> This paper and method is about getting language models to be better at math without changing their architecture. My understanding, memory is that already dec

> This paper and method is about getting language models to be better at math without changing their architecture. My understanding, memory is that already decades ago there was some software that was good at doing calculus manipulations. The software was Mac... something or other. Just now a search gave the name Macsyma and a PDF Reference Manual at https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refman16.pdf https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refma... So, right, long ago there was some software good at some of "Mathematical Reasoning" and, I'd believe, also "reliable". For "mathematical reasoning" in an LLM (large language model), when ChatGPT 4 entered the news I gave ChatGPT 4 two exercises, one from high school plane geometry and one from first calculus. The results for "mathematical reasoning" were no progress at all. From what I know about the LLM approaches and about mathematical reasoning, I don't see any promise for "reliable" results. Then I repeat, math results that are not "reliable" will be about as welcome as week old fish. But just now there is a lot of interest in LLMs as a case of AI. As I glanced at some of the news, apparently the value of Nvidia is now $1 trillion. Sooo, a lot of interest. And we can regard the work on LLMs as research and expect in a few years either (1) reliable mathematical reasoning or (2) not and, thus, evidence that LLMs are not a promising path to such reasoning and AI. We can spend years concluding (2). Heck, I participated in an earlier popular approach to AI. I wrote software, gave talks at Wharton and Stanford, published papers. But I kept looking for anything worthwhile in that work and never found any. Now that work is no longer "popular" and apparently nearly no one believes that there is anything worthwhile there. I'd like to see some progress in software for automation of significant cases of reliable mathematical reasoning, but, sorry, again from what I know about such reasoning and LLMs, I just don't see LLMs as a promising path to such reasoning. So, it is likely the case that for LLMs doing significant cases of reliable mathematical reasoning, people can believe me now or spend some months/years and believe me later. I'd like to see some promising paths to the desired reasoning, with/without the LLM "architecture".