Mark Iosifovich Vishik and His Work:
Award Ceremony of the Honorary Doctorate
at the Free University of Berlin
Bernold Fiedler (ed.)
Institut für Mathematik I, Freie Universität Berlin
Arnimallee 2-6, 14195 Berlin, Germany
|
Ehrenpromotion Prof. Dr. Mark Iosifovich Vishik
Gerhard Braun
|
 |
| Gerhard
Braun |
Dear Professor Vishik,
spectabilis,
dear colleagues and guests,
On behalf of the Freie Universität Berlin I would like to welcome you
to this academic ceremony. It is our great pleasure to greet you as
participants of this special event, the presentation of an Honorary
Doctoral Degree to an outstanding person in the international
mathematical community.
Therefore, I would like to welcome you, Prof. Vishik, in
particular. We feel honoured that you give us, the University, the
Faculty of Mathematics and Computer Science and the Department of
Mathematics, and all participants, the opportunity to celebrate this
academic colloquium by accepting that degree. It is also my great
pleasure and an honour for me to congratulate you not only to this
degree but also to your 80th birthday. I wish you good health for the
years to come, more of your new and wonderful ideas and contributions
to mathematics, new talented students and continuing contacts to our
university.
When studying the evaluations of your life time work and the related
laudationes, presented in academic ceremonies, key expressions like
'for the first time he did, he presented, obtained or constructed' are
encountered. As author and co-author you received this predicate for
your 'theory of statistical solutions of non-linear parabolic
equations and of the Navier-Stokes system with random initial data and
fluctuations of white noise type'. The same predicate is also given to
your work on 'attractors of autonomous partial differential equations,
especially on the existence of an attractor for a hyperbolic equation,
and their applications to systems of reaction-diffusion equations',
for the 'non-linear dissipative hyperbolic equation', for the
'two-dimensional Navier-Stokes system' and others more. I could
continue with more 'for the first time', like in obtaining 'a lower
estimate for the Hausdorff dimension of Kolmogorov flows' or related
to the 'equations with quasi-periodic and almost periodic symbols with
respect to time', only to demonstrate the exceptional success of
Prof. Vishik's life time work.
I am sure that the colleagues from the department and the faculty of
mathematics and computer science will concentrate their own greetings
and speeches on these disciplinary contributions, appreciation, and
honours paid to the academic guest of honour.
Therefore, let me concentrate on the discipline as such.
You all know: Mathematics is structuring all our daily life and
mathematics is fundamental in its explanatory character to all parts
of what human beings have created. That the public is not aware of
this, is caused by the fact that mathematics just functions, as a
rule. Nobody is really interested to know more about it. That
ignorance hurts the mathematical feelings. While biotechnology is
popular and discussed everywhere in all newspapers and journals,
however with the same low basic knowledge as to the public; there is
unlimited quietness about the mile stones in mathematics - and that
statement is particularly true for pure mathematics.
The decoding of
the genome is rejoiced by the public and the results are explained to
the public with great effort. But jubilation and public debate about -
as an example - the final proof of the 'four colour theorem' or the
'Goldbach Conjecture' is mostly restricted to the small international
community of mathematicians. Outsiders remain unimpressed by that
incomprehensible problem and challenge.
The public's perception and
even the internal mathematician's perception of mathematics, of what
mathematicians are doing, are more or less the same: mathematicians
serve as servants of the pure mind. They are characterised as having
in mind nothing but truth and cognition. In his book 'Uncle Petros and
the Goldbach Conjecture', Doxiades blames mathematicians for their
'déformation professionelle'. It is the term for a specific syndrome
which characterises the mathematicians' human respectively
professional loneliness because nobody else shares their intellectual
patience respectively mathematicians avoid to share their interest.
As
a result, mathematicians are taciturn in words. If mathematics is
presented as a story, however, there will be many interested readers
despite its abstraction, difficulty and complexity.
The Fermat Conjecture, written as a marginal note in 1637, has widely
challenged many mathematicians and the final proof could only be
presented at the end of the 20th century. Without the book by Simon
Singh, describing Andrew Wiles' search for solutions, tries and
errors, the breathtaking proof, without that bestseller, nobody would
know anything about a fundamental problem of pure mathematics.
However, those examples are very are. By contrast, Dixiades' book is
next to unknown. In the view of non-mathematical experts modern,
highly abstract mathematics is far beyond the public's perception,
mathematics is practiced behind closed doors and in closed heads and
minds; it results in human and professional deformation, in that
loneliness. What is really done, why and how it is done, remains
unknown to the public as a secret in which the public is not really
interested in. In our sometimes decadent society, many people do not
feel embarrassed when called ignorant even to simple basic rules and
operations in mathematics. Some are proud of their illiteracy in basic
mathematics.
However, in times of strong demand of application and market
constraints mathematicians come under pressure; they will be asked
quite often what their work is 'good for'. Today, not even pure
mathematicians will claim to be proud of the uselessness of their
work, will claim to be obliged exclusively to the pureness, the truth,
the aesthetics, beauty and elegance as well as the solution of more
and more complex problems.
In the past, contemplative monastic orders suffered the same problem
of self-justification. They also devoted themselves to pureness, the
findings and recognition, the path to the absolute. As expression of
their pure intellectual orientation those Asian monks carried half of
a human skull for begging.
Of course, today there is a lot of money even in pure mathematics. The
established mathematicians live well honoured in research and
teaching, they travel a lot as well as establish and cultivate their
contacts intensively within their international communities. Their
contribution to research, however, passes almost unnoticed, when
compared to experimental science, but is really economical and hardly
cost-intensive.
Pure mathematicians are of a different, but changing character. In
contrast to the scientific computing community they describe their
relation to computers as different and as one with mixed feelings. It
is a fact that theorems must be proved because their statements are
related to infinite sets, in principle. Computers are only able to
handle finite sets; with computers one can test hypotheses but not
proofs.
No question, mathematicians like to construct proofs. These proofs are
designed in their minds at their desks. They only present proofs which
can be controlled by the mathematical community. To prove theorems
with the help of computers may consume many life times before the
final computation is done, really and truly. Therefore, proofs are
exceptionally and completely intellectually designed and
conceptualised in heads and minds, in loneliness. Only there, they can
be finally accepted and generalised. Only these proofs reflect the
beauty and elegance which mathematicians are interested in and which
makes them feel well. Mathematics is synonymous to elegance. It is of
apodictic validity.
Esoteric as that statement may sound, in reality it means progress,
guarantees wealth and designs culture. Mathematics can also be called
a very practical discipline, useful and necessary, to handle our daily
life which is complex indeed.
Professor Vishik's whole mathematical life was and is still devoted to
applications, especially to mathematical physics. His school,
operating since 1961 as one of the principal Russian seminars on
partial differential equations and mathematical physics in the world,
has attracted thousands of students and scientists because of its
elegance
and
its practical applications.
Right on these two characteristics, I will finish my welcome speech. I am sure we will have the opportunity to hear more about that elegance and its transfer.
References:
Goettle G., Apodiktische Gültigkeit. Nur Mathematiker k&önnen glücklich sein. In: TAZ Nr. 6586 vom 20.10.2001, S. 15-16.
Hammerstein, M., Das geheime Leben der Zahlen. Onkel Petros und die Goldbachsche Vermutung. 10.01.2002.
http://www.telepolis.de/deutsch/inhalt/buch/11525/1.html
Agranovich, M.S. et al., Mark Iosifovich Vishik: on his seventy-fifth birthday. 1996.
Continue reading with the contribution from Misha
Shubin.