ndriscoll

6 ms·

61.
by ndriscoll 1mo ago
There are vanishingly few research mathematician positions and it's one of the most competitive fields, so no. But I'm not sure how that's relevant. As the OP says, usually the value of a proof is not the knowledge that somet
62.
by ndriscoll 1mo ago
One of the awesome things about LLMs is they make it quick and easy to make PoCs, so yes. Proving that an approach will work before spending a bunch of deep design effort is absolutely valuable. Your exact scenario is something I've li
63.
by ndriscoll 1mo ago
But it does produce value. We now have an explicit solution and even a proof. Humans can then work on clarifying why it's true. Unsurprisingly, not all that different from software, where models can generate working code just fine. The
64.
by ndriscoll 1mo ago
Or the joke about two economists on a walk paying each other $100 daring the other to eat dog shit, increasing the GDP by $200 and creating 2 jobs.
65.
by ndriscoll 1mo ago
We're talking about professionals here. People who (at least in the US) often make several multiples of the median worker. Competence is assumed, and every company I've been at has had programs to pay for additional school if the
66.
by ndriscoll 1mo ago
I don't see why you'd be any less "entitled" than you would be to go outside and play in the dirt or watch birds. What difference does it make to them? They've told you they don't want you as a customer anyway,
67.
by ndriscoll 1mo ago
It's not a tiny minority; at least in the US, ~1/4 mothers stay at home, or for mothers with pre-school children, it's ~1/3. It's actually quite normal outside of maybe certain urban professional circles, and spans
68.
by ndriscoll 1mo ago
It doesn't show that. Subsidies will shift the margin of who can afford to have a stay at home parent, so if being raised by a parent is better than childcare, you expect people on the margin to lose out. This is in contrast to somethi
69.
by ndriscoll 1mo ago
I only have an undergrad in math, so very little understanding, but I'd be pretty surprised if it couldn't do forall just as well. Like, say it found this counterexample which relies on axial stretching or whatever approach. Then
70.
by ndriscoll 1mo ago
Attributing training data seems pointless for trustworthiness. The way you trust a model is the same way you trust a human; you ask it to: 1. Provide a chain of reasoning from agreed premises. These days LLMs can even do this airtight w
71.
by ndriscoll 1mo ago
I suppose, but then your definition of composition requires checking compatibility of codomain/domain instead of it being automatic (and your definition of composition does not fit the shape to form a category), which seems way worse t
72.
by ndriscoll 1mo ago
Typically one defines relations before functions anyway (unless you're doing type theory/programming, in which case types matter), and relations also offer a fix (the empty relation from the empty set is left inverted by the empty
73.
by ndriscoll 1mo ago
But f's codomain is B, and g isn't a function on B, so you can't compose them in the first place. And saying "well yeah but you could compose f's restriction" is exactly making f surjective. The basic result he
74.
by ndriscoll 1mo ago
That's basically saying you'll just take all functions to be surjective though, and it's stronger than you really need; the non-surjective case works fine for non-empty A. You could of course interpret some of these basic the
75.
by ndriscoll 1mo ago
No, empty A is critical to the counterexample. In your example, g(x) = 1 is a left inverse. The point is you either send an element of the codomain to its (unique by injectivity) preimage if it's in the image, or to an arbitrary elemen
76.
by ndriscoll 1mo ago
I ran into this same thing formalizing some of my old notes in Lean a few days ago. The tricky thing I suppose is that 0. Injectivity and A non-empty or B empty implies left invertibility, 1. Left invertibility implies injectivity. 2. Surje
77.
by ndriscoll 1mo ago
That sentence just says why we're making a national government (i.e. giving up some of our rights). It does not create some unlimited requirement for governments (especially state) to do whatever they can to promote general welfare, wh
78.
by ndriscoll 1mo ago
No, I quite strongly believe it actually. I likewise find it hard to believe you're serious, so I'll raise my question again: if not even a municipal library (which, I'll remind you, aren't even open the majority of the
79.
by ndriscoll 1mo ago
If it's only a few minutes, you could just as well fix it at the start of the day. And if it's not, oh well? People can still read books. The librarian can still help them to find a book. If they want to manually track until the c
80.
by ndriscoll 1mo ago
> nothing gives you the right to use the software in ways that violate the EULA Correct, that right is innate. > your right to create an archival copy does not extend to a right to run the media on unsupported/licensed hardware &
81.
by ndriscoll 1mo ago
They can use an online service in the middle of the night, but as a citizen, I'd be upset if I learned my public library were paging someone in the middle of the night if it weren't working. That's incredibly inappropriate. I
82.
by ndriscoll 1mo ago
High traffic doesn't mean high urgency. New York Public Library is huge and looks to have even more restrictive hours than mine. They're closed on Sundays! People donate because they believe in the mission, and most of the money p
83.
by ndriscoll 1mo ago
My local library isn't open at 6am either (opens at 9, or 10 on Sat and 1 on Sun), and closes before 7 on Fri-Sun. > someone needs to Do they though? Why is there some assumed urgency? What happens if they don't do it "whe
84.
by ndriscoll 1mo ago
Is it very important that they have someone to restore service at 3am? This isn't a hospital here; it's more like a library. My library is closed at 3am every day!
85.
by ndriscoll 1mo ago
I'm not sure who's even meant to be whom in your sentence, but it's approaching things from an entirely wrong angle. Like, my wife is a full-time mother. Economically, I bring in the income for everything, but we're marr
86.
by ndriscoll 1mo ago
Basically no one has a requirement to track what someone else is looking at. In fact, if not given explicit consent by the person being tracked (like they've specifically sought you tracking it for them , e.g. marking their place), we
87.
by ndriscoll 1mo ago
Jeremy Jethro seems to be an example. His lawyer claimed he had no knowledge of what the exploit would be used for, and that it didn't even work, but he ultimately pled guilty to criminal conspiracy.
88.
by ndriscoll 1mo ago
It would be absurd to jail someone for accurately describing a bug on their blog or whatever. Not so much for taking money from someone who the buyer should know has no reason to be interested in buying the information. And either you know
89.
by ndriscoll 1mo ago
Raising children is probably the epitome of character building, self-actualizing work. There are no external stakeholders to motivate you. No one's going to do it for you if you don't. You get out of it exactly what you decide to
90.
by ndriscoll 1mo ago
The thing is, assuming you get married as a step toward building your own family, once you have kids, there isn't an out that doesn't involve damaging them for life. Your contingency plan is going to be bad no matter what, and n

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