ogogmad

6 ms·

1.
by ogogmad 6d 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.
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by ogogmad 6d 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.
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by ogogmad 11d 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
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Tao's reservations on future AI-only solutions to NS finite-time blowup problem
3 points by ogogmad 11d ago|1 comments
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by ogogmad 13d 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
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by ogogmad 13d 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
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by ogogmad 14d 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
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Eisenstein Integers(en.wikipedia.org)
5 points by ogogmad 14d ago|1 comments
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Grassmann's Law (Linguistics)(en.wikipedia.org)
1 points by ogogmad 19d ago|0 comments
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by ogogmad 19d 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 19d ago|0 comments
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Grimm's Law(en.wikipedia.org)
1 points by ogogmad 20d ago|0 comments
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Simple Machine(en.wikipedia.org)
4 points by ogogmad 20d ago|0 comments
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by ogogmad 27d 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
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by ogogmad 28d 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
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by ogogmad 28d 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 29d 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 29d 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 1mo 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 1mo 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 1mo 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 1mo 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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by ogogmad 1mo ago
Dual numbers are basically big/little O notation. They combine beautifully with Robinson's NSA to give the most 18th century-like approach to deriving integral/derivative formulas that I know. And it's fully rigorous!
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by ogogmad 1mo ago
> This doesn't follow. The sense in which they are equivalent is that they are equifinal, which doesn't mean isomorphism or even homomorphism That's what I meant. I also tried to provide one justification (out of many) for
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by ogogmad 1mo ago
See also the Blackletter imitation "bastard" https://en.wikipedia.org/wiki/Bastard_(typeface) : The face is available in three weights: Spindly Bastard, Fat Bastard, and Even Fatter Bastard.
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by ogogmad 1mo ago
Most foundations are in a sense equivalent. In that sense, "ZFC" is as good a choice as any. I think there might be some confusion around the different meanings of the word "foundation": A foundation is a formal system t
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by ogogmad 1mo ago
Slightly tangential to your point, but I'm leaning towards programming languages no longer limiting themselves to ASCII. IOW, I'm leaning more towards APL than to J. I'm wondering how much of a blocker it's been to not e
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by ogogmad 1mo ago
Regular expressions will always remain fundamental to computer science: They characterise all of those - and only those - conditions on bytestrings (or bitstrings, or Unicode strings, etc) which are checkable in constant memory.* In other w
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by ogogmad 2mo ago
I think we should create a masculine-sounding word for "nurse", like "(patient/care) (guardian/maintainer/technician)". Nursing still sounds like breastfeeding (check the etymology!), which I'd reckon
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Gap in Mochizuki's proof of ABC confirmed by Lean(twitter.com)
35 points by ogogmad 2mo ago|1 comments

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