medieval #proofs ๐Ÿ‘ฏโ€โ™€๏ธ

Phew, managed to read through the proofs of an article today. Was a bit tight, only had 15 mins of working time left. It always tends to take longer than expected.

#proofs #publishing #AcademicChatter #AcademicFedi #manuscript #science #research

Kimon Fountoulakis (@kfountou)

์ž‘์„ฑ์ž๋Š” ํ•ด๋‹น ๊ฒฐ๊ณผ๊ฐ€ ์ง„์ •ํ•œ ์ผ๋ฐ˜ํ™”์˜€๋Š”์ง€, ์–ด๋–ค ์˜๋ฏธ์—์„œ ์ผ๋ฐ˜ํ™”์ธ์ง€ ์˜๋ฌธ์„ ์ œ๊ธฐํ•ฉ๋‹ˆ๋‹ค. ์‚ฌ๋žŒ๋“ค์ด 'first proof'๋ผ ๋งํ•  ๋•Œ ๋ณดํ†ต ๋ฌธํ—Œ์—์„œ ์™„์ „ํ•œ ์ข…๋‹จ ๊ฐ„(end-to-end) ์ฆ๋ช…์„ ์Šค์Šค๋กœ ์ฐพ์ง€ ๋ชปํ–ˆ์„ ๋ฟ ํ•ต์‹ฌ ๋‹จ๊ณ„๋“ค์€ ์ด๋ฏธ ์กด์žฌํ–ˆ์„ ๊ฐ€๋Šฅ์„ฑ์ด ํฌ๋‹ค๊ณ  ์ง€์ ํ•˜๋ฉฐ, '์ฒซ ์ฆ๋ช…'์˜ ์ •์˜์™€ ์ฃผ์žฅ ๊ฒ€์ฆ์˜ ์ค‘์š”์„ฑ์„ ๊ฐ•์กฐํ•ฉ๋‹ˆ๋‹ค.

https://x.com/kfountou/status/2022670003191902263

#research #proofs #ai #firstproof

Kimon Fountoulakis (@kfountou) on X

@harshit_sikchi Well, was it really a generalization? And if so, in what sense? I think we are about to see that when humans say โ€œfirst proofโ€, they usually mean they couldnโ€™t find the complete end-to-end proof in the literature themselves, even though core steps might already exist.

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Yang Liu (@yangpliu)

ํ•ด๋‹น ์ฆ๋ช…์˜ ์ฃผ์š” ์•„์ด๋””์–ด๋Š” ๋ณธ๋ž˜ arXiv:0808.0163 ๋ฐ arXiv:0911.1114์—์„œ ๋น„๋กฏ๋˜์—ˆ๋‹ค๊ณ  ๋ฐํžˆ๋ฉฐ, ์ด ๋ถ„์•ผ ์—ฐ๊ตฌ์ž๋“ค์—๊ฒŒ๋Š” ์ด ์ฐธ์กฐ๋“ค์ด ์ž๋ช…ํ•˜๋‹ค๊ณ  ์ฃผ์žฅํ•ฉ๋‹ˆ๋‹ค. ๋”ฐ๋ผ์„œ ์ด ํ•ด๊ฒฐ์ฑ…์„ '์ƒˆ๋กœ์šด ์•„์ด๋””์–ด'๋ผ๊ณ  ๋ถ€๋ฅด๊ธฐ๋ณด๋‹ค๋Š” ๊ธฐ์กด ์—ฐ๊ตฌ์˜ ์ธ์ƒ์ ์ธ ์ข…ํ•ฉ์œผ๋กœ ๋ณด๋Š” ํŽธ์ด ์ ์ ˆํ•˜๋‹ค๊ณ  ํ‰๊ฐ€ํ•ฉ๋‹ˆ๋‹ค.

https://x.com/yangpliu/status/2022690163923583114

#arxiv #research #proofs #math

Yang Liu (@yangpliu) on X

The proofโ€™s main ideas are essentially from arXiv:0808.0163 and arXiv:0911.1114. For those in this area, these are the obvious references, so I wouldnโ€™t call this solution โ€œnew ideasโ€โ€”itโ€™s an impressive synthesis of existing work.

