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What does the end of mathematics look like?
71–80 of 94 posts
Re: What does the end of mathematics look like?
#72Earlier quoted context omitted.
The human brain runs on about 20 watts of power -- the entire body on 80 watts (at rest). Those numbers are at least good within an order of magnitude. The largest supercomputer consumes 29 megawatts of power for 1.7 exaflops. And the largest supercomputers are nowhere near the flexible generality of a human brain -- they're calculating FFTs for the test. The amount of parallelism in the human brain is enormous. Not…
The next logical step, perhaps ethically questionable, seems to be growing human brains for computational purposes (parallel or quantum) with high bandwidth and very efficient power consumption.
"perhaps ethically questionable"?
I find it hard to think of a more ethically questionable programme!
Re: What does the end of mathematics look like?
#73Earlier quoted context omitted.
> The camera didn't kill painting But it did. Painter used to be a trade where you could sell your painting skills as, well, a skill applicable for other than purely aesthetic reasons, simply because there were no other ways to document the world around you. It just isn't anymore because of cameras. Professional oil portrait painter isn't a career in 2025.
Well, it is still a career, but it's very niche, and more attuned to 'art' than 'documenting the world'.
and instead we have photographers who can document the world at a great volume. My Grandparents had no visual record of their wedding. My wife is a wedding photographer...
Re: What does the end of mathematics look like?
#74The camera didn't kill painting. Neither the bicycle nor the motor-car killed running. There are already subfields of mathematics where it's believed that all the interesting discoveries have been found and no-one is looking except for the occasional amateur - and other subfields where to even have a hope of doing cutting edge research you would need to both do multiple years of postgraduate study and then get accept…
> The camera didn't kill painting But it did. Painter used to be a trade where you could sell your painting skills as, well, a skill applicable for other than purely aesthetic reasons, simply because there were no other ways to document the world around you. It just isn't anymore because of cameras. Professional oil portrait painter isn't a career in 2025.
>Painter used to be a trade where you could sell your painting skills as, well, a skill applicable for other than purely aesthetic reasons, simply because there were no other ways to document the world around you.
Source? If anything I suspect there are more people making a living as painters now than at any point in history.
Re: What does the end of mathematics look like?
#75Earlier quoted context omitted.
> he energy efficiency perspective human brain is very, very effective computational machine Can you explain why you think that? Very often, mechanical efficiency outperforms biological. Humans have existed for thougsands of years, neurons even longer. Computers and AI and relatively recent, we haven't really begun to explore optimisation possibilities.
The human brain runs on about 20 watts of power -- the entire body on 80 watts (at rest). Those numbers are at least good within an order of magnitude. The largest supercomputer consumes 29 megawatts of power for 1.7 exaflops. And the largest supercomputers are nowhere near the flexible generality of a human brain -- they're calculating FFTs for the test. The amount of parallelism in the human brain is enormous. Not…
> we have no idea what a general intelligence algorithm looks like
What's the goalpost here though? modern "AI" stuff we previously thought not possible, Proper full human-brain simulation; or General form of higher AI that could come from either place?
> The amount of parallelism in the human brain is enormous.
That only demonstrates the possibilities yet to be explored. biology has millions-of-years head start; what's possible today could be balked out a few centuries ago by the same argument as yours. You say "We are just now getting multimodal LLMs" like it's somehow late.
At a fundemental level, what holds back biology is all the other things it does (ala staying alive) and the limits imposed (e.g. heat etc) that a purpose-made device can optimise on. Any physical, thermodynamical of communication-theoric argument over what's possible would hold back both biological and mechanical devices. Only there are fewer material constraints for machines - they can even explicity exploit quantum mechanics.
> Sorry, but the notion that we are close to AGI
Seems we are arguing different things. I went back through the thread, and believe the proposition is: "us, humanity, being able to build AI or something being very close to that", which I translate as a comment on our literal species. I took your statement "From the energy efficiency perspective human brain is very, very effective computational machine" as being in that scope, and not just a reference to the current era (or Decade!).
Re: What does the end of mathematics look like?
#76Test-driven development is not about tests. It's about writing code. The tests are there just in order to keep the bugs away.
Mathematics is just proof-driven development. For an spectator it might look like mathematics is about writing proofs, but that's not different than seeing a software developer write a lot of tests. The proofs are the best tools against insidious logic bugs that the society of mathematics has come up with in the last few hundred years. Mathematicians would welcome automating all the proofs, just like software engineers are happy for code assistants to take over the task of writing tests.
Re: What does the end of mathematics look like?
#77I think people like author are positive about us, humanity, being able to build AI or something being very close to that. I am not. From the energy efficiency perspective human brain is very, very effective computational machine. Computers are not. Thinking about scale of infrastructure of network of computers being able to achieve similar capabilities and its energy consumption... it would be enormous. With big infr…
I hope you are right - the point about energy efficiency is certainly spot on, and I do think it is possible that people are getting carried away by analogies when discussing the topic (I wrote something about that too, but will avoid linking to it here to avoid excessive self-promotion).
