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What? Children's play is now work? What timeline are we living in? Is this real life?

100% agree, and I experienced that behaviour first hand. I got confident, started giving less guidelines, and suddenly two weeks have passed and the LLM put me into a state of horrible code that looks good superficially because I trusted it too much.

Nicely written! I was thinking about this the other day. What is the benefit from your point of view of procesing information full of null pointers? (I know what the benefit of not halting its programming is :P)

If i get your point based on your answers: "intelligence" cannot be divided into categories. If you are intelligent, you can be trained to do whatever skill you want, its just a matter of being taught or exposed to the probelm. So it does not make sense for it to have its own category. So if you train intelligent people to be social, they will be social, its just software.

What i have seen: people can perform outstandingly well on classical intelligence without almost being taught. Think about mathematics or logic. But when you get into social/emotional territory, then it has a bigger correlation with how you were taught or your experienced when you where a small kid (but its not 100% causal). So in that sense its not the same thing.

Now, if you are unconfortable by calling it "intelligence", feel free to call it "skills". For me its the same thing as a football player having spacial awareness of the field. Sure, they have to be trained, but it is some "skill" that some people have an easier time using and improving.

Finally a comment which is clearly 100% human

This site is getting invaded by AI bots... how long before its just AI speaking with AI, and just people reading the conversations thinking that its actual people?

To me that graph seems to say that the pure "subconscious" stuff or "ML similar" stuff peaks earlier, but comprehension peaks much later. So you perfect your tools in the brain at around 25, but then it takes another 20 years to really know how to use them correclty.

I would go even further: Not only the vast majority, but 100% of non pacifist like AI weapons.

I finished reading this comment wondering what should I take away from it. Is it better to include alarming titles and be read? Or the other way around? Or what would be the sweet middle point?

I quote for context:

But what about those of us who are well into the flattening part of the curve, what can we do for ourselves? You can seek new experiences perhaps. If time goes faster because your life has fewer firsts and more routine, then it can be extended by adding firsts. You can learn new things, travel, take up hobbies, or new careers.

This works, to a point, but there are only so many firsts for you, and chasing this exclusively seems to lead to resentment. You remember the things you had as a kid. You remember the excitement and warmth of that world, how immediate and raw everything felt, and you want to go back. You start to regret that the world has changed, even though what changed the most is you.

I like to think that life slows down once you form a stable image and story of yourself. The more you convince yourself that that image is fixed, the faster time will go by. That might justify why childhood seems longer, since that image seems to form around adolescence.

Experiencing new "firsts" but keeping that image of yourselfe fixed just works for a while. That is why it may lead to resentment, as the article says.

So dont fool yourself: some image of who you are gives you some stability, but just use it for that, so that you dont run crazy with options.

If you treat every event as something that might reshape your ego, then suddenly a big number of experiences are new, and time suddenly slows dont. It may even appear to dissapear from time to time.

It completely depends on the way you prompt the model. Nothing prevents you from telling it exactly what you want, to the level of specifying the files and lines to focus on. In my experience anything other than that is a recepy for failure in sufficiently complex projects.

I think that the main missunderstanding is that we used to think programming=coding, but this is not the case. LLMs allow people to use natural language as a programming language, but you still need to program. As with every programing language, it requires you to learn how to use it.

Not everyone needs to be excited about LLMs, in the same way that C++ developers dont need to be excited about python.

That would be the case in an idealized world. As with everything this depends on the circumstances and the economic activity of where the person is living in. I guess that with the north american eyes it is the employee's fault if the employee cannot find some other job since the only constraint for doing it is the personal drive. But there are other economical/educational constraints that don't allow people to have the necessary mobility for your example to be efficient and accurate.

You were talking about exploitation. Using the fact that the employee cannot obtain a better employment elsewhere to extract as much of the production or value from the employee smells a lot like exploitation to me.

In the end this depends on your definition of "fair". What percentage of your generated production do you think is fair for the company to take? 95%? 50%? 10%?

Notation an symbology comes out of a minmax optimisation. Minimizing complexity maximizing reach. As with every local critical point, it is probably not the only state we could have ended at.

For example, for your point 1: we could probably start there, but once you get familiar with the notation you dont want to keep writing a huge list of parameters, so you would probably come up with a higher level data structure parameter which is more abstract to write it as an input. And then the next generation would complain that the data structure is too abstract/takes too much effort to be comunicated to someone new to the field, because they did not live the problem that made you come with a solution first hand.

And for you point 2: where do you draw the line with your hyperlinks. If you mention the real plane, do you reference the construction of the real numbers? And dimensionl? If you reason a proof by contradiction, do you reference the axioms of logic? If you say "let {xn} be a converging sequence" do you reference convergence, natural numbers and sets? Or just convergence? Its not that simple, so we came up with a minmax solution which is what everybody does now.

