Hauling the pyramid blocks is what gives people intuition and understanding. It is true that school systems usually have way too much computation -- it is easier to test and grade computation. But the only way that you were able to use computer algebra systems fluently is because you had internalized how algebra worked by hand. If we tell students that they no longer need to learn how to solve equations we are seriously depriving them of a mathematical education.

You can use AI like a telescope, and alleviate your inherent organizational problems or other ailments, which in my opinion is a great use case, as it is empowering. But there will also be plenty of people who are not looking to alleviate any mental/physical quirks they have to do more, but simply want to make a "quick buck" for the least possible effort from the work and thinking of others, without adding much value of their own. Lowering the bar makes things easier for both, the ones who bring value and the ones who merely exploit in some context.

> this is insane. the "speciesist" people aside (the best way for all other species to flourish is for humans to eradicate themselves right now, which is completely mad), i have the opposite problem: the _axiom_ seems to be: we should help ME flourish. "Me" as in people who are raking in trillions for their own very special selves right now, at the cost of everyone else's future, while none of them can be trusted to hold my cell phone for a second.

I don't think there are actually any "speciesist people." I think most, if not all, are the selfish "me people," who have disingenuously created "speciesism" by mad-libbing racism and sexism in a ham-handed attempt deflect criticism/opposition to whatever they want to do. Most of them aren't even "raking in trillions," they just don't like thinking about others or being told "no."

That wouldn't do much for rice, pigs, chickens, or rats.

One counter-point: Humans have not figured out how general anesthesia works, but we use it every day to great effect.

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

I'm a little more flexible, if the new knowledge (that human's don't understand) can be put into a mechanism and have an observable effect, I'd be happy enough. e.g. a new type of rocket fuel that burns 1000x more efficiently.

If I vibecode a video game and manage to sell it on Steam, the information definitely mattered even though I didn't understand any of it.

There are drugs that nobody truly understands how they work and they are being used by professionals in actual treatments literally right now. We know purely statistical facts like "if drug X is used for condition Y it will help Z% of patients" and can only speculate as to their mechanism of action. They are used anyway and still benefit a lot of people.

Why though a human? Mathematical proofs are very ivory-towery, but if OpenAI would solve a subkind of Cancer, without mortal humans understanding, cancer is still be healed.

"I own nothing, have no privacy, [never have to think, and am not required to solve any problems,] and life has never been better."

https://en.wikipedia.org/wiki/You'll_own_nothing_and_be_happ...

Does it need to be a human or can it be some other form of life?

I guess Terence's main point has been all the time that if we let AI solve all these existing problems, we don't notice the new ones and then there is stagnation.

The universe is bounded by rules, as far as we can tell, and not a lot of them

Meanwhile, as people got used to the clock, the society became used to staying in synch at hour and sub-hour intervals. As better clocks were invented, synchronization became counted in minutes. This simplified things, allowing people to do more in the day and coordinate less, as they learned to rely on agreements to independently do things at specific time. Shops started posting opening hours, school started posting lesson plans, professionals started billing by minutes.

Clocks became widespread, and synchronized remotely - first from the church clock, then over the wire, over the radio, finally over the Internet. The loss of shared time reference at minute-granularity became rarer and rarer, until it became unheard of (except in excuses of those who failed to keep their commitments).

Losing a clock now would indeed throw society into disarray. If all clocks magically stopped tomorrow, many would starve and die before society figured out some way to restore time-keeping by proxy.

Clocks are a perfect example of the ratched effect of technology. A new technology at first helps you, or gives you advantage. As it spreads out more, it becomes relied on. Eventually, reaching ubiquity, it becomes a dependency, and everyone is assumed to be using it.

In a modern society, you cannot live without a properly synced clock anymore.

I loved mathematics when I was young and wanted to be good at it, but I got burnt so many times by teachers who could not explain even if their life depended on it.

Asking an LLM and discovering how different theories belong together and what are genuinely open questions, along with different philosophical interpretations has been a wonderful gift.

I have long accepted that Mathematics is a language where you must go "all in" because for the most parts institutions are fundamentally unable to explain it in an intuitive way. There are people who "just get it" and are blind to the struggle of people who need a different approach in learning it. There's something about the field where a generational survivorship bias has created an environment where math is mostly taught to likeminded people, who then don't see why anybody could not see the difficulties learning it.

I know this is not true everywhere, but the only reason I could finish my studies was because there are some genuinely excellent online lectures on youtube, along with massive support from friends who have already been through the ordeal.

