Workshop "Hilbert’s Sixth Problem”

University of Leicester, May 02-04, 2016




·        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.


Francois Golse

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 long-lasting relevant science must be built on solid foundations.


Giacomo Mauro D'Ariano 

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 long-term 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. 


Leo Corry,

Bert and Barbara Cohn Professor of
History  and Philosophy of Science

Dean, The Lester and Sally Entin Faculty of Humanities,
Tel Aviv University


·        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.


Masanao Ozawa


Graduate School of Information Science

Nagoya University



·        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 cross-fertilization of the ideas and solution methods in the interdisciplinary area between applied mathematics, physics and a bit of engineering.


Katalin Hangos

Research Professor
Process Control Research Group
Computer and Automation Research Institute
Hungarian Academy of Sciences


Professor, Head of Department
Department of Electrical Engineering and Information Systems
Faculty of Information Technology
University of Pannnonia,

·        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.

Isabelle Gallagher

Professor of Math

Université Paris-Diderot (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 self-interestedness. It was a remarkable event.


Marshall Slemrod

Professor, Dept of Mathematics,

University of Wisconsin,

Madison, WI 53706 USA