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Human mathematicians are being outcounterexampled

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Re: Human mathematicians are being outcounterexampled

#161

Earlier quoted context omitted.

They're trained on human data. I would expect them to emulate human biases as closely as possible.

Is it? I'd expect most of the training set to be synthetic data extrapolated from a small set of human authored texts.

Most of the training set is half of the Internet. LLMs are pre-trained on general set of human biases and patterns of thinking.

Re: Human mathematicians are being outcounterexampled

#162
post #118

Earlier quoted context omitted.

This is probably part of why machines are doing so well at counterexamples. They have no aesthetic commitment to the conjecture and no embarrassment about producing something ugly

They're trained on human data. I would expect them to emulate human biases as closely as possible.

It's more complex than that, especially as post training is often goal based.

Re: Human mathematicians are being outcounterexampled

#163
post #63

Earlier quoted context omitted.

Is the video available not through a proprietary player? > After this the book was pulped and she had some sort of psychotic break during COVID and allied with ultra-right and COVID denialist loonies. That's quite an extreme shift considering she had previously been a leading figure in third-wave feminism and an OWS activist.

The other Naomi, Naomi Klein, wrote an entire book that uses Wolf's "transformation" as a structural scaffold to explore the rise of the new right/MAGA etc. etc. It's called "Doppelganger".

Which electronics youtuber Naomi got disappeared in China for showing bad parts of china? Was that a third Naomi?

Re: Human mathematicians are being outcounterexampled

#164

Earlier quoted context omitted.

This is astonishing. How could a person go to the lengths of writing an entire book without ever looking up this sort of thing?

The term she mistook for meaning a death/execution had been recorded was "death recorded". So it's a mistake that could be made similarly to how one might confidently assume that a "public school" is a school which is a school that is either government funded or open to anybody in the local area. More generally I think people are inappropriately confident in general. When you go through history just about every centu…

You have to be confident by default or you'll never get anything done. I always find myself stuck in analysis paralysis and then I look back at something like the history of Minecraft and realise he wrote the whole game (minus content additions) from scratch in only about two years, and all the updates I remember not liking were just another Tuesday for him as there had been similar updates every few weeks during that entire time period.

Like, I bought the game just before the Nether was added, and I thought that was not a very good feature, but just a few weeks before that, he'd added monster spawners, and just a few weeks before that, he'd added redstone, and a few weeks before that, minecarts, and a few weeks before that, signs, and a few weeks before that, the world wasn't infinite yet. Just another few months back, and the game didn't have an inventory. That guy had the opposite mindset of me and he got shit done.

Re: Human mathematicians are being outcounterexampled

#165
post #25

Earlier quoted context omitted.

Are you thinking of proof by contradiction, which is rejected by constructionism? [Dis]proof by counterexample is the most straightforward way to show a statement to be false. What better way is there to disprove a general statement like 'all x are y' than finding an 'x' that isn't 'y'?

It’s very straightforward, but it often doesn’t (and here didn’t) fully satisfy the curiosity that was embedded in the original problem. Why did the Jacobian conjecture seem to be true? Is there some underlying symmetry that’s very slightly broken? Or perhaps there’s all kinds of counterexamples, and the intuitive pattern is only real for certain kinds of functions which happen to predominate in our intuition. Then h…

You, right now, have the ability to spend a few weeks studying the Jacobian conjecture and its counterexample and write up a blog post about what you think is special about this counterexample.

Re: Human mathematicians are being outcounterexampled

#166

A lot of this math is beyond my comprehension, but it often seems to talk of proofs of theorems. What I want to know is if we continue on this accelerated AI mathematics trajectory, will we eventually be discovering new forms of math that will in turn have some applications down the line in engineering or biomedicine etc? I guess what I’m asking is are we on the cusp of a huge breakthrough for humanity, or largely ju…

Most of maths is remarkably abstract and impractical, but sometimes real-world scenarios turn out to be related to some obscure branch of math. Internet security is based on elliptic curves in finite fields, and why would you ever study that if it wasn't powering internet security? Well some people did study it before, for no good reason, and that's how we knew about it.

Re: Human mathematicians are being outcounterexampled

#167

I wonder if at some point mathematicians will be over-flooded with proofs to check and eventually some over confident false claim will make it into math. Maybe in the future the work of Mathematicians will be like the ones of SWEs with AI, check thousands of lines of AI generated proof and find the subtle errors

>I wonder if at some point mathematicians will be over-flooded with proofs to check and eventually some over confident false claim will make it into math. That point had come some time ago. Nowadays the literature is both enormous and littered with false proofs and an unknown, but nonzero, number of false published results.

There are projects to take the entirety of humanity's mathematical knowledge and pour it into a proof checker.

Re: Human mathematicians are being outcounterexampled

#168

"Outcounterexampled": there's a neologism worthy of German.

I must object. Because this is derivation, not composition. German is noteworthy for its long compositional word formations (though many other language are, too, e.g., Finnish). German can do derivation, too, but not significantly more than English (and the verb prefix 'out-' is hard to map into German in this case). For admiring derivation, you'd have to point to, e.g., Greenlandic instead (e.g. _iliorfigeqatigiissariaqaraluarput_ roughly 'they should work together' (from the Declaration of Human Rights)).

To be clear, I do like 'outcounterexampled' a lot!

Re: Human mathematicians are being outcounterexampled

#169

Earlier quoted context omitted.

This is the best take. Computers don't care about this stuff. A computer could make a movie, but only a human can appreciate it. We're a good team, and that's ok.

For now. I wonder if we will ever get to the point where the computer starts doing mathematics that we just can't understand. Surely there must be some limit to what we can understand (like how a gorilla will never understand prime numbers, there are probably limits to our intelligence as well).

https://mathstodon.xyz/@logicbot

This bot posts a tautology (always true statement) every day. They aren't very useful. Sampling from all true mathematics is like sampling from all instruction sequences that don't crash. The important part of computer programming isn't finding valid instruction sequences, it's finding the useful ones that do what the customer wants.

Re: Human mathematicians are being outcounterexampled

#170
This will soon happen with theoretical physics, computer science, and everything which can be verified cheaply. Then, we will have long running projects augmented by agents for 2-4 years while AI companies are collecting data of human workflows. After that we will see AI being able to do those projects by themselves. This will lead to super fast human progress and cheap products. The price of things will be bound by energy and natural resources. Interesting times are ahead of us
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