ALGORITHMS IN MODERN MATHEMATICS AND ITS APPLICATIONS

                                                      UZBEKISTAN, October 1979

---------------------------------------------------------------------------------------------------------------

Prof. Donald Knuth                                                                                                 USSR

Computer Science Dept                                                                               Novosibirsk, 630090

Stanford University                        Response addresses                                        Computing Center

Stanford, Ca., 94305                                                                                               of USSR SBAS

USA                                                                                                                         Prof. A.P. Ershov

Dear Colleague!

Some time ago a group of specialists in mathematics and its computing applications (the authors of
this letter being among them) had an idea of carrying out a kind of scientific pilgrimage to the places
of birth and youth of Al-Khorezmi – an outstanding mathematician of Middle Ages, after whom an
algorithm  –  one of principal  mathematical  notions  –  was named.  As  is  obvious from the name
Al-Khorezmi itself, by origin he  is  from  Khorezm  Oasis  –  historically  well-known  center of
civilization that bestowed upon mankind a whole galaxy of remarkable philosophers, scientists, and
poets. If one also recalls that algebra also owes its name to one of the main works of Al-Khorezmi,
then one can be sure that no mathematician – irrespective of him being a profound theorist
philosophically reflecting upon the foundations of mathematics, or a specialist in applications
preoccupied with the details of correct allocation of computation in time and space – can stay
nonchalant during a visit to these places.

As a result of discussing this idea with a circle of scientists as well as of consultations with USSR
and Uzbek Academies of Sciences, it took on organizational form of conducting at one of
appropriate places of Khoresm region in October of 1979 an international symposium “Algorithms
in modern mathematics and its applications”. It is supposed that the symposium will be organized by
Uzbek SSR Academy of Sciences with the assistance of the USSR Academy of Sciences and its
Siberian Branch.

The symposium is intended to be a not numerous scientific forum based on personal invitations from
organizers, around thirty participants in number with approximately one half of them being the
Soviet side, and another half – foreign guests.

Admittedly the symposium will last for about a week, including four days of scientific program and
three days of visiting historical places. For foreign participants it will mean a ten-day trip to the
USSR – a journey to the spot and back and jetlag adaptation will take three more days.

The role of the authors of this letter is to prepare proposals to organizers on symposium membership
and program contents by means of negotiations with potential participants.

It seems to us that a special atmosphere of the planned symposium makes for a style supposing not
reading papers prepared in advance, but rather a series of mutual discussions concentrated on
fundamental problems in mathematics and computations. We believe that the atmosphere of desert
nature and the feeling of time scope will permit us to distract ourselves from day-to-day work that
fills our life at home, will add to our communication more profundity and philosophy. Nevertheless,
according to our opinion, the work of the symposium should not be of totally voluntary and
spontaneous nature. Among the symposium participants we expect specialists with highly different
style of work and thinking, and even if we do not aim at working out a certain consensus on
algorithm, a thorough preparation is necessary to identify the problems of most common interest and
to obtain mutual understanding.

Enclosed to this letter is the list of possible problems suggested to us during the discussions on the
symposium idea, and the list of scientists to whom this letter is directed. We would appreciate very
much any remarks concerning your eventual participation and also symposium membership and
problem scope.

You can send your reply, however preliminary, to any of us at any opportunity but preferably no
later than October 1, so that we could deliver all necessary preparation data to symposium
organizers in proper time.

Looking forward for your reply, sincerely yours

Donald Knuth,                                                                                            Andrei Ershov,

USA National Academy                                                                            USSR Academy of Science

of Sciences Member                                                                                   Corresponding Member