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Ten advances in mathematics and theoretical computer science

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Re: Ten advances in mathematics and theoretical computer science

#981

Earlier quoted context omitted.

>let people express their own values in democracies, or will we just get much better at manipulation? Both are the same thing. Two sides of the same coin.

The distinction is between information flowing from people to power (elicitation), vs. it flowing from power to people (persuasion). These are not the same, even if they are closely related.

I guess I wasn't clear enough, _generally_ democracy = manufactured consent by manipulation of people by 'power'

Re: Ten advances in mathematics and theoretical computer science

#982

Earlier quoted context omitted.

When you can formalize it in Lean or some such, why would this be? I can understand the desire to separate out other forms of research from the human corpus. But theoretical math that is decidable/provable, I’m not sure I see the risks.

I just want to state that having "lean proofs" that build does not mean the actual real theorems we care about hold. Ultimately a human has to verify the lean encoded theorem statements that the lean proofs are checked against. For non-trivial theorems such as these, this is an arduous and tricky task where even a little mistake could be fatal.

Agreed that confirming “This proposition has been faithfully translated to Lean” matters. As a side note, though, this is an area where LLMs used interactively can be helpful.

Also in the case of these recent counterexamples turning up, we have good qualitative evidence that this pathway is effective.

Re: Ten advances in mathematics and theoretical computer science

#983

Earlier quoted context omitted.

Nobody in this thread is trying to predict when the sigmoid is going to bend. Perhaps they should

A lot of HN posters thought it was already bending at GPT4o/GPT4.5. Turns out, it kept accelerating (at agentic tasks).

I suppose it depends what you're expecting. From my perspective it bent around november 2025

Re: Ten advances in mathematics and theoretical computer science

#984
post #467

Earlier quoted context omitted.

If it doesn't help average people, why do millions of them pay for it?

So if millions of people pay for something it must be helping average people but if 10s of millions of average people express concerns about a thing than what? I would assume since you were happy to go with the will of the people when it supported your argument, you would be in complete support of actually regulating ai and addressing the many concerns of society at large? https://www.reuters.com/world/us/americans-f…

I'm fine with regulating AI. I'd note that saying something in a poll is cheap talk whereas paying 20$ a month is not. But I can understand e.g. that people may derive value from their cars, whilst simultaneously being concerned about global warming and traffic jams.

Re: Ten advances in mathematics and theoretical computer science

#985

Earlier quoted context omitted.

The distinction is between information flowing from people to power (elicitation), vs. it flowing from power to people (persuasion). These are not the same, even if they are closely related.

I guess I wasn't clear enough, _generally_ democracy = manufactured consent by manipulation of people by 'power'

Does AI make real opinion easier to hear, or fake opinion easier to spread? Even if you believe wholly in manufactured consent, how easy it is to manufacture matters.

Re: Ten advances in mathematics and theoretical computer science

#986
post #494
post #329

Earlier quoted context omitted.

There's a full fledged 'reasoning' step that basically expands your prompt. As long as you are not missing important information, how you word the prompt does not have any effect.

Isn’t that a huge simplification? Of course the way you phrase the prompt can carry semantic meaning, maybe subtly, but still. And sometimes that matters a little and sometimes a lot. I’ve stopped numerous agent sessions over the last few weeks to reword my initial prompt to get the agent off an unintended track.

> reword my initial prompt to get the agent off an unintended track.

The signal here is the action of stopping the agent “do something else, this is stupid”, not a tweak to the initial prompt.

Re: Ten advances in mathematics and theoretical computer science

#987

Earlier quoted context omitted.

I guess I wasn't clear enough, _generally_ democracy = manufactured consent by manipulation of people by 'power'

Does AI make real opinion easier to hear, or fake opinion easier to spread? Even if you believe wholly in manufactured consent, how easy it is to manufacture matters.

>Does AI make real opinion easier to hear, or fake opinion easier to spread?

The latter.

(caveat: we are talking about the vast majority of people, since you are on this forum your personal situation will be the opposite)

>Even if you believe wholly in manufactured consent, how easy it is to manufacture matters.

I believe it's easier.

(same caveat applies)

Re: Ten advances in mathematics and theoretical computer science

#988

Earlier quoted context omitted.

In my opinion, after seein the Jacobian conjecture go, the Riemann hypothesis only has about a year left. I’m not sure if people just aren’t as aware, but the Jacobian conjecture practically was on par with those other great problems.

Whether or not it’s on par famously or difficulty level doesn’t predict whether the others will fall. They’re unique problems and math isn’t linear - the Jacobian it managed to find a counterexample and relied on other proofs that had been developed showing >3 case == 3 dimensional case. However, the Riemann may not fall in the same way because it may actually be true or the surrounding math isn’t quite ready to tack…

When I was in grad school we talked about the Jacobian conjecture as something that would never be solved, and not really even worth thinking about since it’s impossible. There’s been a lot more big open problems solved by AI than which reach the front page of news websites like this. Based on all of these problems getting solved fast I’m just saying I’d be surprised if the Riemann hypothesis lasts another year.

Re: Ten advances in mathematics and theoretical computer science

#989

Earlier quoted context omitted.

> Part of this can be good (you talk about what they care about, where 90% of broadcast messaging might not apply) and part of it can be bad (manipulation.) Side note: it's manipulation either ways because you chose what to talk about, with a goal in mind.

Actually, no. "Manipulation" is a negatively loaded word, and you wouldn't use that word if f.ex. someone helpfully & truthfully helps others see they've misunderstood sth.

I disagree. Whether something is manipulation depends on whether you are trying to change someone’s opinion or behavior, not on whether the manipulator has “good” or “bad” intentions, since those judgments are not objectively universal.

Re: Ten advances in mathematics and theoretical computer science

#990
post #530

Earlier quoted context omitted.

I’m not talking about the actions we take or how we might perform at certain tasks, I’m talking about how our brains actually work. My point is that we have no idea how I’m able to imagine an apple and see it in my mind’s eye. It’s basically biological magic to us at this point. There are processes at work there that we don’t even have the language to describe.

Not only that, but we do it with a processor that is basically required to operate in a narrow temperature band below 40C, using a mere 86 billion neurons (although the equivalence with either machine-learning "neurons" or LLM parameters is not at all clear) operating on a few dozen watts; and with this we operate many other systems besides language processing. It's not clear that our reasoning process requires langu…

I recently read a blogpost from a human neuroscience student who came across this question (https://ccli.substack.com/p/the-biggest-mystery-in-neuroscie...), and she looked up the study behind this number (https://ora.ox.ac.uk/objects/uuid:1f559b3b-97fd-48c2-b2ac-29...), and it seems that the actual current state of knowledge is that the number is somewhere in the range 60-100 billion, with probably some of that variation being biological and some coming from uncertainty in the measurement techniques, hard to tell, because all the data comes from nine brains.

For now, caring about a topic (or having somebody you trust care for you) still gets you better information than asking an LLM.

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