Speech at the inaugural session of ACA 2010 in Vlora, Albania
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In 1991, the AMS proposed as the main goals of Mathematical sciences:
The most important long-term goals for the mathematical sciences are: provision
of fundamental tools for science and technology, improvement of mathematics
education, discovery of new mathematics, facilitation of technology transfer,
and support of efficient computation.
The goal of this year's ACA 2010 conference is well suited for this definition
on at least three grounds: improvement of education, the facilitation of
technology transfer, and the support of efficient computation.
Any society tries to understand where it is coming from. In other words: what
are the building stones of its culture? There are several such stones ranging
from language to religion which are specific to each country or society. There
is one that is often forgotten nowadays: Mathematics. Morris Kline wrote a
book explaining that mathematics has been a major cultural force in Western
civilization. I suspect and claim that such a root is not limited to Western
civilization, but is almost universal: Mathematics is culture.
Another general feature of today's society is to understand what makes things
sell. Many (too many?) mathematicians claim that the sole end of science is
the honor of the human mind. In any case, this goal remains valid, but this is
not incompatible with more practical goals.
Some grounds for such a statement are:
1) Mathematics is a framework to describe the world; a faithful description of
the world leads to better technologies. Most of the models describing the
world we live in amount to a system of partial differential equations. You
can easily link this fact to several of the sessions at this conference. We
have sessions that are applied to communication (coding, for instance),
physics and chemistry, solutions of models expressed through systems of
equations (polynomial, parametric or differential, for instance) or special
functions, and to investigate classification of concepts through
methodologies of group theory to discover how our technologies can be
extended to topology. This is a new frontier after having been so
successful with algebra and analysis (integration), we can now investigate
the link of these concepts to topology. Pure mathematics and particularly
Grothendieck have developed theoretical concepts that will lead to
breakthroughs for mechanized mathematics when taking non-linear effects into
account. It would be possible to extend the list of topics covered at this
conference that have very practical applications. For instance, mechanizing
topology may lead to results useful in the area of statistics and insurance.
2) Mathematics is not an isolated domain. Designing algebraic algorithms
amounts to performing mechanical reasoning. One must remember that
mechanical or formal reasoning has been developed by philosophers and
mathematicians since antiquity. Mechanizing mathematics is thus an ever
lasting goal of humanity.
3) As for previous ACA conferences, education is the topic of a specific
session. Computer algebra is a powerful educational tool to teach
mathematics as well as engineering or physical sciences. We live in a
society dominated by managers educated in law or business. However, this
society sometimes exhibit the drawback that the ignorance of mathematics has
attained the status of a social grace. This was pointed out by Morris Kline
in 1977 already and is not a blessing for our society. To be accurate, it
looks like scientific education is still favored in some far east countries
(those with a higher growth factor than most of European societies?). For
instance, Germany lacks 30,000 engineers while China trains 400,000
engineers each year.
4) We must not be shy when dealing with business goals. You may have guessed
that I am a bit interested in the philosophical meaning of what we do. One
French philosopher said that there is "No truth without money". Truth is at
the very basis of our field since we always prove what we implement. Thus,
we must not stop investigating business models of what we are doing. If you
think it is difficult task, then just let me add that you can read the
last section of the Discourse on Method of Descartes as a research grant
application. This claim was partially based on the fact that you can think
of the concept of "essence" as axioms in a mathematical theory. It is due
to a pure mathematician. The main result is thus to outline that the
funding spent to organize ACA 2010 is a smart investment which will pay back
in the future.
Some more technical words on ACA 2010: We have 14 sessions covering many
applications of computer algebra. Some of these sessions are new ones in the
history of the ACA series of conferences: complexity, knowledge bases, and
topology, for instance. These are theoretical sessions, but with the goal of
improving our knowledge and thus to look for applicability. Indeed, it is
often simpler to find meaningful business applications for very elaborated
ideas than for straightforward applicative extensions. Think simply to the
industrial impact of the works of von Neumann, Godel, Shannon, Thom or
Kolmogorov, for instance.
Some applications in the directions of business or philosophy of sciences could
have been added. Let us say that they are on the agenda of future conferences.
We will listen, in parallel, to 96 talks given by 92 attendees.
You know that there are no proceedings for the ACA conferences. However,
several sessions will hopefully see their better papers published in special
issues of well-known journals. I am personally involved in one, and aware of a
few other ones. A total of 5 special issues ought to appear according to some
valuable information. Session directors (and journals' editor-in-chiefs) are
responsible for such special issues.
Our most sincere thanks are due to Prof. Tanush Shaska and to his team for the
tremendous amount of work they did put to organize this meeting. These thanks
must be extended to the various authorities which are present at this inaugural
session for their generous funding of the conference (at least according to the
information I got at the time of sketching some notes for this talk). I want
to thank Michael Wester for support and help to organize the program for this
meeting.
Jacques Calmet