Tobi Lehman

Software Engineer | Mathematician | Catholic | "There are 3 certainties in life: death, taxes and software updates"

[Tobi Lehman @tlehman]

@liminaldoge If u,w are in an Abelian group then uwu = u²w

[Tobi Lehman @tlehman]

Learning Abstract Algebra makes you realize there are only like a handful of algorithms.

[Jirka Knesl @jiriknesl]

If you remove different representations, you find out that many algorithms are either the same, or almost the same.

Shortest path is semiring based computation.

More here: https://t.co/IiKh56Cijg

I realized this when I was writing my book on OR algorighms. There are hundreds of algos I went through. Sometimes, you could find 40-50 algorithms, that are different only in one parameter, or one function in the function composition.

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I am 100% sure, there are abstract algorithms in space search + reduction, that could simplify what already exist and provide dozens of real world useful algos for thousands of various usecases.

[Tobi Lehman @tlehman]

This paper with the brilliant @0xbnd and Dr. Caughman was a big effort, I'm happy to share the preprint now that it's live: https://t.co/xe2QJGPyDu

It uses group theory to analyze how the size of a set of undesirable symmetric configurations scales with n and d (dimension)

[Tobi Lehman @tlehman]

https://t.co/wxPpmhKqyf

[Tobi Lehman @tlehman]

Specification engineering is a great term, it gets at the hard part: actually stating the thing to be proved.

[Tobi Lehman @tlehman]

@Jan_Ni2 Numerical analysis is underrated

[Tobi Lehman @tlehman]

@sebuzdugan Yeah like how if you swap a ring for a semiring, then you lose the ability to invert, so now you can't use FFT

[Sebastian Buzdugan @sebuzdugan]

@tlehman two algebraically equivalent algorithms can have very different memory costs, so representation still matters in production

[Tobi Lehman @tlehman]

@sphere_homotopy Gödel's ontological proof https://t.co/UGnG84dNis

[Tobi Lehman @tlehman]

@emhill2100 It is, lots of things are like that

[Tobi Lehman @tlehman]

@emhill2100 The * operations are constrained by properties like associativity or commutativity, and then we prove general things about them, so you can prove things about number addition, multiplication, matrix multiplication, etc all simultaneously.

[Tobi Lehman @tlehman]

My uncle asked me this when I was talking the class, great question actually!

Algebra as it's taught in primary school uses concrete operations like +,-

But abstract algebra uses variable operations like * where * is some function that takes two elements of a set and returns a third.

[Tobi Lehman @tlehman]

Check out the bottom to see it in action, it's made especially clean because of Lean's dependent type system

[Tobi Lehman @tlehman]

@P33RL3SS That's the positive side of social media

[Tobi Lehman @tlehman]

@QuantaMagazine @kkakaes Autoformalization is awesome, but any autoformalization still needs a faithfulness review to make sure the Lean code matches the natural language statements. https://t.co/aCULsXTbAr

[Tobi Lehman @tlehman]

@vict_ordz @burckmeister https://t.co/jp01Yb3yra

[Tobi Lehman @tlehman]

@hamzzygeek @tonialaribe https://t.co/27PWzkde7H

[Tobi Lehman @tlehman]

It goes deeper, check out Physics, Topology, Logic and Computation: A Rosetta Stone https://t.co/IdBq50eYvy

[Tobi Lehman @tlehman]

@ShirleyYerJokin Do you happen to remember the paper's name or authors?

[Tobi Lehman @tlehman]

@RefinedLurk Great book, read it 8 years ago and took some literate programming notes https://t.co/thTMGkcT1m

[Tobi Lehman @tlehman]

@mat_MTO Interesting, it seems intuitive, but I love it when this level is used to check an intuition

[Tobi Lehman @tlehman]

@malaggan Also true