Recent submissions

Comment · 1 day ago
Comment · 4 days ago
> In our view, these manuscripts are best understood as a form of raw research data. To convert this raw research data into scientific understanding, in this release we are experimenting with a new approach

Mathematics and computer science are turning into an empirical science

Comment · 5 days ago
Comment · 9 days ago
Hot patching is itself a liability
Comment · 15 days ago
"How to rewrite all software in Rust"
Comment · 17 days ago
I'm reading this paragraph with the precedent of AlphaGo in mind, where none of the Go players would have expected that databases of human games would be valuable training material for machines instead of humans:

> I learned mathematics because others gave their time and knowledge freely, and I wanted to do the same for the next generation. The possibility that a student would go on to do something I could not do was part of the point. But I had imagined this as a continuation of a human activity. [...] I could not imagine treating this knowledge as something to be guarded.

But soon after, AlphaZero was trained purposefully without human games in the training data. The "extractive" training was sufficient to show that a certain machine learning model worked, but unnecessary to produce a machine that performs beyond the level of humans.

For coding agents I imagine it is similar: humans introduce so many subtle bugs, and they're only subtle relative to human cognitive capacity. I'm sure subtle mistakes pass peer review in mathematics too, even if it's generally more rigorous.

What I'm getting at is that labs have demonstrated that a certain model architecture is capable of producing mathematics at a (super)human level, and their extractive methodology was sufficient, but possibly not necessary. You can fight in court whether their methodology is against the law, but it would be naive not to look beyond that, which is my main gripe with the AHM statement the author refers to [1]

Fortunately the author of this article has a more nuanced view:

> I can understand the anger, but I am not sure that withdrawing from AI is the answer

[1] https://www.ahmath.org/statements

Comment · 18 days ago
Comment · 19 days ago
Looking at this I'm reminded of https://en.wikipedia.org/wiki/Polymath_Project, in particular "Yitang Zhang's 2013 breakthrough on bounded prime gaps, eventually lowering the upper bound on the gap between consecutive primes from 70,000,000 down to 246".
Comment · 21 days ago
It depends entirely on your trust model. If you just want to be able to compile a rust compiler on a new platform that only has a C compiler, you wouldn't care. If you worry about a Thompson-style trojan horse, then you want to be able to audit all sources in the bootstrap chain.

Some idealistic projects like live-bootstrap go a step further and don't even allow generated sources in the full source bootstrap chain, even if they are readable in principle, because the xz debacle showed that a configure script, which is also readable in principle, can contain a backdoor. In those projects you could probably still bootstrap Eurydice from sources, and then do the rust -> c translation of the rust compiler as an ordinary build step, before compiling it with a bootstrapped C compiler.

Comment · 21 days ago
If it's readable C, this sounds great for a full source bootstrap of the rust compiler.
Comment · 23 days ago
The cost of the N-S disproof was estimated to be $15,000,000 whereas a ChatGPT Pro subscription costs $500.
Comment · 23 days ago
It might as well happen, similar to how AlphaGo was superseded by AlphaZero, at some point a model might produce better math if it's trained through self-play where it poses its own problems, instead of looking for open problems in literature.

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