alt.hn

6/5/2026 at 10:19:39 AM

Arithmetic Without Numbers – How LLMs Do Math

 https://alvaro-videla.com/llm-arithmetic-internals/article_interactive/article.html

by old_sound

6/7/2026 at 12:04:00 PM

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.

by stared

6/7/2026 at 10:16:43 AM

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).

by Npovview

6/8/2026 at 3:02:14 AM

That's an interesting quote, because Feynman's superpower seemed to be his ability to visualize a difficult problem and make it parsable by mere mortals. I think he only scored ~135 on an IQ test (whatever that's worth).

by helterskelter

6/8/2026 at 3:44:58 AM

Pity Feynman didn’t write a Distributed Systems textbook…

by BobbyTables2

6/8/2026 at 2:40:49 PM

It wouldn't have been that out of left field, he did work on massively parallel machines at Connection Machine. Though I guess that was more AI than distributed systems, iirc.

by Chu4eeno

6/7/2026 at 7:57:17 AM

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

by iammjm

6/7/2026 at 11:03:23 AM

For the same reason you don't run "4+6" on a calculator.

External tool call has an overhead. It requires a round trip into an external tool. It requires an LLM to run in agentic autoregression - it can't be used in prefill.

Which means that having native arithmetic capabilities is useful. Forward pass arithmetics are an LLM version of quick mental math.

An LLM can read "#define SILLY_TIME_CONST (3*20*60*60*1000)" and have "SILLY_TIME_CONST is 60 h expressed as 216000000 ms" already cached by the end of the line, before it even emits its first token.

by ACCount37

6/7/2026 at 8:06:11 AM

This is more how an LLM thinks about math internally - an LLM version of drilled tables being used for mental arithmetic "as humans do".

When humans stall on these tasks, they reach for pen and paper, a slide rule, a calculator, etc.

Mathematica is overkill for arithmetic, in addition it's licenced and can cost a bit extra.

If an LLM were to reach for a light cheap arithmetic tool something like bc would be a good first stop - a CLI tool with a language that supports arbitrary precision numbers with interactive execution of statements.

https://en.wikipedia.org/wiki/Bc_(programming_language)

by defrost

6/7/2026 at 9:37:55 AM

They do. I asked CharGPT for 327 x 48 and it used the "ChatGPT Instruments" calculator.

Previously it used to run Python scripts, and may still do for more complex calculations.

by jampekka

6/7/2026 at 3:03:29 PM

What's interesting is that one one hand LLM pumps are claiming a path to AGI.. while on the other hand, they are duct-taping in deterministic plugins for specific prompt types they find it better to offload...

In X years is it just going to be a thin OS-like layer where a majority of work is being handled by other "programs".

by steveBK123

6/7/2026 at 3:50:07 PM

> while on the other hand, they are duct-taping in deterministic plugins for specific prompt types they find it better to offload

So, in essence, just like human beings?

by beernet

6/8/2026 at 3:47:34 AM

How creditable would Claude be if it couldn’t answer “1+2=3?”

Worse, this is really human beings trying to pretend that their AI is AGI.

by BobbyTables2

6/7/2026 at 7:03:42 PM

My point is what makes this terribly different than Alexa skills

by steveBK123

6/7/2026 at 6:49:41 PM

For this category of problems, no, very unlike human beings.

by grey-area

6/7/2026 at 7:07:45 PM

Right.. plumbing in specific plugins for specific prompt forms feels like an expert system, rather than some general purpose intelligence.

Also big picture its hard to see it as some sort of self-improving intelligence if humans are hand crafting these paths and tools for it.

by steveBK123

6/8/2026 at 3:48:09 AM

Exactly, an expert system marketed to nonexperts…

by BobbyTables2

6/7/2026 at 4:12:38 PM

That doesn't seem very persuasive. The one example of a non-A GI we have, humans, does the same thing. We've been offloading arithmetic for at least 4000 years.

by tzs

6/8/2026 at 3:48:59 AM

Sure but we don’t pretend otherwise…

by BobbyTables2

6/7/2026 at 3:05:19 PM

> In X years is it just going to be a thin OS-like layer where a majority of work is being handled by other "programs"

That is my hopeful ideal

by singpolyma3

6/7/2026 at 3:15:44 PM

In which case it’s just a neat extension of search

by steveBK123

6/7/2026 at 8:07:34 PM

I was thinking the same thing. Why not call into a dedicated math tool?

But I don't as well, and I have some intuition about numbers that I would probably not have if I always relied on calculators. Would the same sort of thing apply to LLMs? I'm probably anthropomorphising here...

by ragebol

6/7/2026 at 12:34:38 PM

ChatGPT does, and has since 2023

by breezybottom

6/7/2026 at 2:46:36 PM

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

by 0x59

6/7/2026 at 5:27:43 PM

“You know how when you see prime numbers, they appear red, but when they're twin primes, they're pink and smell like gasoline?”

by throw1234567891

6/7/2026 at 7:24:13 AM

The spirit of Rube Goldberg is alive and well.

by euroderf

6/7/2026 at 2:15:39 PM

We evolved to do incremental fixes, not full refactoring

by soupspaces

6/7/2026 at 8:29:01 PM

Maybe evolutionary, but not ours, as the things we tend to want to refactor have come to exceed our lifespans.

by cwmoore

6/7/2026 at 1:07:24 PM

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.

by dominotw

6/7/2026 at 3:07:45 PM

Everything looked the same before too. One of the same 6 Jekyll temples etc. Fads in design come and go

by singpolyma3

6/7/2026 at 5:00:44 PM

> 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!

by xyzsparetimexyz

6/7/2026 at 6:36:54 PM

You'd think with tool use being as available as it is, the first tool we'd want to give them is a calculator...

by zdc1

6/5/2026 at 10:19:39 AM

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

by old_sound

6/7/2026 at 9:17:26 AM

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

by andrewstuart

6/7/2026 at 10:28:31 AM

writing and calling an entire python setup seems massive overkill, surely just have an internal way of calling a simple calculator function would be millions of times faster

by mavhc

6/7/2026 at 3:37:09 PM

Probably but the cost of running a short lived python interpreter to run "print (100 + 200)" is likely negligable compared to the cost of running the language model itself

by sebzim4500

6/7/2026 at 3:08:00 PM

Usually yes

by singpolyma3

6/7/2026 at 7:15:43 AM

This is a very nice and fresh page layout.

by silvestrov

6/7/2026 at 1:55:03 PM

Why does every exhibit made with AI look the same?

by rubyfan