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There is a great quora answer for this one: https://www.quora.com/How-do-you-find-the-positive-integer-s...
>quora answer for this one
that quora article is written by Alon Amit and fwiw, TFA quotes Alon Amit, so his thoughts are ex post.
now that's peak Quora right there!
I really miss those years when Quora was a decent place. it went downhill when they decided to aggressively monetize it.
the same happened to poe.
I heard they use LLMs to generate questions and answers to those questions to help drive traffic, which is why no matter what insane bullshit you type into google, you will probably get a quora page about it.
Something something dead internet theory.
I saw a reddit thread from sub about {specific retailer} in {specific geographical region} where the OP ends with ChatGPT's classic "Would you like some more variations of this text?" response and the whole damn thread was other users happily replying on topic, totally missing that OP was clearly a bot because they were probably bots too. But hey, they all get karma, all get activity and look they're members of {geographic region} so their opinions on future political threads in {region} are totally legit right?
But yeah, something something dead internet theory indeed.
Yeah, yeah, they just mumble mumble diophantine mumble mumble elliptic curve mumble mumble Weierstrass form mumble mumble like your boring old uncle at Christmas. GET TO THE ANSWER!
154476802108746166441951315019919837485664325669565431700026634898253202035277999
36875131794129999827197811565225474825492979968971970996283137471637224634055579
4373612677928697257861252602371390152816537558161613618621437993378423467772036On a related tangent, when I was teaching my younger kids about math and helping with homework, I would often rewrite things as a formula, or rewrite the formula itself once they got to that point. However instead of things like x I would use things like fluffy cloud, star, etc. They thought it was annoying but it still kept them interested and have said they've done the same when helping their peers. It's easy to forget what it was like learning these abstractions, and it was important to show that x was nothing special, it could be a sun, it could be the phrase "total number of kittens"
> it could be the phrase "total number of kittens"
There is this minimalism present in math culture, while I sort of understand it, when tossing and mixing formulas it helps to have everything as small as possible. but later, when it is published it really sucks for readability, "Okay here is an item doing some heavy lifting in this formula what is it for? hell if I know some joker labeled it 'φ' "
I like to joke, If you think programmers are bad at naming thing you should see the mathematicians, they take a perverse pride in their inability to name things.
The worst are programs derived directly from a math paper, if your variable holds the correlation coefficient call it that. we have thousands of years of language and labels we can use to share our ideas with others. don't encrypt it and call it "rho".
One "fun" aspect to this is that there's not just 1 but 13 extra copies of the English alphabet in Unicode that are there specifically for mathematicians to name stuff in formulae and equations.
And with the exceptions of Fraktur and script, free fonts that are already sans-serif and monospace generally do not make the glyphs visually distinct from the actual English alphabet characters similarly weighted and slanted.
Which gives the sighted people a taste of what the sight-impaired people have to suffer when people abuse these code points as ways to write in italics or boldface, because the screen readers correctly obey the important note in Unicode Technical Report 25 that these letters do not combine to make words, and read them out as mathematical formulae where "d" is multiplied by "o" and then by "g".
> don't encrypt it and call it "rho".
These programmers were not hazed enough in their fraternity days. It was not drilled into them that p is rho and that rho is p. Whichever one they choose was always wrong and punished with pushups.
I tried giving this to ChatGPT. (Just by uploading the image to the base OpenAI interface.) I expected to either (a) have the model already know the question and give the right answer, (b) hallucinate an answer or (c) refuse to engage with the problem at all.
Instead, this happened:
https://chatgpt.com/share/682cce62-c53c-8003-be2c-2929395868...
Basically, the model confidently outputs a guess, then calculates it, determines it to be incorrect, and repeatedly tries again, even repeating the same guesses over and over. It does not recognize any symmetry and acts like a completely unstructured agent. In the end, the model vehemently asserts there to be no solutions to this puzzle. I really did not expect this and will update my beliefs accordingly if the models behave as badly with future puzzles.
Here's gemini https://g.co/gemini/share/ab287b25648f
I also asked Chat GPT o3 and it thought for 11.5 minutes! https://chatgpt.com/share/682d0993-db4c-8004-a66c-3908ef7203...
I'm impressed. There certainly are no "reasonable" solutions, where I am arbitrarily defining reasonable as numbers that humans can work or understand in their heads.
Isn't there a version of ChatGPT that connects to Wolfram Alpha? Did you try that one?