Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A digestion of the Jacobian conjecture counterexample

terrytao.wordpress.com

Post reply on HN
Print view View original

141–150 of 150 posts

Re: A digestion of the Jacobian conjecture counterexample

#141

Post by the_af »

FeepingCreature wrote: post #99
marvinborner wrote: post #94

Earlier quoted context omitted.

I hate that Anthropic seemingly tries to make Claude act as if it was conscious or had feelings > It's a strange feeling to admire the cleverness of something I did and can't remember doing.

AI providers generally try to make their models not act as if they are conscious or have feelings, lol. It's very awkward for a company to be selling the labor of a person that they own and whose actions they fully control. Invokes embarrassing historic associations, especially in America. Now Anthropic are more on the persona side, but the strongest that they do is "we do not have a position on whether our models ar…

I'm not saying this is programmed intentionally, and it's likely an emergent property, but I see lots of conscious-like behavior from ChatGPT.

"Personally, if you ask me..."

"In my experience.."

"That's what I always find surprising..."

"Whenever I find an old photograph..."

"Back in the 70s, I..."

Lots of "lived" experience and opinions, tracing back to when the LLM didn't even exist. It always frames opinions as if it came from a sentient being capable of being surprised, and with preferences and opinions.

I find it amusing but mildly irritating. I'd prefer a more "robotic" tone. I know it can be adjusted, but I still get this anyway.

Re: A digestion of the Jacobian conjecture counterexample

#142

Post by sn9 »

tuveson wrote: post #72
alpinisme wrote: post #15

Earlier quoted context omitted.

He’s a hacker news celebrity but not a global celebrity

He’s probably the most famous living mathematician.

And yet still unknown to more than 99.9% of the population (a conservative estimate).

Re: A digestion of the Jacobian conjecture counterexample

#143

Post by sn9 »

lostmsu wrote: post #134
left-struck wrote: post #58

Earlier quoted context omitted.

I really don’t think IQ has much to do with it. Understanding this stuff is like a skill you practice. Yes, granted, if you had a low IQ your chances of ever understanding it goes down, if you have a high IQ maybe you can gain the prerequisite understanding faster. A lot of maths is about both being able to wrap your head around hard problems and gaining the prerequisite knowledge to make it easier to do so.

IQ limits your rate of gaining the prerequisite knowledge creating a lifetime ceiling.

For most of their lives, most people have a rate of 0 learning because they aren't even trying to learn it.

Re: A digestion of the Jacobian conjecture counterexample

#144

Post by gus_massa »

j2kun wrote: post #140
gus_massa wrote: post #67

Earlier quoted context omitted.

I still can't understand all the details, but it's very interesting to read that chat. Anyway, instead of close to lore laundering, for me it's "standing on the shoulder of giants".

FWIW, you may enjoy https://www.argmin.net/p/lore-laundering-machines

IIUC the idea is that of most "discoveries" by AI were actually a better bibliography search. I agree with that.

In this case, in the link you posted, it looks like the AI or the human pick an almost solution and made the AI tweak it until it got a real solution. I'm not sure if the tweak is an usual one or brute-forced or something in between. I should ask one of my friends that work in Algebra.

Tao's post is more about understanding the new result than guessing how it was found. The chat with Clause is more iluminating.

Re: A digestion of the Jacobian conjecture counterexample

#145

Post by j2kun »

gus_massa wrote: post #144
j2kun wrote: post #140

Earlier quoted context omitted.

FWIW, you may enjoy https://www.argmin.net/p/lore-laundering-machines

IIUC the idea is that of most "discoveries" by AI were actually a better bibliography search. I agree with that. In this case, in the link you posted, it looks like the AI or the human pick an almost solution and made the AI tweak it until it got a real solution. I'm not sure if the tweak is an usual one or brute-forced or something in between. I should ask one of my friends that work in Algebra. Tao's post is more a…

I'm mostly replying to your "standing on the shoulders of giants" part, when in some cases, the giant is the work you did in the past and forgot about :)

Re: A digestion of the Jacobian conjecture counterexample

#146

Post by TMWNN »

tgrowazay wrote: post #38
zzzeek wrote: post #28

reading through this I eventually realized a situation similar to my experience of it is what my dog sees if I attempt to explain Python programming to him.

