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Simon Willison @simonwillison.net · 30/09/2026

I included the reasoning traces in that one for some of the calculations, to show how the LLM handled long addition

Starting from the right:
2 + 0 = 2
2 + 7 = 9
6 + 9 = 15, write 5 carry 1
5 + 7 + 1 = 13, write 3 carry 1
0 + 6 + 1 = 7
1 + 0 = 1
6 + 4 = 10, write 0 carry 1
6 + 9 + 1 = 16, write 6 carry 1
3 + 7 + 1 = 11, write 1 carry 1
9 + 8 + 1 = 18, write 8 carry 1
9 + 0 + 1 = 10, write 0 carry 1
2 + 6 + 1 = 9
4 + 0 = 4

Wait, let me redo this more carefully.

4,299,366,105,622
6,088,794,067,970

Let me align them:
4 2 9 9 3 6 6 1 0 5 6 2 2
6 0 8 8 7 9 4 0 6 7 9 7 0

Adding from right to left:
Position 1 (units): 2 + 0 = 2
Position 2 (tens): 2 + 7 = 9
Position 3 (hundreds): 6 + 9 = 15, write 5, carry 1
Position 4 (thousands): 5 + 7 + 1 = 13, write 3, carry 1
Position 5 (ten-thousands): 0 + 6 + 1 = 7
Position 6 (hundred-thousands): 1 + 0 = 1
Position 7 (millions): 6 + 4 = 10, write 0, carry 1
Position 8 (ten-millions): 6 + 9 + 1 = 16, write 6, carry 1
Position 9 (hundred-millions): 3 + 7 + 1 = 11, write 1, carry 1
Position 10 (billions): 9 + 8 + 1 = 18, write 8, carry 1
Position 11 (ten-billions): 9 + 0 + 1 = 10, write 0, carry 1
Position 12 (hundred-billions): 2 + 6 + 1 = 9
Position 13 (trillions): 4 + 0 = 4

Wait, that gives me 49,081,601,735,92? That doesn't seem right. Let me recount the digits.

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fry69 @fry69.dev · 30/09/2026

With "reasoning" (generating tokens to solve a problem aka "chain of thought"), even small models become good at math. I'd challenge you to test how small a model can be that produces a better result than Qwen 3.8 27B without reasoning. For kickers, I'd start with Qwen 3 0.6B (reasoning finetune).

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fry69 @fry69.dev · 03/10/2026

FYI: I found this video/explanation very illuminating how models learn simple procedural things like arithmetic outside the "chain of thought" reasoning method. It works in an extremely non-intuitive way (for us humans). Highly recommended in this context ->

fry69@fry69.dev

This is a fascinating deep dive by Welch Labs into how LLMs "grok", meaning to move beyond just memorization to generalization after continue to train for long time while seemingly making to progress. Turns how waves, trigonometry and identity functions are everywhere. Highly recommended. #MLSky

youtube.com

The most complex model we actually understand

YouTube video by Welch Labs

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