08/25/2026
Arithmetic Without Numbers
What happens inside an LLM when it tries to calculate with nothing but matrices
How does a large language model do arithmetic when all it has are matrices—no fingers, no scratch paper, no columns of digits? This article looks inside a frozen Llama and asks a sharper question than whether the model can call a calculator: with the prompt text removed, can its own activations reveal the operation and operands? In these experiments, they can. Under a strict no-parser rule, activation-derived readouts supplied a calculator’s arguments for several arithmetic tasks. The same activations reveal number-related directions and rotations, a geometry closer to a clock or spiral than to written columns. Interventions test whether selected internal states affect behavior, while provenance audits trace the calculator arguments back to model activations. Together, the results show one way arithmetic structure can take shape inside a language model.