact definitions.
If you don't want to argue about definitions, then I'd recommend you don't start arguments about definitions.
"AI" is not special-sauce. LLMs are transformations that map an input (a prompt) to some output (in this case the implementation of a specification used as a prompt). Likewise, a C compiler is a transformation that maps an input (C code) to some output (an executable program). Currently the big difference between the two is that LLMs are usually probabilistic and non-deterministic. Their output for the same prompt can change wildly in-between invocations. C compilers on the other hand usually have the property that their output is deterministic, or at least functionally equivalent for independent invocation with the same input. This might be the most important property that a compiler has to have, together with "the generated program does what the code told it to do".
Now, if multiple invocations of a LLM were to reliably produce functionally equivalent implementations of a specification as long as the specification doesn't change (and assuming that this generated implementation does actually implement the specification), then how does the LLM differ from a compiler? If it does not fundamentally differ from a compiler, then why should the specification not be called code?
It's commonplace for a compiler on one computer to read C code created on a second computer and output (if successfully parsed) machine code for a third computer.
China has built their Great Firewall over many years gradually, and they have a lot of resources inside, so almost everything from the "western" Internet has a Chinese analog.
Russian government simply does not give a flying fuck about people and economy on either side of the border, so they can just pull the plug completely if they see it necessary from the political point of view.
So these countries are hardly reference points for what UK can achieve (although Russia is closer than China).
reply