Having said this, there are a lot of articles books that are not easy to understand. But that is probably more of an issue of them being written by someone who is bad at communicating, than because of the notation.

As Venkatesh concludes in his lecture about the future of mathematics in a world of increasingly capable AI, “We have to ask why are we proving things at all?” Thurston puts it like this: there will be a “continuing desire for human understanding of a proof, in addition to knowledge that the theorem is true.”

This type of resoning becomes void if instead of "AI" we used something like "AGA" or "Artificial General Automation" which is a closer description of what we actually have (natural language as a programming language).

Increasingly capable AGA will do things that mathematitians do not like doing. Who wants to compute logarithmic tables by hand? This got solved by calculators. Who wants to compute chaotic dynamical systems by hand? Computer simulations solved that. Who wants to improve by 2% a real analysis bound over an integral to get closer to the optimal bound? AGA is very capable at doing that. We just want to do it if it actually helps us understand why, and surfaces some structure. If not, who cares it its you who does it or a machine that knows all of the olympiad type tricks.

Right now, even people who reject meritocracy understand its logic. You develop rare skills, you work hard, you create value, and you capture some of that value.

The premise is that AI does not allow to do this any more, which is completely false. It may not allow to do it in the same way, so its true that some jobs may disappear, but others will be created.

The article is too alarmist by someone who has drank all of the corporate hype. AI is not AGI. AI is an automation tool, like any other that we have invented before. The cool thing is that now we can use natural language as a programming language which was not possible before. If you treat AI as something that can thin k, you will fail again and again. If you treat it as an automation tool, that cannot think you will get all of the benefits.

Here i am talking about work. Of course AI has introduced a new scale of AI slop, and that has other psycological impacts on society.

So is what i wrote a third one? Fourth? Fifth? :)

I get your point, but i think the real issue is -(1/(-1/x)). It is the one that is being overlooked the most in our society, as if it were something normal, but it contains some of the deepest truths imho.

Ahh nothing better than seeing someone on the wild thinking that their life decisions are 100% independent from their environment. Enjoy your false sense of freedom while you can!

The reward functions in the problems that they proposed alphaevolve are easy. The reward funtions of at least 50% of maths are not. You can say that validating if a proof is correct is a straightforward reward, but the size of interesting theorems over the space of all theorems is very small. And also what does "interesting" could even mean?

AlphaEvolve did not perform equally well across different areas of mathematics. When testing the tool on analytic number theory problems, such as that of designing sieve weights for elementary approximations to the prime number theorem, it struggled to take advantage of the number theoretic structure in the problem, even when given suitable expert hints (although such hints have proven useful for other problems). This could potentially be a prompting issue on our end,

Very generous from Tao to say it can be a prompting issue. It always surprises me how easily it is for people to says that the problem is not the LLM, but them. With other types of ML/AI algorithms we dont see this. For example, after a failed attempt or lower score in a comparison table, no one writes "the following benchmark results may be wrong, and our proposed algorithm may not be the best. We may have messed up the hyperparameter tunning, initialization, train test split..."

The closest thing that you may get is a manifold + noise. Maybe some people thing about it in that way. Think for example of the graph of y=sin(x)+noise, you can say that this is a 1 dimensional data manifold. And you can say that locally a data manifold is something that looks like a graph or embedding (with more dimensions) plus noise.

But i am skeptical whether this definition can be useful in the real world of algorithms. For example you can define things like topological data analysis, but the applications are limited, mainly due to the curse of dimensionality.

True, but 4 years old? The reactions that 4 year olds have to videos on screens is like drugs. They are fully hipnotized while watching the video, to the point that its difficult to get them to react to the outside world, and turning off the screen triggers some hard withdrawal reactions. At that age they have 0 tools to control and understand their emotions.

Theorems discovery is amenable to verifiable rewards. But is meaningful theorems discovery too? Is the ability to discern between meaningful theorems and bad ones an emergent behaviour? You can check for yourself examples of automatic proofs, and the huge amount of intermediate theorems that they can generate which are not very meaningful.

Thank you for the 91 proof! I didnt know about that

An ugly proof is super useful. It turns a statement into a theorem.

There is a famous quote by Riemann: "If only I had the theorems! Then I should find the proofs easily enough. "

Once you have a proof, simplifying it should be much easier, even for computers.

It's a fundamental problem with using AI to do "intuitive" math, but not a fundamental problem with AI to do formal math.

As you have stared, a lot of mathematics can be formalized. For me the problem for AI with math is going to be the generative part. Validating a proof or trying to come up with a proof for a given statement may be within reach. Coming up with meaningful/interesting statements to proof is another completely different story.

Hmm... I thought every ML algorithm was already intelligently self-modifying software. I would love if the release was just a linear regression optimization algorithm :)