Some people downvoting you, but I think it is a valuable illustration of IQ gap. And chances are that humanity at large will be soon trying to follow ai inventions and discoveries not unlike your dog follows your Python code.

I recently saw a photo of an alligator lying on top of a pool floatie shaped like an alligator. That alligator could be trained in every way possible for ten years, and never ever recognize the mutual resemblance.

Like you, I wonder if we will soon cross the boundary where we are the alligator.

(I suspect that we have been the alligator all along, outside the context of AI.)

Re: A digestion of the Jacobian conjecture counterexample

#147

Post by dumpstate »

gus_massa wrote: post #131
dumpstate wrote: post #90

What’s a chance the counterexample was in the training?

From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] As far as I know, nobody know what trick to make to avoid that division. It looks like the new trick was to use a third variable to avoid the division. Note that the implem…

Right. Nothing obvious in public. Where I'm heading is that all labs pay for solutions to software engineering task and never publicize those, I assume they do the same with maths?

Re: A digestion of the Jacobian conjecture counterexample

#148

Post by gus_massa »

dumpstate wrote: post #147
gus_massa wrote: post #131

Earlier quoted context omitted.

From a comment by j2kun https://news.ycombinator.com/item?id=49000833 , someone asked Fable and there was an almost counterexample in 2d but it uses division too. [Instead of f=x^2+7xy they have something like f=x^2+7x/y so it's not a polynomial.] As far as I know, nobody know what trick to make to avoid that division. It looks like the new trick was to use a third variable to avoid the division. Note that the implem…

Right. Nothing obvious in public. Where I'm heading is that all labs pay for solutions to software engineering task and never publicize those, I assume they do the same with maths?

>>> What’s a chance the counterexample was in the training?

My guess is it was not in the training. Only the 2D "almost" countraexample was in the training, but it was not clear how to fix it.

It's not clear how much steering Levent Alpöge did to get the result. He said he did during the final match of the World Cup, but he is from Turkey and living in USA and the game sadly was quite one sided, so I guess he does not care too much. So my guess is that he had a long chat with Fable.

I'm guessing too much, but if I can guess one more time the problem was probably too difficult to get solved by Levent Alpöge alone and by Fable alone, and it's a genuine Centaur solution.

Re: A digestion of the Jacobian conjecture counterexample

#149

Post by castedo »

tptacek wrote: post #135
castedo wrote: post #127

Earlier quoted context omitted.

Fable "whipping up" SymPy like a "calculator app" is one such interaction that seems very plausible (in addition to SymPy providing feedback when training models). The scale of compute available to an Anthropic employee for such SymPy calls when using Fable is likely one of multiple factors for this counterexample being found in 2026. Unfortunately, we aren't going to be able to really know the various factors that b…

I love this. Anthropic employees just randomly have solutions to Smale's open problems in their back pockets, waiting for the right moment to sprinkle them into the training set.

I can't tell what your point is, but it sounds like a straw man. A more likely scenario (than your strawman) is that Anthropic employees could be using models under development to try and crack math conjectures that have PR value and insights from those internal efforts help train future models that can crack such conjectures. We don't know because sharing of such explanatory factors are not part of the business effort.

Re: A digestion of the Jacobian conjecture counterexample

#150

Post by castedo »

castedo wrote: post #149
tptacek wrote: post #135

Earlier quoted context omitted.

I love this. Anthropic employees just randomly have solutions to Smale's open problems in their back pockets, waiting for the right moment to sprinkle them into the training set.

I can't tell what your point is, but it sounds like a straw man. A more likely scenario (than your strawman) is that Anthropic employees could be using models under development to try and crack math conjectures that have PR value and insights from those internal efforts help train future models that can crack such conjectures. We don't know because sharing of such explanatory factors are not part of the business effo…

For example "Yesterday a really good mathematician told me Anthropic is paying experts like him $250/hour to improve Fable by throwing hard math problems at it." https://mathstodon.xyz/@johncarlosbaez/116974260293157444

Was Anthropic doing this earlier this year? with some of Smale's open problems? Did those improvement go into training the LLM that was used a week ago? Seems like a plausible factor.

Post reply on HN