TeX was invented to typeset math but is now used for reasoning

I'll keep this short, since it's a simple observation that I haven't seen anybody else make, about the way computer systems do math. If you ask a language model to do a multi-step math problem (let's take GLM-5.3 as an example because you can see the entire CoT — nothing up its sleeve), you might see something like this: We need to evaluate the integral $\int_0^\infty \frac{x^3}{e^x - 1} dx$. The standard approach: Use the geometric series expansion. We have $\frac{1}{e^x - 1} = \frac{e^{-x}}{1 - e^{-x}} = \sum_{n=1}^{\infty} e^{-nx}$ for $x > 0$. So the integral becomes: $$\int_0^\infty x^3 \sum_{n=1}^{\infty} e^{-nx} dx = \sum_{n=1}^{\infty} \int_0^\infty x^3 e^{-nx} dx$$ What are all these symbols like \int , \infty , \frac ...? They're TeX of course! Donald Knuth created TeX to typeset math, you know, for display . It had nothing to do with the actual computations, which would either be done with pencil and paper, [1] or else with Mathematica or Maple or something, which work completely differently. If you'd asked Knuth in the 1980s about doing algebra in TeX he'd have looked at you very funny because the idea doesn't make sense. [2] Then, generative language models were trained on corpora including many TeX/LaTeX documents and learned how TeX works (and more importantly the mathematical meaning of the symbols). So, nowadays when an LLM solves a math problem, it will very often use TeX for the intermediate steps of the math problem, like it's actually manipulating the Te…