In the computer business, technologies which solve essential problems tend to survive; extensible technologies which solve essential problems tend to grow.

When you look at the largest open source projects, the majority of the actual code tends to come from people working in large companies that depend on the tech stack. Linux, for example, has benefited enormously from IBM's investment of engineering-hours into the project. Ruby on Rails is another example, as are many other web-related frameworks.

The SAGE math environment was a noble effort to displace MAGMA and similar systems, which were benefiting from code contributions from academia, but which remained commercial and not widely available. Later SAGE would evolve to compete with Mathematica and other math suites. Unfortunately, the essential problem being solved was a matter of taste-in-licensing, which is not always essential-enough for a project to take hold.

Coq, Agda, Lean, etc, all solve an essential problem, namely that of providing a theory of higher-order machine-checked proofs. The implementations tend to be extensible, at least for experts. Different segments of the CS and math community are becoming aware of these tools and producing new, impressive artifacts all the time. Overall it's a small community, but it's growing. At the very least, the diversity of artifacts demonstrates that these tools are expressive-enough to be useful in many domains, not just in principle but in practice.

Though it is currently difficult to apply these methods to problems of interest in industry, progress in the field of program logics is real and has lead to real tools (Infer, at least) with real users. The ability to prove properties of programs inevitably leads to the desire to prove properties of fairly technical programs, and in that way a bridge to more abstract, less-computery branches of math will emerge. An ecosystem will form, and pure research which contributes to this ecosystem will begin to take on its own appeal. Other paths to industry-awareness may exist, this is just the one I've been tracking.

In my opinion, patience will be rewarded.

-t



On Sun, Jun 12, 2016 at 4:05 AM, Andrej Bauer <andrej...@andrej.com> wrote:
While the efforts expanded on Coq and Agda are truly impressive and
chivalrous, both pieces of software compare poorly to something like
Mathematica in terms of software quality (documentation, professional
GUI design, technical support, cloud support, etc.) This is not a
criticism of the Coq and Agda teams, just an observation which in
Slovene could be summarized by the phrase "that's the music you get
for the money you paid".

Also, I am not trying to start a war with the lurking Knights of the
Open Source. I am just saying we have no idea how to bring open-source
mathematical software to the level of professional software without
sacrificing the careers of several PhDs and at least one tenured
professor.

With kind regards,

Andrej



On Sun, Jun 12, 2016 at 12:55 PM, andré hirschowitz <a...@unice.fr> wrote:
> Hi,
>
> I have been thinking to this issue for years (decades?). In France we have
> this research agency INRIA which has been supporting the Coq project for
> decades, leading to a fairly "good quality software" (in my opinion). Say
> twenty years ago, the Coq project was targetting the computer science
> community and was not ready to "attack" the mathematical community. From
> this side, the picture seems much better nowadays.
>
> A possible strategy toward the investment of the mathematical community is
> as follows:
>
> ------------------------
>
> 1- create a body tying (part of) this community with for instance (part of)
> the Coq project (and/or the Agda project, about which I know little).
>
> 2- obtain specific funding from a Research Agency (NSF, CNRS?) for partly
> formalized PhD fellowships, together with companion funding for the
> technical support (eg from the Coq team) to the (partial) formalization.
>
> 3- obtain good applications, coming from ouside this community.
>
> 4- select the winning applications regarding both the interest of the naked
> thesis, and the feasability of the (partial) formalization.
>
> 5- help collectively the success of each selected project.
>
> 6- Write assessments in particular for the formalization efforts of these
> newage doctors, so that they win positions whenever they deserve.
>
> ---------------------------
>
> I leave it here.
>
> ah
>
>
>
>
> 2016-06-12 10:04 GMT+02:00 Andrej Bauer <andrej...@andrej.com>:
>>
>> Apologies for a slightly off topic post, but I think it is relevant to
>> many people on this list.
>>
>> I just looked at some slides by William Stein, the author of Sage (an
>> open-source alternative to Mathematica) at
>> http://www.smbc-comics.com/index.php?id=4127
>>
>> The conclusion is: it's impossible to make good quality software in
>> academia because there isn't enough money and because making software
>> doesn't give one any academic credit.
>>
>> I am afraid formalization of math might fall into the same category,
>> unless we somehow elevate it to a "true science" level. A great deal
>> has been done in this respect recently by projects lead by Gonthier,
>> Hales and Voevodsky, but is it enough? Are we even making a dent?
>>
>> At my department, for instance, the folk knowledge propagated from one
>> generation to another is that "someone" formalized "Landau's book" (I
>> suppose it was the Automath formlaization of Landau's Grundlagen der
>> Analysis by Jutting) which proves that "it can be done" but is
>> otherwise an intellectually barren exercise without academic value. I
>> still remember one of the professors saying this to the whole class
>> when was an undergraduate.
>>
>> With kind regards,
>>
>> Andrej
>>
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