Agost Biro

@agostbiro

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I added some comments to the subset transitivity proof

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You don't get a louder warning than this https://www.nbcnews.com/politics/2024-election/13-former-trump-administration-officials-sign-open-letter-backing-john-rcna177227

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After a two week hiatus I was considerably rustier, so just a short exercise today to prove the transitivity of subset relations: https://github.com/agostbiro/mathematics_in_lean/commit/16ae0aad2173868f365d147e43b7fee1fa65cc71 Gotta prioritize daily progress no matter what

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constraints gud

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Petition for the next commission to get eu/acc on their agenda: https://www.eu-inc.org/

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Is anybody headed to Eurorust in Vienna? Hit me up if you do! I’ll be at the async workshop tomorrow

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Did a few more exercises in the Logic section of Mathematics in Lean. I like that they're introducing a bit of analysis with monotone and even/odd functions in this section to make it less dry. The exercises went quickly as I managed to guess the required theorem names the first or second time. This was previously a source of frustration, but it looks like I'm getting the hang of it. The naming is logical. One interesting bit is that I managed to write a simpler solution than the book for one of the exercises (dark picture is mine and bright is the book). The reason is probably the pattern matching in the rewrite tactic becoming more powerful since the book was written. https://github.com/agostbiro/mathematics_in_lean/commit/f0e5f3b3d40f3ca7d8b7810f7e58b49d24196021

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Apple open sourced a break through model for monocular (single image) depth estimation. This is a huge unlock for many things from robotics to computer graphics. https://venturebeat.com/ai/apple-releases-depth-pro-an-ai-model-that-rewrites-the-rules-of-3d-vision/

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Did some more exercises in the Logic section of the Mathematics in Lean book.[1] These introduced proof terms which are just a series of function applications with a more elegant lambda-like syntax. Proof terms underscore that proofs in Lean are really just functions from types to types that compile. As a I side note, the annoyance about having to guess theorem names to solve exercises remains. Hopefully I'll get better at this in the future or find better tools to help. https://github.com/agostbiro/mathematics_in_lean/commit/4aa78ca0f8d8dc4c983b429f5dab26d26b726aa7

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Prof Kevin Buzzard gave a talk[1] at Microsoft in 2019 how he got started with Lean as a teaching tool for undergrads and how he intends to transform modern mathematics by formalizing it with Lean. There has been a lot of progress in that and he has now a research grant to formalize the proof of Fermat's Last Theorem with Lean.[2] What was not foreseen at the time of his 2019 talk is that AI researches have adopted Lean for models that generate proofs.[3] [1] https://www.youtube.com/watch?v=Dp-mQ3HxgDE [2] https://xenaproject.wordpress.com/2024/01/20/lean-in-2024/ [3] https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/

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To be clear, this is not a light show, it's a military display https://x.com/MarioNawfal/status/1840466077785923952

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So I've been following the Mathematics in Lean book which I mostly like, but the exercises are not well designed. To solve the pictured exercise,[1] it gives you a bunch of theorems to use, plus you're supposed to remember a magic incantation (`linarith`) from the previous chapter to solve it. But `linarith` isn't really well explained there, nor is there an exercise to practice its usage. Removing the hand-wavy magic from math is exactly why I started learning Lean, so instead of taking these as given, I rabbit-holed on how `linarith` and `abs_nonneg` work and added my findings as comments. And this shows the power of Lean. Just by using jump to source and a bit of Googling, I was able to get a good understanding of how these things work. If this exercise was in a text book presented like this, I probably wouldn't have gotten there. [1] https://leanprover-community.github.io/mathematics_in_lean/C02_Basics.html

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Lean is quite elegant. Multiple if conditions are curried meaning partial application of an implication is a breeze

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Awesome to see that developer momentum has been maintained since FarCon irrespective of markets

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Nothing like the present 🙏

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Did the final three exercises in the Proving Identities in Algebraic Structures section. These involved proving theorems about groups using only the group axioms. Normally multiplying by the inverse is defined to be commutative in text books, but not here. So the first task was proving that fact. I had to look up the helper lemma for `mul_inv_cancel`, but after that proving the lemma and the theorem + `mul_one` was easy (see pic 1). The last exercise was proving `(a * b)⁻¹ = b⁻¹ * a⁻¹`. This I'm rather proud of, because I think my solution is more legible than the official one (see pic 2).

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Did some more proofs and learned the apply tactic which is pretty cool. It lets you change the goal of a proof to proving the hypothesis of something that you've already proved (see pic for example). I also had a go at proving `theorem mul_inv_cancel (a : G) : a * a⁻¹ = 1` from group axioms (`a⁻¹ * a = 1` is given as an axiom). This was a pretty humbling experience. I thought it was easy and I wrote down two lines on paper as a sketch, but when I expanded it step by step as Lean would want it, it turned out to be wrong. Gonna have a go at a rigorous proof again later. https://github.com/agostbiro/mathematics_in_lean/commit/62ad33dfef38a29e7cf94e038696adbf6addd647

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Sat down to get some Lean done before the day starts. Good news is that that the VSCode plugin works again. Turns out it was the old have to accept Xcode CLI tools license after an update issues. After this the toolchain failed to build the mathlib so I had to reinstall that too, but now it all seems to work again. 🙏 No time for proofs though

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I did some UI coding tonight which I’m not very good at so I tried out Cursor for it, and for the most part it wasn’t really better than a Copilot-style extension, but once I just highlighted some components that were misaligned and told it to make it nicer and it nailed it. That was magical

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This is why I'll never use a closed source browser or terminal app from a startup

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