The "method of an incomplete separation of variables" seems to be appropriate for the solution of the Lamb's problem and related problems. In the two-dimensional case of a pulse due to stresses concentrated in a part of the boundary the solution is built up from double integrals and the relationship of this method to the method of complex solutions is shown. The use is made of Fourier and Mellin integrals and Laplace transforms but the single quoted investigation from the world literature is that of Rayleigh (1885).

In 1997, Guri Ivanovich Marchuk told me how, in 1951 as a brand new Candidate of Science, he was visited at his home by two people in a car, who told him he had a half hour to get his things together, he shouldn't worry about his family, everything would be fine. They didn't answer his questions during the subsequent two-hour car trip. It was only on the following day that he learned that the director at the 'object' was Dmitrii Ivanovich Blokhintsev (1908-1979), and that he would be working in the department of Evgraf Sergeevich Kuznetsov (1901-1966); both these names were well known to him. The 'object' then came to be called the Physics Energy Institute; three years later, the world's first reactor providing five megawatts of electrical energy was put into operation there, and the city came to be known as Obninsk of the Kaluga Region.

From 1953 to 1956, I was engaged on the hydrogen bomb. One project was undertaken by the team of Academician Vladimir Anatol'evich Dorodnitsyn, another was done by the scientists of Arzamas-16 [the nuclear weapons facility in Sarov], and they were helped by Academician Mstislav Vsevolodovich Keldysh, and we conducted the third project. When all the options were ready, the Arzamas project turned out to be the best. The most interesting, it seems to me, was our option, tritium-deuterium. But tritium has a very short half-life, it needs to be updated and updated all the time ...

As head of the department of higher mathematics at the Obninsk branch of the Moscow Institute of Engineering and Physics, Marchuk was able to attract a large group of talented young people into science during those years. In a short period he built up a strong staff of applied mathematicians in the field of nuclear energy and took part in the planning of the world's first nuclear power station. Marchuk proposed new methods for nuclear reactor calculations and even nowadays these form the basis of mathematical modelling and imitative calculations.

... the book is an attempt at a more or less systematic exposition of numerical methods for the calculation of thermal, intermediate, and fast neutron reactors. Particular attention is devoted to the problems of critical mass, the space-energy neutron flux distribution, and the neutron importance.

The book is clearly not addressed to mathematicians. A familiarity with nuclear reactor theory is assumed; terms such as "cross section" are used without definition. ... Emphasis throughout the book is on the derivation of equations and the mechanics of their solution. The stability of a number of the numerical methods against the exponential growth of round-off errors is considered. Problems related to the existence of solutions and the accuracy with which solutions of the various approximate equations represent the desired solutions are mentioned only occasionally. In the foreword the author mentions that the numerical methods were "first tested on a large quantity of theoretical and experimental data and were later used in operation." It is unfortunate that the results of some of these calculations were not included in the book. Results of specific calculations are not given. ... This book is a very useful addition to our literature. It is hoped that its presence and imperfections will act as a stimulus for the publication of another book in the area of numerical methods for nuclear reactor calculations which will give a more satisfying mathematical treatment of this subject ...

Our submarines became the fastest, they were called 'hunters'. At the same time, we took part in the calculations of the first nuclear power plant (and this I am proud of!), Then of other reactors. I wrote two books, they are published in the USA, China, and other countries.

Under Marchuk's leadership at the Computing Centre, intensive research developed on real trends in computational mathematics and its applications to a number of important problems in science and technology - the physics of the atmosphere, the theory of radiation transfer, geophysics, mechanics of a continuous medium, and also work on computer technology and programming security. Marchuk continually organized working scientific seminars, thematic conferences, and symposia on these topics. Soon the group headed by Marchuk became the foremost academic centre in Siberia for research in computational mathematics and one of the most important in our country and abroad.

The theory of radiation transfer is primarily one of the leading problems of modern science, rapidly developing on the basis of the achievements of theoretical physics and quickly penetrating into various fields of natural science and technology. Currently, transport theory is gradually becoming a part of mathematical physics. Astrophysics played the initial leading role in the development of the theory of radiation transfer, and since the 40s this role has passed to atomic physics. It should be noted that precisely in connection with the problems of atomic physics, powerful mathematical methods have been developed for solving problems of the theory of radiation, in particular, machine methods.

In computational mathematics, Marchuk's well-known studies are concerned with the development and application of finite-difference schemes for classes of equations arising in nuclear reactor theory with the theory of finite-difference and variational-difference schemes for various problems in mathematical physics, etc. Marchuk contributed much to the development of splitting methods and perturbation algorithms based on adjoint equations. Much attention was given to the development and substantiation of novel numerical methods for linear algebra. In the design of nuclear reactors, on the basis of the theory of adjoint equations and perturbation algorithms, Marchuk developed the construction principles for effective multigroup models of nuclear reactors, created mathematical reactor models in various spherical harmonic approximations, and proposed numerical schemes for solving arising equations.

Marchuk contributed much to numerical weather prediction and the modelling of the atmosphere and ocean general circulation, climate, and its changes. He was awarded the A A Friedmann Prize of the USSR Academy of Sciences for his achievements in numerical weather prediction and the State Prize of the Russian Federation for his results in atmosphere and ocean physics.

Considerable contributions were made by Marchuk to the creation of the theory of mathematical modelling of optimization problems in environmental protection. He proposed algorithms for the general problem of determining an admissible area for plant location, for construction site planning with allowance for permissible pollution of economically significant zones, etc.

In many of his studies, Marchuk addressed mathematical modelling in immunology and medicine. He constructed and solved a system of nonlinear differential equations governing immune responses in humans to virus and bacterial infections.

When creating the Institute in 1980 in Moscow, I was guided by the experience of organizing the Computing Centre of the Siberian Branch of the Academy of Sciences. This is a unique institution. It has no traditional departments and laboratories, all work is carried out through projects by creative teams. The project can be proposed by any employee and any member of the team can by invited to carry out the work. To prepare young scientists, we have our own department at the Moscow Institute of Physics and Technology, where I have been teaching for many years. Every year, 6 to 8 of the best students enter our graduate school, after graduation we invite the most talented young scientists to work for us. We managed to achieve the absence of a brain drain problem - at least in our Institute. On the contrary, talented scientists from other countries - the USA, France, and Germany - often come to us under a contract.

Soviet science showed high efficiency and amazing vitality in a very difficult domestic political and international situation because it was a holistic system. Despite weaknesses and structural defects, we had a united front of scientific research. Now the science of all sovereign states of the former USSR, including Russia, is spasmodically becoming structurally flawed. God grant that we can compensate for such a flaw by integrating into the world scientific community, building up the missing links, but this may not work out soon, even under the most favourable circumstances, which we are very far from at present. Hopes that it is possible to finance and save at least one part of it (for example, only basic science) are illusory. Science is a single living organism, not a conglomerate of autonomous mechanisms. Unfortunately, neither the politicians nor the scientific community have the concept of saving domestic science, its survival and rebirth. Real dramatic processes are obscured by new ideological myths, utopian projects and abstract judgments.

It is very difficult to predict the development of science, nevertheless, it can be argued that the 21st century will be the century of global study of the human, animal and plant genome. Now there is a massive search for ways to exclude unnecessary genomes that impede the development of flora and fauna, and how to replace them with those that are needed. I am convinced that the problem of "constructing" genomes in the 21st century will be solved.