Arithmetic Without Numbers – How LLMs Do Math

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.

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).

Why does every exhibit made with AI look the same?

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

The spirit of Rube Goldberg is alive and well.

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.

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

This is a very nice and fresh page layout.

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