If I had had access to an LLM, I could have actually taught myself from scratch and be more playful in learning it. And no, I am not willing to learn lots of math "for fun", I can think of better "for fun" things that actually help my profession and cater to my actual interests and not just some academic ideal.

But please elaborate a bit on your statement.

How is mathematics gated and inaccessible? How do you specify mathematics without notation or some language? What intuition do you mean, as many mathematical ideas are non-intuitive?

(Attn: pls read more than the title before you downvote)

Plus, in the good articles I've read, the structure is usually: dissection of subproblem, intuitive description of solution, converting that solution into notation, proceed to next subproblem. If you see an unfamiliar symbol in an article, look it up. If you don't understand its definition, you don't yet have an intuitive grasp of the concept. Keep going down that rabbit hole until you have the intuitive building blocks to understand the article.

Frankly, I love how much math we can teach before a kid graduates high school. Thousands of years of mathematical ideas, up to calculus invented less than 400 years ago. All before they're 18 years old and probably don't care much about math.

Is it really that common for musicians to not be able to read music? I'm not a musician so I wouldn't know, but it seems far-fetched. Like the story that Einstein failed math. I likewise doubt that there are many people who would be good mathematicians but unable to learn the language.

Sure notation is arbitrary and not the actual "truth" of math, but we need some way to talk about it, so why not just learn the accepted standards?

There might be at least one awesome author out there who never learned to write or type, but they're probably extremely rare, because becoming great at something usually entails a lot of practice, and that's hard to get when you're not making the effort to learn the basics.

In any case, LLMs are probably a bad way to "pivot math towards intuition and accessibility" because they, as language models, are great at generating a bunch of jargon that is hard for somebody with no training to tell apart. See the recent story [0]. Here the author (perhaps) succeeded with his proof, but was it because of superior intuition? Or just throwing compute at the wall to see what sticks?

[0] https://news.ycombinator.com/item?id=49755024

This has always been my problem with math going all the way back to college. It was obvious to me that the concepts were far less hard than the combination of notation and esoteric jargon with liberal use of symbols and weird letters made them seem. Math felt (and still does feel) "encrypted."

The impression math gave off is of an arcane discipline that uses its arcane-ness as a gatekeeping tactic, intentionally or not, and makes itself intentionally hard for newcomers to learn without being hand-held by members of the guild.

Of course I can say the same about a lot of computing, and I'm old enough to remember efforts to make computing more approachable like easier to learn languages and GUIs being mocked and scoffed at by "real programmers."

I think this is a pretty typical human group behavior.

I think this underlies a lot of AI hate from these communities today. AI makes it easy for outsiders to bash their way into the field with the help of an LLM. Yes, this often results in low-effort "slop," but if used correctly it can also help people climb the learning curve really fast. I've had great luck having an LLM make me some passable "slop" and then explain it and go around with me as we fix and refine it, explaining each step, and as it does so it feels like we are learning together. It's very powerful and I, as the student, can control exactly how the teacher presents the material.

I was able to do this to finally start grasping the math behind LLMs themselves: attention layers, tensors, etc.

A lot of people have a powerful visceral probably instinctive reaction to large numbers of migrants entering their area. "Build the wall!" I suspect this is brain stem stuff going back to evolving under conditions of scarcity where migrants meant less food.

Let's be honest: we don't know. Maybe you're right, but for the moment it's more likely that you're not. And countries cannot bet on that vague intuition at the cost of destroying their research communities and world leadership (which takes decades if not a century to achieve).

A better analogy: look at all these highly trained engineers, mathematicians, doctors, writers, philosophers, writers, scientists.

How many dumbass politicians do we need to keep it all running smoothly?

Turns out no matter how dumb politicians were, overall society has been developing positively over the history of mankind.

Do you think this applies to say, surgery, as well? There are few useful problems that share these properties.

We're building tools to serve the human society.

But within the sample of the human species it is more common for less intelligent people to control more intelligent people.

This happens within political systems (political leaders are usually above average intelligence, but hardly the most intelligent) and within companies and other economic systems.

I don't see this fairly obvious point discussed, and not really sure what it shows.

I think there are other species that could be considered more capable than humans, such as E. Coli, octopuses or ants.

And it's not even clear whether the AI will have its own individuality. It might become an extension of human brains, in the same way neocortex is an extension of amygdala. In that case the statement of who has control might become meaningless.

For guest post on Tao's blog, after a decent start this fell short of expectations rather rapidly.