[Axiom-developer] Creative Destruction and Computational Mathematics

[daly]

http://www.aei-ideas.org/2014/08/fortune-500-firms-in-1995-vs-2014-89-are-gone-and-were-all-better-off-because-of-that-dynamic-creative-destruction

"12.2% of the Fortune 500 companies in 1955 were still on the list
 59 years later"

"Steven Denning pointed out that a few years [ago] in Forbes that
 fifty years ago the life expectancy of a firm in the Fortune 500
 was around 75 years. Today, it's less than 15 years and declining
 all the time"

So what does this have to do with Computational Mathematics?

Consider what happens if Maple, Mathematica, and Matlab disappear.
It can happen and probably will. REDUCE almost disappeared (Hearn
open-sourced it). DERIVE went private (TI). MACSYMA died when 
Symbolics died (Bill Schelter revived a government version and
called it MAXIMA). Axiom nearly died when it was withdrawn from
the market. Maplesoft was sold and is now owned by Cybernet Systems,
specializing in Mechanical Computer Aided Engineering. So it is
no longer an independent computer algebra company.

Many of the algorithms are either private or, if public, undocumented.
The results are amazing but the level of expertise needed to maintain
and modify these systems is intimidating. Many of these algorithms are
the implementation of Ph.D. work understood deeply by only one person.
As we all know, there is a long step between theory and implementation.
And, in my experience, that long step is never documented.

Even if systems like Mathematica were open sourced it would be very
hard to maintain them. Large systems suffer from what I'll call
"Daly's Pyramid Law:" Systems get an order of magnitude harder to
maintain for every order of magnitude of code. A system with 2x10^n
lines of code is an order of magnitude harder to maintain than
2x10^(n-1) lines of code.

Axiom is about 1.2 million lines, about half-way between n=5 and n=6
on the scale. I suspect that Mathematica is between n=6 and n=7.  I
don't know how any single person or small group could maintain that.
The pyramid law suggests that it needs about 10 maintainers active on
a daily basis. I don't know of any non-profit funding source for that.
The implication is that the loss of Mathematica will cause a "black
hole" in computational mathematics.

But, wait, ... the article cited above says we are all better off
because of "creative destruction"...

That may be true for physical goods but it is clearly not true
for computational mathematics.

The large systems all had their roots in early work in the field.
"New CAS" systems appear all the time (in fact, I collected and
distributed over 100 on a CD at ISSAC). Everyone who discovers a
new programming language seems to write a new CAS.

But the large systems are the result of hundreds of person-years
of implementation of research. Small, unfunded systems can't begin
to approach that power and complexity.

We need to move this vital collection of algorithm implementations
into a form that can preserve the level of complexity we have already
achieved.  If we don't, we face a serious crisis in computational
mathematics.

"Creative Destruction" may have a much different meaning soon.

Tim