That said, the article doesn't assume such a thing will happen soon, just that it may happen at some time in the future. That could be centuries away - I would still argue the end result is something to be concerned about.
Re: What does the end of mathematics look like?
#78Earlier quoted context omitted.
The human brain runs on about 20 watts of power -- the entire body on 80 watts (at rest). Those numbers are at least good within an order of magnitude. The largest supercomputer consumes 29 megawatts of power for 1.7 exaflops. And the largest supercomputers are nowhere near the flexible generality of a human brain -- they're calculating FFTs for the test. The amount of parallelism in the human brain is enormous. Not…
> we have no idea what a general intelligence algorithm looks like What's the goalpost here though? modern "AI" stuff we previously thought not possible, Proper full human-brain simulation; or General form of higher AI that could come from either place? > The amount of parallelism in the human brain is enormous. That only demonstrates the possibilities yet to be explored. biology has millions-of-years head start; wha…
I wish I had a nickel for every time an AI hypester complained about goalposts. I thought it was clear that I was talking about AGI, or a general purpose intelligence on the level of humans. You know, what the hypesters have been saying is just around the corner if only they can have another trillion dollars. Sorry for the confusion
> That only demonstrates the possibilities yet to be explored. biology has millions-of-years head start; what's possible today could be balked out a few centuries ago by the same argument as yours.
Yes, we may only have a few centuries left to go before AGI. I was going with a few decades, but now that you mention it, a few centuries is more likely given we are running into Moore's Law limits with transistor technology.
> At a fundemental level, what holds back biology is all the other things it does (ala staying alive) and the limits imposed (e.g. heat etc) that a purpose-made device can optimise on.
You don't honestly believe that AGI will not have to deal with continuity, reliability, and heat dissipation issues that living things have to deal with, do you? All the more reason megawatts vs handful of watts is relevant. You just pointed out that it's not just an algorithmic optimization problem, but a much more complex problem of which we are barely scratching the surface.
> Seems we are arguing different things. I went back through the thread, and believe the proposition is: "us, humanity, being able to build AI or something being very close to that", which I translate as a comment on our literal species. I took your statement "From the energy efficiency perspective human brain is very, very effective computational machine" as being in that scope, and not just a reference to the current era (or Decade!).
I was replying to a literal statement about increased mechanical efficiency over biological efficiency. Which, in the case of AGI is completely inverted. Biological systems are so much more efficient that the comparison is embarrassing.
Also, I was saying our species is at least 3 decades from in-silico AGI. That doesn't mean we'll have some wild new tech that no one thought of next year. But the chances are so slim you might as well be saying we will genetically engineer flying pigs.
Re: What does the end of mathematics look like?
#79Earlier quoted context omitted.
It may be possible to optimise silicon further, but the brain does all of its work with less than a hundred watts, while the silicon closest to its capabilities needs more like tens of kW.
> while the silicon closest to its capabilities needs more like tens of kW. I think looking at power consumption for the very edge of what technology is just barely capble of may be misleading, since that's inherently at one extreme of the current cost-capability trade-off curve[0] and stands to drop the most drastically from efficiency improvements. You can now run models equivalent in capability to initial version…
Well, sure, but the capabilities of the edge of tech is still not matching the human brain. And the fact the you can run older models on less power also doesn't say anything for certain. I'm not saying it won't happen, I'm saying it's not happened and it's not certain it will.
Re: What does the end of mathematics look like?
#80The camera didn't kill painting. Neither the bicycle nor the motor-car killed running. There are already subfields of mathematics where it's believed that all the interesting discoveries have been found and no-one is looking except for the occasional amateur - and other subfields where to even have a hope of doing cutting edge research you would need to both do multiple years of postgraduate study and then get accept…
A recurring problem I see is that people have absolutely drunk the koolaid of the utilitarian worldview. They've been marinating in it for so long, with no exposure to anything else beyond this parochial and base existence, that they have no idea they've been marinating in it. Everything is reduced to economic exchange. Everything is reduced to economic output. Learning is reduced to something that has value only if…
Another problem this creates is that every action is evaluated as a competition. Even collaborative work must be encapsulated in a team. The only success that can be imagined is victory. The only path to consent is by concession and contract.
This framework is explicitly enforced by copyright law. Because a copyright monopoly is automatically granted to every content creator, every person is automatically expected to participate in the copyright system.
Copyright law hinges on incompatibility. The easier it is to make compatible work, the easier it is to make derivative work, which copyright defines as the penultimate evil.
Generative statistical models (what everyone is calling AI) are calling this bluff harder than ever. Derivative work is easier than any time in history.
So what do we do about it? It's pretty obvious from my perspective that the best move forward is to eliminate copyright for everyone. It seems instead, that the most likely outcome is to eliminate copyright exclusively for the giant corporations that successfully launder their collaboration (derivative work) through large generative models.