




Workshop
"Hilbert’s Sixth Problem”
University of
Leicester, May 0204, 2016
OPINIONS OF
PARTICIPANTS
·
In 1900, the German mathematician
David Hilbert laid out a program (known as Hilbert's 6th problem) calling for
no less than the ``axiomatization of physics''. As an example, Hilbert proposed
to derive the classical equations of fluid mechanics from the atomistic
description of gases  at a time when even the existence of atoms was a
matter of heated scientific debate. Since then, new paradigms have emerged in
physics: relativity, and quantum mechanics have altered our understanding of
the world. Today, the quest for a mathematical coherence in modern physics is
even more formidable a challenge than in the days of Hilbert. The workshop
organized by Prof. A. Gorban and his colleagues at the University of Leicester
has been a unique opportunity to assemble a panel of mathematical physicists
from various countries (including for instance China, France, Italy, Russia,
Sweden, Switzerland, in addition to the UK), with a great variety of viewpoints
on Hilbert's 6th problem.
Professeur à l'Ecole polytechnique
Président du département de mathématiques
École Polytechnique,
Paris, France
·
The Workshop on "Hilbert’s
Sixth Problem” organized by Alexander Gorban in Leicester will have a great
impact on the community of physicists and mathematicians. For the first time a
workshop has been devoted to a problem of the outmost relevance at the
methodological level for the advancement of theoretical physics, in a time of
great evolution of theoretical physics. Indeed, the solution of the VI Hilbert
problem, namely the axiomatization of physics, will play a pivotal role in
finding the correct answer to the major problems in contemporary physics,
including the solution of the logical clash between General Relativity and
Quantum Theory, and that of the emergence of Hydrodynamics from Statistical
Mechanics. We have attended very interesting talks during this conference, and
we have come back home with a todo list of relevant issues
to address and a set of methodological recipes for improve the quality of theoretical
research. David Hilbert has changed the history of physics with his research
and his teaching in Göttingen during the quantum
and relativity revolution, and he is still teaching to us nowadays the most
important lesson: that the longlasting relevant science must be built on solid
foundations.
Professor
of Theoretical Physics
Quantum
Foundations
and Quantum Information
Istituto Nazionale
di Fisica della
Materia,
Unita' di Pavia,
Pavia, Italy
·
As
a historian of mathematics who has devoted many years of his academic life to
research the origins, the development and the overall impact of Hilbert's sixth
problem, this conference has been for me a unique kind of scholarly experience.
Historians of mathematics are used to work in intellectual isolation.
Typically, our work is too technical and daunting for historians of science in
general. At the same our work is too "historical" for what should be
one of our main natural audiences, namely, that of the mathematicians (and in
the case of Hilbert's sixth problem, also the physicists). I have had previous
opportunities to speak to mathematical audiences about my work on the problem,
but with special attention to the encounter between Hilbert and Einstein around
the final formulation of the field equations of general relativity. Quite
unsurprisingly, this has proved to be an appealing enough topic for such
audiences. But this conference was fully devoted to the much broader topics
associated with the Hilbert problem, and to a truly wide range of topics, and
it was very refreshing to realize the extent to which the ideas put forward by
Hilbert more than 115 years proved to be much more relevant and of longterm
impact than Hilbert himself could have ever conceived when formulating his
programmatic call for the axiomatization of physical theories in 1900. The
talks were not only informative but also inspiring, and for me they were an eye
opener in many directions. I was also glad to come out with the feeling that my
own historical talk arose significant interest among the attendees.
Bert and Barbara Cohn Professor of
History and Philosophy of Science
Dean, The Lester
and Sally Entin Faculty of Humanities,
Tel Aviv University
Israel
·
Hilbert was one of the most successful
leaders to set foundations of mathematics by axiomatic methods.
Hilbert's sixth problem called for
extending this method out of mathematics to physical science. Mathematicians who made significant
contributions to this problem in the last decades world wide gathered and discussed the significant roles of
the problem playing mainly in hydromechanics and quantum physics.
The workshop revealed the unexhaustive value of the problem, which has enriched both
physical science and mathematics for more than 100 years and will lead to
unexpected mutual interactions between those intellectual arts.
Professor,
Graduate School of Information Science
Nagoya University
Japan
·
The
Workshop on "Hilbert's Sixth Problem'' was an inspriring
experience that shed a new light on the problem itself and on the approaches of
its solution. The carefully selected lectures from both the classical and
quantum problems of mathematical physics have clearly showed that Hilbert's
Sixth Problem has not been completely solved but presents a lot of interesting
research questions to be answered even today not only in applied mathematics
and physics but also in engineering.
Thanks to the excellent organization
and to the friendly and relaxed atmosphere there were plenty of opportunities
for discussions and hopefully crossfertilization of the ideas and solution
methods in the interdisciplinary area between applied mathematics, physics and
a bit of engineering.
Research Professor
Process Control Research Group
Computer and Automation Research Institute
Hungarian Academy of Sciences
Budapest,
and
Professor, Head of Department
Department of Electrical Engineering and Information
Systems
Faculty of Information Technology
University of Pannnonia,
Hungary
·
This workshop was rather unique in
its kind as it brought together mathematicians from very different horizons
(from probability theory to statistical physics, partial differential
equations, logic and complexity), whose common interest lies in Hilbert's sixth
problem. The statement of Hilbert's sixth problem is indeed so broad that it
can be studied from a multitude of angles, and it was really extremely
interesting for me to hear some of the best specialists from those various
fields explain their viewpoint of the problem, and the progress that has been
made recently. I think all the participants share this impression on having
gone on a wonderful tour of the sixth problem for three days, and have come
home with new ideas, and lots of new questions.
Professor
of Math
Université
ParisDiderot (Paris 7),
UFR de Mathématiques,
Paris, France.
·
In 1900 David Hilbert provided the
mathematicians of his day with a list of problems for the twentieth century and
in particular his sixth problem which called for the axiomatization of physics
in the same spirit as we would treat geometry. The problem in its various
interpretations has provided a fertile ground for mathematicians for over one
hundred years with a rather impressive list of results and even unintended
consequences. This conference (perhaps the first of its kind) expanded on the
physics known to Hilbert in 1900 (statistical and continuum mechanics) and
included the issues of the very small (quantum mechanics), very large (general
relativity), and basic fundamental issues of probability which is the key
component of both the statistical and quantum view of nature. At first thought
it seems like a workshop with this broad view would have the difficulty of too
large a perspective but the just the reverse was true. The participants
excelled at thinking about the big picture and their presentations and
conversations went far beyond any possible narrowness and selfinterestedness.
It was a remarkable event.
Professor, Dept of Mathematics,
University of Wisconsin,
Madison, WI 53706 USA