Mathematics is fun

Joined April 2018
546 Photos and videos
Category Witch retweeted
I can suggest an equation that has the potential to impact the future: 𝐍𝐚𝐭(𝐇𝐨𝐦(βˆ’, 𝐢), 𝐹) β‰… 𝐹(𝐢) AI Given a category π’ž, a functor 𝐹 : π’žα΅’α΅– β†’ π’πžπ­, and an object 𝐢 ∈ π’ž. This equation combines Yoneda’s famous Yoneda lemma, which relates a category (π’ž) to a functor (𝐹: π’žα΅’α΅– β†’ π’πžπ­) and the speed of light (𝐢 ∈ π’ž), with the addition of Al (Artificial Intelligence). By including Al in the equation, it symbolizes the increasing role of artificial intelligence in shaping and transforming our future. This equation highlights the potential for Al to unlock new forms of energy, enhance scientific discoveries, and revolutionize various fields such as healthcare, transportation, and technology.
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I think this is more like a particular choice of semantics for programs, which makes sense in some contexts but not others. Or maybe I'm missing the point that all programs can be reduced to these somehow?
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Bohmian interpretation of quantum mechanics
Mention one scientific opinion that you’d defend like this ✍️
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What is pip then?
Sometimes I don't know how else to convince people to try Functional Programming
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Projective geometry is when you draw a lot of lines
Projective geometry 😍
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People just learning that Israel is an authoritarian theocracy are like:
Whoa I just learned that interfaith marriage is illegal in Israel!! What the fuck?? This is insane.
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Still getting weirded out about how: Lax functors C -> Span And Lax normal functors C -> Prof are the same thing
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Category Witch retweeted
For R&D community nucleation, it’s exciting that @ToposInstitute opened a UK office, relocating @u_map_prop and @myers_jaz; while @JadeMasterMath and @tangled_zans used our funding to launch a new nonprofit research institute in Glasgow (GLAIVE: Glasgow Lab for AI VErification).
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If you're in Glasgow you can come see me play music here
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Category Witch retweeted
Math Roadmap:
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Category Witch retweeted
Cats are invariant under SO(3) transformations! 😼
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Category Witch retweeted
\newcommand{\R}{\mathbb{R}}
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You, foolishly: a double category has horizontal and vertical morphisms Me, wise, laying flat: no those are vertical and horizontal morphisms
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Freestyling is left adjoint to forgetting the lyrics
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Zariski inventing algebraic varieties was like:
24 Sep 2024
Crazy stuff is happening on reddit
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Yes exactly. The trick is to find the right generality where the definitions have canonical choices
A function a -> a only has one sensible implementation, a function Int -> Int has manyβ€”polymorphism is recessive. The implementation is constrained/clarified by the generality of the interface. Programmers warn of "premature abstraction," but this is confused w.r.t. foundations
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Above
If you were the empty set, where would you want your face to be?
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Linear algebra is mother
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I don't think this is fair. Think about how hard it is for a machine to distinguish "hallucination". There are just endless unknown unknowns.
The fact that LLMs still hallucinate 2 years after the initial release means: 1. Nobody knows how they actually work to fix them 2. Nobody actually cares
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Category Witch retweeted
14 Sep 2024
it just like me fr
14 Sep 2024
it’s so over
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