> Do you think LLMs can understand Axiom? Can it help people > to complete the goal of document Axiom in literature programming > style? So that humans can understand Axiom completely?
Barry Trager sent me a copy of the book "Integration in Finite Terms: Fundamental Sources"[0]. The book has a series of papers leading up to his PhD thesis. Years ago I tried several times to read and understand his PhD work in integration and failed completely. Now I am working through the background material. While working through the book I revisited the resultant algorithm. I asked an LLM about it. The result was "When integrating rational functions, finding the logarithmic part of the integral requires determining the poles and their associated residues. Computing these algebraically without finding the roots of large denominator polynomials requires the Rothstein-Trager Resultant." Pulling on that thread leads to Barry's Masters Thesis. I asked an LLM to explain the resultant algorithm. The LLM not only explained it in great detail (I'm a slow learner), it constructed many examples until I could compute it by hand. That leads to WHY you need the resultant algorithm which leads to further LLM question-answer sessions. Without LLMs I'm not sure I could fully understand Trager in any reasonable amount of time. The point is that the LLMs can already explain Trager. The question then becomes "When can they use that understanding to compute integration". My guess is it already can when given the correct series of prompts. I had advocated developing an MCP (Model Context Protocol) server to give LLMs access to the computer algebra system, part of the goal of making the algebra available to other systems. However I think the time has passed when this is useful. The LLMs already "know" most of the answers to computer algebra questions. Whether the answer is correct or not is questionable at the moment but I think that will change. It would be an interesting study to discover how much computer algebra system output is already "known" to an LLM. The LLM output requires careful prompt construction (known as "skills"). I suspect the likely path going forward will be constructing "skills" that give the same or better output than the current computer algebra systems. It has the added feature of being able to explain the result (aka machine-to-human) in any desired amount of detail. So the forward-looking path is "skill development" rather than hand written algorithms. I am trying hard to learn this new game. As the Red Queen in Carroll's "Through the Looking-Glass" said: "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" Tim, the trailing edge runner. [0] Clemens G. Raab and Michael F. Singer (ed) "Integration in Finite Terms: Fundamental Sources" (2022) ISBN 9783030978664 https://www.amazon.com/Integration-Finite-Terms-Fundamental-Computation/dp/3030987663/ On Tue, May 26, 2026 at 8:39 PM Hill Strong <[email protected]> wrote: > > > On Wed, 27 May 2026, 9:29 am Qian Yun, <[email protected]> wrote: > >> On 5/26/26 11:00 PM, Tim Daly wrote: >> > Even more amusing is that I have written several programs recently >> > using Claude Code. I haven't even looked at the generated source code. >> > Indeed one of the systems now just generates binary without code. >> > So clearly I have no idea what I'm talking about. History is harsh. :-) >> > >> > The goal these days is to communicate from machine to machine >> > not human to human. The task is to create "skills", essentially >> > sets of prompts that focus the LLMs attention and indicate goals >> > for agents. For example, >> > https://github.com/human-avatar/skills-for-humanity < >> https://github.com/ >> > human-avatar/skills-for-humanity> >> > >> What about machine to human? >> >> Do you think LLMs can understand Axiom? Can it help people >> to complete the goal of document Axiom in literature programming >> style? So that humans can understand Axiom completely? >> > > LLMs understand nothing and never can. At best, these systems are partial > pattern recognisers and at worse the results are garbage. > > What we see today is the same effect that occurred when database > technology became common. People of all stripes including DBAs and other > technical people had a trust of the technology which was unwarranted. > > I have spent many many years having to analyse software systems and the > vast majority are, how shall I put this, not doing what they are supposed > to be designed for. The results obtained may appear to be correct. However, > on deep analysis of the code base, one realises that the results obtained > aren't real. > > If one using any LLM has a detailed understanding of the code related to > the specific LLM system, one can use that system somewhat effectively. > Otherwise, one will face certain problems with whatever is produced. > > I have found that subject matter experts are not necessarily au fait with > the problems of the systems they use or build and trust those systems more > than they should. > > Mind you, most non-subject matter experts are worse in the trust they have > for these systems. > > One should trust these systems like you would a politician or a used car > salesman or anyone trying to sell you a bridge in New York City. > > I am not saying that one should never use these systems, but be very very > very careful about trusting the results obtained. Check and recheck the > results very very thoroughly before accepting those results. > >> >> - Qian >> >> -- >> You received this message because you are subscribed to the Google Groups >> "FriCAS - computer algebra system" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To view this discussion visit >> https://groups.google.com/d/msgid/fricas-devel/2ee4746e-e977-4145-a7d1-9eabc6df83e5%40gmail.com >> . >> > -- > You received this message because you are subscribed to a topic in the > Google Groups "FriCAS - computer algebra system" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/fricas-devel/iSKff3NyqFM/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/fricas-devel/CAEnaMTGw6FpGs1MQTCCZxxRwqh30YP4xb31ijzsW%3D5%3Dahc%3DuEA%40mail.gmail.com > <https://groups.google.com/d/msgid/fricas-devel/CAEnaMTGw6FpGs1MQTCCZxxRwqh30YP4xb31ijzsW%3D5%3Dahc%3DuEA%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. 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