> So, why exactly it is not going to happen ? Axiom was a research platform for new ideas and new algorithms, originally developed at IBM Research as "Scratchpad". The funding dried up and we had to shut it down. The idea was proposed of selling it but, for various reasons, IBM was not going to sell it as an IBM product.
Axiom was removed from IBM Research and sold to the Numerical Algorithms Group (NAG). NAG sold it for a few years and withdrew it from the market. They generously gave me the source code. It took a while to restructure Axiom for open source. As one of the original IBM team I had a lot of knowledge about the program no one else working on the open source had. It was clear that when I stopped working on it the knowledge would be gone. This was already a problem as some of the algebra authors were dead. I thought about ways we could make it possible to capture, structure, and pass on the knowledge. Eventually I settled on Knuth's Literate Programming idea. Textbooks, such as Lisp In Small Pieces, were what attracted me to the idea. Like the Physically Based Rendering book, it should be possible to find any algorithm. Each algorithm would have an explanation (note: NOT documentation), literature references (since many algorithms are PhD research results), proofs, cross references to supporting algorithms, limitations, examples, tests, etc. I gave a talk on this at a conference: https://www.youtube.com/watch?v=Av0PQDVTP4A&ab_channel=NextDayVideo When I introduced the Axiom project I also announced project goals. One of those goals was to restructure Axiom into a literate program. Apparently, like other project goals, this one was ignored. So far I have done the primitive restructuring. See: https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system) These books contain the actual source code which, during the Axiom build process, is "tangled" and compiled. So most of the system is "literate" but only in skeleton form. I've been concentrating on collecting and entering historical documents that only I own as well as getting permission from Scratchpad-related paper authors for re-creating and re-publishing as part of the books. Along with other project goals (e.g. the Computer Algebra Test Suite) http://axiom-developer.org/axiom-website/CATS/index.html no-one seems to want to contribute. At the moment, and for the last few years, I've been working on another project goal. I'm trying to prove Axiom algorithms correct. I spent 6 years attached to CMU as a visiting scholar working on merging proof technology with computer algebra. Like other work I have it partially implemented. The problems are hard and subtle. I gave a talk on this effort at ICMS 2018 http://icms-conference.org/2018/sessions/session14/ This is taking up all of my Axiom-related time and effort so although I really want to expand and improve the literate programs I can't seem to find the time to do it. The potential for proven, explained, and tested computational mathematics that anyone can "pick up, read, and contribute" exists but won't happen. "Literate Axiom" is not going to win a Fields Medal. Tim On Sun, Apr 2, 2023 at 1:30 AM Svjatoslav Agejenko <svjatos...@svjatoslav.eu> wrote: > Hello Tim ! > > > Idea is wonderful! > > It can also serve as a living math book. Book that captures human > understanding about math. It starts with basic concepts and next > chapters can build upon this. Book can contain executable code > alongisde explanation. So someone learning particular subject can > also run the related code in the book to see it in action and solve > equations symbolically or numerically. > > Math is a timeless thing and is worth preserving in some canonical self > contained way. > > Another interesting finding: This Chat-GPT is very good at teaching and > explanation. Yes, sometimes it lies convincingly, so everything it says > have to be verified. Despite that, most of the time it is correct. It > can also write code in different languages and problem domains. Maybe > it can be good tool to facilitate this effort. > > By the way, there is The Long Now Foundation. They encourage long term > thinking and preservation work. Maybe they can finance this project ? > https://longnow.org/contact/ > > > > > > > So, why exactly it is not going to happen ? > > > Best regards, > Svjatoslav > > > > On Fri, 2023-03-31 at 22:21 -0400, Tim Daly wrote: > > I just received the 4th edition copy of Physically Based > > Rendering[0]. > > Donald Knuth wrote "This book has deservedly won an Academy Award. > > I believe it should also be nominated for a Pulitzer Prize." > > > > It is a 1200 page literate program. It not only contains the actual > > source code, it contains complete explanations of the physical theory > > and the implementation ideas. This textbook is used in a various > > upper-class and graduate programs. I can highly recommend it. > > > > I had hoped that Axiom could have been reborn as a literate program. > > The idea was to "make it live beyond the authors". Each algorithm > > would provide an explanation, various literature references, and some > > examples as well as limitations. That way a person with no background > > knowledge in computer algebra could learn and contribute. Such a > > literate program would have set the standard for mathematical > > software. > > > > Sadly that's not going to happen. > > > > Tim > > > > [0] Matt Pharr, Wenzel Jakob, and Greg Humphreys "Physically Based > > Rendering" > > https://www.pbr-book.org/ > > > > -- > Svjatoslav Agejenko > WWW: http://svjatoslav.eu > > > > > >
