iiinova — where your digital self keeps evolving

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dan @danabra.mov · 18/09/2026

we're on hnnnn

dan@danabra.mov

i spent all of my free time for a month on this. it's done. so i wrote about it.

overreacted.io

How I Vibed a Proof of Conway’s Conjecture — overreacted

You can just prove things, apparently.

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dan @danabra.mov · 18/09/2026

heh i like this

gbjcantab 1 hour ago | next [–]

For some reason, this approach makes me think of the difference between “wizardry” and “sorcery” in some fantasy magic systems. The magic of “wizards” is fundamentally based on a deep study and understanding of arcane things, perhaps assisted by some (necessary or helpful) tools of great power. “Sorcerers” summon supernatural beings and are able to control them, cajole them, and protect themselves and others against them (with more or less success)... but the actual desired magical effect is performed by those beings.
Computing has historically been a field of wizardry. It's... interesting (?) to see so many people pushing so hard in the direction of sorcery, and in fact applying that sorcery to other fields, in which they themselves aren't quite able to validate whether the spell worked or not.

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patcon 1 hour ago | unvote | parent | next [–]

Heh, I like this. but it should be pointed out that from the other point of view, software developers were the supernatural beings (dare I say demons), which the sorcery of a good project manager could tame (with more or less success) to perform the desired magical effect
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KyleTheDev 1 hour ago | root | parent | next [–]

All this time, I've been considering myself the warlock. When, in fact, I've simply been the Imp. Dastardly news.

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dan @danabra.mov · 19/09/2026

a reply from Prof. Mantova! news.ycombinator.com/item?id=4976... honestly this is the best kind of outcome i‘m hoping for with amateur-driven AI proofs: maybe they aren’t usable directly but can offer a couple of nudges that help the mathematicians uncover the actually interesting connections

xworld21 31 minutes ago | unvote | parent | context | flag | favorite | on: I vibed a proof of Conway's conjecture

Vincenzo (Mantova) here: yes, I have been reading bits and pieces of the proof and I can say for sure that the method is sound, at least for the first half (power series with real exponents). I haven't even tried reading the part that mentions the Cantor-Bendixson rank yet, although given how the rest went, I'd be really surprised if there's a problem there.
As with most interesting proofs, the number of core ideas is actually small, I'd say two for the real exponents, and presumably a third idea for lifting up to omnific integers. I have been redoing the real exponents part of the proof going on the ideas only, and with a few smarter choices, I am converging on something very short. And I mean very short, which is amazing. I didn't think the answer would be this close: it 'just' needs looking at the problem from the right angle, and also make a fairly bold guess at the outcome.
Dan's current proof is of course much longer. Between the fossilized ideas that Dan mentions in the post and the formalisation of previous results, there's a lot of cruft that inflates the proof but does not really help understanding what is going on. Luckily the word 'derivation' pops up early, otherwise it would have been very challenging to wade through the lemmas to find the important points.

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