tmhn2

18 ms·

1.
by tmhn2 5d ago
I certainly didn't intend to imply that the declaration is against using AI. My point is just that I feel a little optimistic that the human culture around math ("ideas we disseminate in talks, private discussions and careful writ
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by tmhn2 5d ago
Hopefully that's true. Instead of bypassing the community maybe it stimulates the community. I think it does disrupt things a bit , but I'm optimistic at the moment!
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by tmhn2 5d ago
I don't think that's entirely fair. I think it's OK that there are some materials designed for a specialist audience, and some materials designed for a wider audience. Technical density serves a real purpose in the former (I
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by tmhn2 5d ago
I'm not totally sure what you mean. You can validate the proof using lean, which is what it's for--the whole magic of it is you don't have to just trust what AI says. That said, to your larger point, there are loopholes,
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by tmhn2 5d ago
I agree entirely with what you're saying, right up until your final question: > why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? I think y
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by tmhn2 5d ago
That's true, but the story would have unfolded differently if Mochizuki had a lean-verified proof and was correct. I guess baked into my premise is that AI is producing reliable proofs (in the long term at least).
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by tmhn2 5d ago
I wonder if they will continue to dump proofs, though? Their point has been made, the novelty will wear off, and it maybe won't be a priority use of their resources to spend however many millions on another big proof--they will move o
8.
by tmhn2 5d ago
As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a
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by tmhn2 5d ago
At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with c
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by tmhn2 5d ago
The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generatio
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by tmhn2 1mo ago
> Are they paid to type code or create programs? The goal is more to understand why something is true than just whether it is true. To oversimplify a lot, it's the difference between industry versus academic motivation. In the for
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by tmhn2 2mo ago
It's important to remember that historically many advances have been made without "customer value" in mind. Indeed, freeing oneself from such concerns can open up unexpected avenues for discovery which only later provide &qu
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by tmhn2 2mo ago
That seems OK to me. I'd rather live in a state that funds beauty than one that doesn't. Think grants for artists, etc. A strictly practical world is not a good world to live in.
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by tmhn2 7mo ago
I think one reason it's discouraged is that it's not completely clear how long it lasts, and getting it early may result in less protection later in life. Also it's only been tested in that age group. (At least, this is wha
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by tmhn2 11mo ago
Research mathematicians have been finding the tools useful [1][2]. I think those problems are interesting, novel, and hard. The AI might stumble sometimes, but it also produces meaningful, quality results sometimes. For experts working
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by tmhn2 2y ago
In that usage the object (football) ends up in the state of spiralling. So the HN title would, strictly speaking, mean that the magnetic fields are causing the black hole to spiral, which isn't right. It's probably sort of bein
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by tmhn2 3y ago
This comment made me curious so I looked up some data (sorry for the formatting, I don't know how to do it better): Guns per 100 people - Finland 2017: 32.49 (total of 1.79 million) [1] - US 2017: 120.5 (total of 393 million) [2] All g
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by tmhn2 3y ago
Right. What "reduction in biodiversity" means is that some species will adapt fast enough and some won't. Unfortunately, there is no lower limit to "reduction in biodiversity".
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by tmhn2 3y ago
> some tropical trees will still be able to photosynthesize in tropical regions. Those will become the dominant species. Unless the environmental changes happen too fast for adaptation to keep up with--the tree of life can have dead ends
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by tmhn2 3y ago
And another fun and powerful technique is "proof by intimidation" ( https://en.wikipedia.org/wiki/Proof_by_intimidation ), in which you don't have to know what you're doing, but other people have to
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by tmhn2 3y ago
Not as prolific as that Nicolas Bourbaki guy, though!
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by tmhn2 3y ago
John Conway showed a generalization of this problem is undecidable. I can't find a PDF but there's a blurb and citation on wikipedia: https://en.wikipedia.org/wiki/Collatz_conjecture#cite_ref-33 I don't
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by tmhn2 3y ago
I don't think it's correct as stated in the article. Looking at the paper, it basically says: the orbit starting with N dips to f(N) for "most" N, where f is a function that goes to infinity. So, you can't pick f(N)
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by tmhn2 3y ago
The authors of the paper are academics in university CS departments with heavy math backgrounds (one with a B.S. in mathematics, another was a visiting professor at MIT dept of mathematics). I don't understand what you mean or how it
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by tmhn2 4y ago
Feedback is critical, though. I imagine many folks who have watched a lot of videos on, say, economics or history or physics or whatever else hugely overestimate what they understand since they get no expert feedback to test their understan
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by tmhn2 4y ago
The little cartoon shows they are ambient-isotopic--that they are just topologically equivalent is pretty clear already!