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#proof

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HistoPol (#HP) 🏴 🇺🇸 🏴

@meduza_en

#WarInUkraine #Ukraine #Russia

Could the #Assasination of #AndriyPortnov, a former top aide to ex-Ukrainian President #ViktorYanukovych be a sign of the #Russian #FSB tying up loose ends?

As the curatorial and investigative journalist Prof. #SethAbramson showed in his national bestseller on the Russia-Ukraine crisis—#Proof of #Corruption (#Macmillan, 2020)—, there were ample connections between the #Kremlin and #Kyiv during that period; to say the least.

masto.ai/@meduza_en/1145454827

MastodonMeduza in English (@meduza_en@masto.ai)Andriy Portnov, a former top aide to ex-Ukrainian President Viktor Yanukovych, was reportedly shot dead outside his children's school in the Spanish town of Pozuelo de Alarcón on Wednesday. https://meduza.io/en/news/2025/05/21/former-ukrainian-official-who-served-in-yanukovych-administration-reportedly-shot-dead-in-madrid
Public
ThePdog

Saw this statement on another site: "Any prime number higher than three, when squared and subtracted by one, will always turn out to be a multiple of 24."

I never heard of this one before. Is there a proof of this property? Definitely needs a bit more investigation.

#PrimeNumber#proof#properties
Public
WordofTheHour

#proof : that degree of evidence which convinces the mind of any truth or fact, and produces belief

- French: une preuve

- German: abdichten, der Nachweis

- Italian: prova

- Portuguese: prova

- Spanish: prueba

------------

Fill in missing translations @ wordofthehour.org/r/translatio

wordofthehour.orgWe need your help!! Help us improve our translations. :)We rely on community members to help us improve our translations. If you are a native speaker in one of our supported languages, we strongly...
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C.

#Mexico and #Canada, and every nation in the #EU, should now insist on proof of vaccination against all generally preventable diseases from Americans prior to entry into their country.

If you want Bobby Brainworm in charge of your public health, it's your funeral, but you don't get to spread those germs in our countries to those of our citizens that are too vulnerable to be immunized.

#RFKjr#BobbyBrainworm#vaccine
Public
claude

inspired by tavis' deep field #nebulabrot #DeepZoom images on #fractal #fractals forums, I did a little shader that for each c in the complement of the #MandelbrotSet M, colours according to how often z <- z^2 + c hits a given small target disc , weighted by derivative (as a proxy for point density).

it looks as though the hit sources are distributed everywhere near the boundary of M, which i think i can prove for target discs outside a sufficiently large esape circle, but i'm not sure how for discs nearer M. intuitively, by the time any cell pair in binary decomposition of exterior escapes, it covers an annulus with radii R, R^2, so any disc outside R will be hit by some region in every cell pair.

boundary of mandelbrot set and some nearby discs in shades of purple, pixelated.
#math#maths#proof
Public
Jan :rust: :ferris:

‘Interpretability’ and ‘alignment’ are fool’s errands: a #proof that controlling misaligned large language models is the best anyone can hope for (Oct 2024)

link.springer.com/epdf/10.1007

"This paper [...] show[s] that it is empirically impossible to reliably interpret which functions a large language model (#LLM) #AI has learned, and thus, that reliably aligning LLM behavior with human values is provably impossible."

This affects much more than just alignment!

link.springer.com‘Interpretability’ and ‘alignment’ are fool’s errands: a proof that controlling misaligned large language models is the best anyone can hope for
#LLMs#Paper#ArtificialIntelligence
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Akshar Varma

For a long time, I didn't know exactly how the Fundamental Theorem of Arithmetic (unique prime factorization) was proved from first principles.

I finally figured out the order of proofs for the fundamental theorem of arithmetic from first principles. Now that I know the sequence, it feels like it was my own fault for not properly going through a textbook and that it was probably obvious to everyone. I'm posting this mainly to reinforce my own clarity on the topic.

1. Well-Ordering Principle, this is either taken as axiomatic or one step away from axioms. This is where I'm drawing the line for "first principles".
2. Euclidean Division: Existence and Uniqueness of quotient 𝑞 and remainder 𝑟 in 𝑎 = 𝑞𝑏 + 𝑟 form. Uniqueness if 𝑟 between [0,1,...,𝑞−1]. Proof is just well-ordering principle (often framed as infinite descent).
3. Bezout's Identity. Proof starts with well-ordering to find 𝑑, then together with Euclidean division shows that 𝑑 is a divisor. A bit more Euclidean division shows that all other factors 𝑑' also divide 𝑑. So 𝑑 is the greatest divisor.
4. Euclid's Lemma: Proof says if 𝑝 doesn't 𝑎 in product 𝑎𝑏, then gcd(𝑎,𝑝)=1. This brings in the above and some rearrangement proves that 𝑏 is a factor as needed.
5. Fundamental Theorem of Arithmetic: Existence usually goes via strong induction (which can be rephrased as Well-Ordering + contradiction). Uniqueness uses Euclid's Lemma to show that the primes in the factorization must divide each other (which implies equality).

#math#proof#NumberTheory
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Rafael

I'm still working through that algebra and trig book by Fisher and Ziebur. I just finished the section on linear functions and I picked up another gem. I always knew that y=mx+b was linear but I'd never seen it proved. Or even thought about proving it. But, they provide a nice proof (starting on p.64). There isn't space to reproduce it here but it relies on the triangle inequality and is a satisfying bit of algebra!

#math#algebra#proof
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