Arithmetic Without Numbers – How LLMs Do Math

Turing Award Winner: Thinking Clearly, Paxos vs Raft, Working With Dijkstra | Leslie Lamport

https://www.youtube.com/watch?v=U719vQz-WFs

Leslie Lamport : "I am not smart. I have the gift of abstraction."

Real mathematics isn't about details. Its about concepts and abstractions and how we compose them (LLMs are good at those aspects).

> The original dream > A just-in-time compiler for arithmetic

What is it with LLM writing where it gives a smaller heading just before the main heading? Its nonsensical!

There is a beautiful MathOverflow thread on how mathematicians imagine concepts, https://mathoverflow.net/questions/38639/thinking-and-explai....

Very often it involves spatial thinking. Vide one example there:

> Once I mentioned this phenomenon to Andy Gleason; he immediately responded that when he taught algebra courses, if he was discussing cyclic subgroups of a group, he had a mental image of group elements breaking into a formation organized into circular groups. He said that 'we' never would say anything like that to the students. His words made a vivid picture in my head, because it fit with how I thought about groups. I was reminded of my long struggle as a student, trying to attach meaning to 'group', rather than just a collection of symbols, words, definitions, theorems and proofs that I read in a textbook.

One could use many things to do arithmetic:

- color wheel

- oxidation reactions

- interpretive dance

- migratory patterns of curlew sandpipers

Whether one should is another question

Why doesn’t it just call tools such as Mathematica for such operations?

The spirit of Rube Goldberg is alive and well.

What happens inside an LLM when it tries to calculate with nothing but matrices.

Why does every exhibit made with AI look the same?

This is a very nice and fresh page layout.

i dont like this new trend of generating html with ai to say something. i think some guy from anthropic started this trend .

now everything looks the same and i can no longer read on kindle.

I assumed it wrote Python or some sort of other code.