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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

#701

Post by sdenton4 »

pama wrote: post #513
sdenton4 wrote: post #496

Earlier quoted context omitted.

Some of them... The two places were seeing lots of movement are: * Updates to lower/upper bounds. In many cases, these kinds of problems are the deep-math equivalent of calculating more digits of pi. Yes, if you throw time at it you'll break the record, but it may not be terribly worthwhile. * Finding counter examples which disprove conjectures. This is really useful, and helps offset some positivity bias on the huma…

It is unfair to dismiss contributions to decades old open problems as equivalent to calculating more digits of pi. It missed the mark by a lot—as does the two bucket simplifaction.

Five (maybe six?) of the results are improvements on bounds. These kinds of problems tend to have some initial advances, and then stall out as the complexity of the bound skyrockets... until some grad student is bored enough to push the boundary. The big-O complexity of matrix multiplication is a good example of how this works: yeah, it's a useful problem, but the solutions are galactic algorithms, and increasingly convoluted.

As someone with a PhD in combinatorics, I believe that I'm qualified to say that, yes, there are problems as useless as calculating more digits of pi.

Re: Ten advances in mathematics and theoretical computer science

#702

Post by kortilla »

scns wrote: post #669
lettergram wrote: post #552

Earlier quoted context omitted.

> My guess is that, in the US, the right will cynically adopt manipulation to great effect and the left will take a moral stand against shady practices and lose elections. I think that statement may itself highlight how prevalent manipulation is. I fully anticipate all groups to continue maximal manipulation they can. One thing with LLMs is that it'll be a far less unified view, so a "divide and conquer" strategy is…

It is way harder to manipulate people to do the right thing i think.

That presupposes that the left in the US wants to do the right thing. Something like government run grocery stores is not clearly correct and there is very little evidence supporting that it will work well yet it is a very popular leftist policy in New York.

Re: Ten advances in mathematics and theoretical computer science

#704

Post by oblio »

10dpd wrote: post #668

While these advances are genuinely impressive, I'm curious when we will see practical implications for this work. For example, will we see advances in material science, medical cures, etc? Would love to read about some examples of practical impact.

The big example predates LLMs as a unified tech and it's protein folding, from Google DeepMind.

OpenAI and Anthropic are too greedy for cash to do anything of the sort.

I don't expect this current economic cycle to bring anything else that will directly greatly improve the life of the average person on the planet, more than it hurts it.

Re: Ten advances in mathematics and theoretical computer science

#705

Post by s1artibartfast »

evenhash wrote: post #407
DrBazza wrote: post #96

Replace philosophers for mathematicians and Douglas Adams was spot on again. Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this. -- "Yes we are," insisted Majikthise. "We are…

> Whilst current models can't 'intuit' and come up with conjectures People keep saying this. Why? Surely the AI can complete the prompt “Generate new research questions based on these observations”? When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.

Because people have internalized an inaccurate model of LLMs as "stochastic parrots" that was incorrect at the time of formulation and is also significantly outdated

Re: Ten advances in mathematics and theoretical computer science

#707

Post by yazaddaruvala »

throwaway27448 wrote: post #692
conformist wrote: post #682

Earlier quoted context omitted.

Isn’t the point more “it’s easy to fall into the trap to believe that predicting when the sigmoid is going to bend is possible and the right heuristic is to instead extrapolate locally”? That aside, I’d question whether applying the Lindy effect in particular to something that’s not really a life expectancy but more a growth rate is credible… or perhaps a bit circular since it “assumes away” the ceiling.

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

Predicting when the sigmoid bends is difficult and predicting how long until it unbends is equally difficult.

The simpler assumption is that over enough time, the S functions stack together for long enough that working backwards from exponential is a better predictor of reality.

These stacked S curves have continually been true with most technology.

Re: Ten advances in mathematics and theoretical computer science

#708

Post by casey2 »

sothatsit wrote: post #534

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results. The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let…

We definitely are not on an exponential. Don't say we are because this isn't up for debate. AI progress is logarithmic the million dollar question is 2x or 10x for linear improvement. The nearest qualitative shift would be very fast inference so people could start writing real software on top of LLMs. A 0.001% optimization on a packing problem just isn't interesting for the amount of investment.

Re: Ten advances in mathematics and theoretical computer science

#709

Post by oblio »

roncesvalles wrote: post #681
amazingamazing wrote: post #137

Can’t wait for this stuff to have quality of life increases for the average person. So far all I see is that AI has made owning a computer more expensive, made some jobs redundant, increased spam and distrust with questionable authenticity of content and of course made some Americans very rich.

It has had significant quality of life increases for me. I use LLMs for everything from: - travel and restaurant recommendations. my last few outings have been entirely LLM-advised and they turned out excellent. LLMs seem to have ingested every single Google review, photo, and menu of every business on Earth and can answer very nuanced questions like "is the garlic chicken at garnished with coriander?" - fitness, nut…

1. Do frontier lab LLMs make your rent cheaper? Groceries? Healthcare?

2. Do LLMs reduce the loneliness epidemic?

3. Do they reduce population aging in almost all counties around the world?

4. Do they reduce political polarization?

5. Do they bolster democracies?

6. Do they decelerate climate change and general environmental destruction?

7. Do they accelerate sustainability and the circular economy (not circular financing!)?

8. Do they reduce the workweek and give people more free time for family and hobbies?

Etc, etc.

I would hold off on calling anything a "superpower" unless it solves the hard problems in life. Heck, computers and even the internet barely score better than LLMs when measured against the important things in life.

Re: Ten advances in mathematics and theoretical computer science

#710

Post by oblio »

dash2 wrote: post #700
voxl wrote: post #616

Earlier quoted context omitted.

This is not the argument. It's not a comparison to gambling but a comparison to something that does not materially improve a person's life. Economic expenditure does not equate to human benefit. This is the original argument, and the onus is on THAT person to explain why people spending for AI actually benefit, not the other way around. Perhaps you can ask Claude to explain it to you.

I think it’s widely accepted that most things are bought because they satisfy people’s needs or wants. Sure, there are exceptions, like drugs or gambling. Is there any reason to think AI is one of them?

Drugs, gambling, alcohol, tobacco, vaping, ultra processed foods, social media, luxury goods/conspicuous consumption, etc.

A lot of humans are incredibly bad at allocating money.

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