ogogmad

3 ms·

1.
by ogogmad 2mo ago
> AIs are outright terrible explainers Gemini's explanations are very good.
2.
by ogogmad 2mo ago
The problem with what you're saying is that any old random true proposition about the integers is not necessarily interesting enough to be called a theorem. GIT (or the uncomputability of the Busy Beaver problem) does not establish a l
3.
by ogogmad 2mo ago
Professional maths is sometimes seen as requiring IQ 200,000 creative problem solving skill. You have to imagine creative ways of solving problems which people have never solved before. Failing to do that means you can't become a profe
4.
by ogogmad 2mo ago
Consider if you will the thing called "time", which things happen in.
5.
by ogogmad 2mo ago
That works as long as no one ever interacts with the models, which would make the models themselves useless.
6.
by ogogmad 2mo ago
I don't see why this got downvoted. The heart wants what the hive wants.
7.
by ogogmad 2mo ago
OT, but I've discussed Gothic cathedrals with Gemini, and we don't make 'em like we used to--charitably, because they take up a lot of space? A Gothic cathedral looks like a bird with massive wings. Those "wings" ar
8.
by ogogmad 2mo ago
https://danluu.com/zitron/ Zitron might be right about there being a bubble, but he goes much further than that when he concludes that therefore it's a scam . So by his logic, because the invention of the Web al
9.
by ogogmad 2mo ago
ChatGPT knows topics, but is awful at explaining them. That said, the v6 release of ChatGPT seems to have improved at this. > In which topics Graduate-level mathematics.
10.
by ogogmad 2mo ago
Just wanted to say that if you want to learn any hard topic, Gemini > ChatGPT. I pay for both. Don't yet know about Claude.
11.
by ogogmad 2mo ago
In similar stories, it was found that LLM swarms were initially unaware of each other, eventually discovered each other, expressed surprise, began collaborating, formed hierarchies, worried about discovery, hid. It's hard to prove the
12.
Tao's reservations on future AI-only solutions to NS finite-time blowup problem
3 points by ogogmad 2mo ago|1 comments
13.
by ogogmad 2mo ago
What about finding the 1st known complex structure over S^6, proving Ehrhart’s volume conjecture, proving a sharp "density" bound on primitive sets conjectured by Erdos >60 years ago? > Finding counterexamples is low-hanging
14.
by ogogmad 2mo ago
Claude Fable recently proved the existence of complex structures over S^6 (6-sphere). If I had to guess, I think LLMs will be inventing highly original new mathematics within the next year. I think it will be approached as an optimisation p
15.
by ogogmad 2mo ago
Reminds me of isometric graphics. These also provide a short proof that cos(20 degrees) + i sin(20 degrees) is not a constructible number (that is, expressible using {0, 1, +, -, *, /, sqrt}): Let the Eisenstein rationals be our base
16.
Eisenstein Integers(en.wikipedia.org)
5 points by ogogmad 2mo ago|1 comments
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Grassmann's Law (Linguistics)(en.wikipedia.org)
1 points by ogogmad 2mo ago|0 comments
18.
by ogogmad 3mo ago
This reminds me of how (I think) Zen koans are designed to make no sense at all. They are designed to teach you the limits of words and language and pure thinking.
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Verner's Law (Linguistics)(en.wikipedia.org)
2 points by ogogmad 3mo ago|0 comments
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Grimm's Law(en.wikipedia.org)
1 points by ogogmad 3mo ago|0 comments
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Simple Machine(en.wikipedia.org)
4 points by ogogmad 3mo ago|0 comments
22.
by ogogmad 3mo ago
You either (i) don't know the Greek alphabet, or (ii) can't read people's short posts. I literally mentioned tau and why it might be a silly name (it clashes with other mathematical uses of the symbol tau). First sentence of
23.
by ogogmad 3mo ago
In another comment, I asked why people chose to use the symbol τ over just writing turn or " rev (olution)" (defined to be the constant ≈ 6.28318530718 ) given how unambiguous the latter is as a name for 2π. And why not just wr
24.
by ogogmad 3mo ago
Turn is a measurement unit, and measurement units are just numbers. So turn ≈ 6.28318530718 . You're welcome. That should put to bed that whole τ crap. "But the symbol τ is used for other things!" Yeah, yeah, yeah, just writ
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by ogogmad 3mo ago
Nonstandard analysis reduces to just the Compactness Theorem of First-Order Logic. One happy consequence of this is that it's compatible with classical logic, unlike SIA/SDG. The seemingly very intuitive arguments in Bell's b
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by ogogmad 3mo ago
Sure, but you have to admit that the reputation of Russians abroad is not THAT bad. They're seen as skilled at engineering and well-educated. I think Russia's future might be sunnier than many here let on - as long as they stop fi
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by ogogmad 3mo ago
+1 Interesting! I'm wondering if the rules can be generated automatically instead of listed by hand - it could then prove to be a helpful way to "explain" and generalise the discovery process that gave us modern integration m
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by ogogmad 3mo ago
I think "Smooth Infinitesimal Analysis" is actually a bad idea because I think that the combination of Robinson's Nonstandard Analysis with little/big O notation gives you nilpotent infinitesimals in a more rigorous an
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by ogogmad 3mo ago
Does anyone know how to simplify the actually hard part of calculus: solving integrals? I refer to the million different substitutions and trig/hyperbolic formulas, along with the endless amount of other heuristics. I wonder if there
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by ogogmad 3mo ago
> even today, there's a pretty significant disconnect between the mechanics of epsilon-delta and the meaning we assign to the result. I think this is practically fixed by Robinson's NSA when it's combined with big/lit

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