> Still, Framework said that it will not take this lying down. Its event announcement also doubled as its own manifesto, saying that "as long as there is a person in the world who still wants to own their means of computation, we will be here to build the hardware that enables it," and that it "will always be fighting for a future where you can own everything and be free."

[1] https://www.tomshardware.com/tech-industry/big-tech/framewor...

To attempt to answer it, I think there are many engineers who care deeply about creativity, ingenuity, and craft, because those are key qualities (among others) needed to solve real-world problems. The question you hinted at is whether LLMs are compatible with that, and I think more people are asking those types of questions now.

LLMs are a non-free way for you to make use of less of your brain. It seems to me that these are not the same thing.

To be clear, there's much more to math than writing down and checking proofs. Some of the most important contributions to math have been simply figuring out the right questions to ask, and also figuring out the useful abstractions. Those are both firmly on the "analog" side of math, and they are every bit as important as writing the proofs. But to say that we have this huge body of rigorous argumentation in math, and then to finally do the work of checking it formally is "taking it too far," is a really bewildering take to me.

No, I don't think formalizing proofs in Lean or other proof systems should dominate the practice of math, and no, I don't think every mathematician should have to write formal proofs. Is that really where we're heading, though? I highly doubt it. The article worries about monoculture. It's a legitimate concern, but probably less of one in math than in many other places, since in my experience math people are pretty independent thinkers, and I don't see that changing any time soon.

Anyway, the conclusion from all this is that the improved ability for mathematicians to rely on automated tools to verify mathematical reasoning would be a great asset. In my opinion the outcomes of that eventuality would be overwhelmingly good.

    git config --global merge.conflictstyle diff3

> Laplace distilled this structure into a simple formula, the one that would later be known as the central limit theorem. No matter how irregular a random process is, even if it’s impossible to model, the average of many outcomes has the distribution that it describes. “It’s really powerful, because it means we don’t need to actually care what is the distribution of the things that got averaged,” Witten said. “All that matters is that the average itself is going to follow a normal distribution.”

This is not really true, because the central limit theorem requires a huge assumption: that the random process has finite variance. I believe that distributions that don't satisfy that assumption, which we can call heavy-tailed distributions, are much more common in the real world than this discussion suggests. Pointing out that infinities don't exist in the real world is also missing the point, since a distribution that just has a huge but finite variance will require a correspondingly huge number of samples to start behaving like a normal distribution.

Apart from the universality, the normal distribution has a pretty big advantage over others in practice, which is that it leads to mathematical models that are tractable in practice. To go into a slightly more detail, in mathematical modeling, often you define some mathematical model that approximates a real-world phenomenon, but which has some unknown parameters, and you want to determine those parameters in order to complete the model. To do that, you take measurements of the real phenomenon, and you find values for the parameters that best fit the measurements. Crucially, the measurements don't need to be exact, but the distribution of the measurement errors is important. If you assume the errors are independent and normally distributed, then you get a relatively nice optimization problem compared to most other things. This is, in my opinion, about as much responsible for the ubiquity of normal distributions in mathematical modeling as the universality from the central limit theorem.

However, as most people who solve such problems realize, sometimes we have to contend with these things called "outliers," which by another name are really samples from a heavy-tailed distribution. If you don't account for them somehow, then Bad Things(TM) are likely to happen. So either we try to detect and exclude them, or we replace the normal distribution with something that matches the real data a bit better.

Anyway, to connect this all back to the central limit theorem, it's probably fair to say measurement errors tend to be the combined result of many tiny unrelated effects, but the existence of outliers is pretty strong evidence that some of those effects are heavy-tailed and thus we can't rely on the central limit theorem giving us a normal distribution.

It might fade, but it will take a while. You need a generation of gamers to grow up in a world where AI-generated content is normalized and then become old enough to start driving these trends. It could actually happen in as little as ten years or so, but it also might never become fully normalized, which I think is more likely.

In the second part of the question you asked if you should just learn all of the skills...buddy, does that question not answer itself? Of course you should learn all of the skills. Obviously that's much easier said than done, but TBH I think the quality bar to producing something viable is not super high, so as long as you're not a perfectionist, you can probably do it.

Since I could be labeled as an "AI hater" based on those comments, I want to be clear that I'm saying all this to keep you from falling into a trap and not to further my own agenda. The generative AI route is not a magic shortcut to success, although it is being aggressively marketed as such. The shortcut only seems to lead to success if you ignore the fact that people don't want to be subjected to other people's AI content.

Second, Rice's theorem states that no nontrivial property on the set of partial recursive functions is decidable. However, there are subsets of the set of all recursive functions that do have decidable properties, and it's pretty trivial to cook some of them up. Since some of these sub-languages also consist only of total functions, there are "total languages" for which the analogous statement of Rice's theorem is false. To fix this we would need to choose a specific total language. There could be some interesting ones for which the analogous statement of Rice's theorem still holds, but I'm not an expert on that.

For the record, I don't have a dog in this fight. As long as it runs on Linux, I'm willing to test drive it when it's ready.

https://en.wikipedia.org/wiki/Polis

> Webster's Third New International Dictionary, Unabridged, together with its 1993 Addenda Section, includes some 470,000 entries. The Oxford English Dictionary, Second Edition, reports that it includes a similar number.

[1] https://www.merriam-webster.com/help/faq-how-many-english-wo...