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[Axiom-developer] Computational Mathematics and Sage

From: daly
Subject: [Axiom-developer] Computational Mathematics and Sage
Date: Mon, 25 Aug 2014 14:16:54 -0500

"You will have to close source and commercialize Sage. It's inevitable"
Michael Monagan, cofounder of Maple, to William Stein.

Sage is a computer algebra system led by William Stein, originally
in the area of number theory but branching out to include other
systems including Axiom at one point. I've quoted from his post

Stein tried hard to duplicate Magma, a large computer algebra system.
By his own admission, Sage has failed.

Consider this as an example of what will happen when Magma disappears,
an inevitable event by my own reasoning. 

There is no funding source for open source computational mathematics. 
I've tried with government, university, and commercial sources. Stein 
had a Google grant and university support but it was not enough. 
Without the university connection even Google wouldn't fund him.

The area of openly available computational mathematics is a love-it
or leave-it situation. I'm 14 years into the love-it side but I
understand why most people choose leave-it. Large systems like
Axiom are mind-bendingly complex to maintain, modify, and extend.
It is even a challenge to document obscure implementation details.
Do you really want to spend your nights, weekends, and vacations
debugging p-torsion bounds on elliptic curves? And do it for free?
Or fix up a broken port to Fedora because the NSA SELinux team
doesn't understand the Princeton architecture? (If so, email me).

Closed source, commercial computational mathematics is not inevitable.

We, as a community, cannot afford to let computational mathematics
depend solely on commercial software. Since all companies die, the
commercial software will disappear, taking all of us with it.

We need standard algorithms that are open, well documented, and
well implemented, supported by a standards organizations (NIST? ISO?),
published in a standard format and kept up to date.

We need computational mathematics courses based on openly
available, well-documented software to teach the next generation. 

We need it now.



Sage is Failing

Measured by the mission statement, Sage has overall failed. The core
goal is to provide similar functionality to Magma (and the other Ma's)
across the board, and the Sage development model and community has
failed to do this across the board, since after 9 years, based on our
current progress, we will never get there. There are numerous core
areas of research mathematics that I'm personally familiar with (in
arithmetic geometry), where Sage has barely moved in years and Sage
does only a few percent of what Magma does. Unless there is a viable
plan for the areas to all be systematically addressed in a reasonable
timeframe, not just with arithmetic geometry in Magma, but with
everything in Mathematica, Maple., etc, we are definitely failing at
the main goal I have for the Sage math software project.

I have absolutely no doubt that money combined with good planning and
management would make it possible to achieve our mission
statement. I've seen this hundreds of times over at a small scale at
Sage Days workshops during the last decade. And let's not forget that
with very substantial funding, Linux now provides a viable free open
source alternative to Microsoft Windows. Just providing Sage
developers with travel expenses (and 0 salary) is enough to get a huge
amount done, when possible. But all my attempts with foundations and
other clients to get any significant funding, at even the level of 1%
of the funding that Mathematica gets each year, has failed. For the
life of the Sage project, we've never got more than maybe 0.1% of what
Mathematica gets in revenue. It's just a fact that the mathematics
community provides Mathematica $50+ million a year, enough to fund
over 600 fulltime positions, and they won't provide enough to fund one
single Sage developer fulltime.

But the Sage mission statement remains, and even if everybody else in
the world gives up on it, I HAVE NOT. SMC is my last ditch strategy to
provide resources and visibility so we can succeed at this goal and
give the world a viable free open source alternative to the Ma's. I
wish I were writing interesting mathematical software, but I'm not,
because I'm sucking it up and playing the long game.

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