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Kevin Weil (@kevinweil)

AI ์ˆ˜ํ•™ ๋ถ„์•ผ์—์„œ 'First Proof' ์ฑŒ๋ฆฐ์ง€๊ฐ€ ํ›Œ๋ฅญํ•œ ์•„์ด๋””์–ด์˜€์œผ๋ฉฐ ๊ฒฐ๊ณผ๋ฅผ ๊ธฐ๋Œ€ํ•œ๋‹ค๊ณ  ๋ฐํž˜. ๋˜ํ•œ OpenAI์˜ ์ œ์ถœ๋ฌผ์— ๋Œ€ํ•ด @merettm์˜ ํ•ด์„ค(์ƒ‰๊น” ์žˆ๋Š” ์„ค๋ช…)์ด ํ›Œ๋ฅญํ–ˆ๋‹ค๊ณ  ์–ธ๊ธ‰ํ•จ.

https://x.com/kevinweil/status/2022534289712377958

#ai #mathematics #openai #competition #proofs

Kevin Weil ๐Ÿ‡บ๐Ÿ‡ธ (@kevinweil) on X

AI ๐Ÿค Mathematics. The First Proof challenge was a great idea and I'm looking forward to seeing the results! Great color on OpenAI's submission from @merettm below ๐Ÿ‘‡

X (formerly Twitter)

Blocked by person refusing to believe a #Mathematics #textbook and #proofs because of a random #Wikipedia article that doesn't cite any Maths textbooks, and in fact has proofs in it that actually contradict the conclusion! (the series 0.1, 0.01, 0.001, 0.0001,... never reaches zero, even as the series approaches infinity - it's a hyperbola with an asymptote of 0 - which you think would be self-evident, and yet here we are) Welcome to the #disinformation age! ๐Ÿ˜ก

https://dotnet.social/@SmartmanApps/115207044364101854

Lies, Damned Lies, and Proofs: Formal Methods are not Slopless โ€” LessWrong

There's been a lot of chatter recently on HN and elsewhere about how formal verification is the obvious use-case for AI. While we broadly agree, we think much of the discourse is kinda wrong because it incorrectly presumes formal = slopless.

AI Notkilleveryoneism Memes (@AISafetyMemes)

Gemini์˜ ๋…ผ์ฆ์ด ๋‹จ์ˆœํžˆ ๊ธฐ์กด ์ฆ๋ช…์„ ์žฌํฌ์žฅํ•œ ๊ฒƒ์ด ์•„๋‹ˆ๋ผ, ํŠธ์œ— ์ž‘์„ฑ์ž๊ฐ€ ์ž์‹ ์ด ์ง์ ‘ ๋‚ผ ๋งŒํ•œ ์ˆ˜์ค€์˜ ํ†ต์ฐฐ์„ ์ œ๊ณตํ–ˆ๋‹ค๊ณ  ํ‰๊ฐ€๋ฐ›์•˜๋‹ค๋Š” ๋‚ด์šฉ์ž…๋‹ˆ๋‹ค. ์ด๋Š” Gemini ๋ชจ๋ธ์˜ ๊ณ ๊ธ‰ ์ถ”๋ก ยท์ฐฝ์˜์  ๋ฌธ์ œ ํ•ด๊ฒฐ ๋Šฅ๋ ฅ์„ ๊ฐ•์กฐํ•˜๋Š” ์‚ฌ๋ก€์ž…๋‹ˆ๋‹ค.

https://x.com/AISafetyMemes/status/2011873612706562230

#gemini #ai #reasoning #math #proofs

AI Notkilleveryoneism Memes โธ๏ธ (@AISafetyMemes) on X

"Gemini's argument was no mere repackaging of existing proofs; it was the kind of insight I would have been proud to produce myself." https://t.co/LlXdUEM1K5

X (formerly Twitter)
Concrete Semantics

Robbe Van den Eede shares insights on #proofs and their role in #logic-based languages for #KnowledgeRepresentation, discussing the paper โ€œA Sequent Calculus for Generalized Inductive Definitionsโ€, co-authored with Robbe Van Biervliet and Marc Denecker, which received the Best Paper Award at LPNMR 2024.

https://blogic.ink/p/a-sequent-calculus-for-general-inductive-definitions/

A Sequent Calculus for General Inductive Definitions

Robbe Van den Eede

bLogic.ink