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(disclosure: I'm the Axiom Lead Developer)

I really applaud William's effort to build a company. I wish him all the best and will be willing to provide what help I can.

I wrote an AMS diatribe http://www.ams.org/notices/201202/rtx120200320p.pdf about publishing computational mathematics, making several points, one of which was that

"Algorithm implementations are proprietary. This needs to end. Science is not done behind a curtain. At least, it has not been hidden since Tar- taglia and Cardano fought over solving the cubic."

However, even if the Ma* software were suddenly open sourced it would be obvious that there was a huge problem.

Mathematics rests on several pillars which are currently absent in computational mathematics.

Mathematics rests on proofs. Where are the proofs for computational mathematical software?

Mathematics rests on research papers, books, and references. Where are the explanations of the theory behind the code? Where are the explanations of the design choices, such as which version of an equation was used and why? Computational mathematics needs much more than bare code.

Mathematics rests on courses and students. There may be one course but a whole focused curriculum on computational mathematics needs to exist.

Mathematics rests on funding. Universities, government, and some government organizations, like Oak Ridge, are the primary support.

William and I have had several discussions around our common problem of finding funding. I was the lead on Magnus (Infinite Group Theory) at City College of New York. We struggled for funding all the time. Axiom can't be funded because there is no organization to handle receipts. Funding agency like accountants.

Indeed, accounting is vital to open source funding. I contacted several large organizations asking them to set up an "open source accounting firm" (OSAF) which would accept and administer the grants to open source projects. OSAF would accept the grant, maintain the account, disburse funds for valid receipts, and maintain financial records for inspection. Such an accounting organization is needed if an open source project is going to get government or company funding.

If SageMath could handle the OSAF issue then the various contributing projects used by Sage could apply for grants from companies or government, knowing that there is an organization capable of managing the funds. This has the non-trivial side benefit of making SageMath the primary focus.

Oh, and SageMath could take the "overhead" (more than 50% at most schools) for "paperwork". My provost lived rather well on the grants.

Thanks for posting. (1) I strongly agree that the problems of rigorous computational mathematics are far, far deeper than anything I even begin to hint at in my talk. It's daunting. (2) I think http://www.numfocus.org/ -- a new org I think Travis Oliphant co-founded -- may be an attempt to solve some of the accounting organization issues. What do you think of what they are doing? Maybe the best thing is to work with them.

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