U.S.S.R. Compur. iMarhs. .lfcrli. Phy. \‘oL 31. So. 6. pp. l-2, 1981. 004~-~~~3~~1~060001-0~~0-.~0 0

Rinted in Great Britain c 1983. Perpmon Press Ltd.

ACADEMICIAN ANDRE1 NIKOLAEVICH TIKHONOV CELEBRATES HIS SEVENTY-FIFTH BIRTHDAY *

THE CELEBRATED scholar, pedagogue. and science organizer Academician A. K. Tikhonoi

celebrated his 75.th birthday! on 30 October 1981.

His fundamental results, both in abstract and applied mathematics. have gained the widest

recognition both at home and abroad. His achievements embrace abstract topology,. functional

analysis, mathematical physics. the general theory of differential equations. computational

mathematics, and many problems in the processing of experimental data. His first success came in

his twenties. when he introduced the concept of the product of topological spaces (“T~~~IOJIOI

product”) and proved that the product of bicompact spaces is itself a bicompact space: then he

obtained various results in the theory of bicompact extensions of topological spaces, which placed

him at the forefront in topology-.

A striking feature of his work has been his ability to state problems of natural science in

strictly mathematical terms. For instance, he was the first to state mathematically certain problems

in prospecting by electrical methods. and thereby make a vital contribution to deve!oping the

theory of electromagnetic methods for studying the interior structure of the Earth. Moreover. apart

from reducing applied problems to a familiar mathematical form, he was able to state new classes of

mathematical problems, investigate their properties, and devise effective methods of solving them.

In the decades following Hadamard it was thought inadmissible to state problems of natural

science as ill-posed problems, It was only after Tikhonov introduced his principle of regularization

that a new meaning could be given to the concept of the solution of an ill-posed problem. and

stable methods could be devised for solving them. His work on the theory of equations with a small

*Zh. ~~cbisl. Mar. mat. Fiz., 21, 6, 1363-1364. 1981.

2 Academician Andrei Nikolaevich T’ikhonov celebrates his seventy-fifth birthduy

parameter has particular elegance and refinement; his new approach to the statement of the

problems, the rigourousness of his methods, and the strict nature of his results have led to this work

becoming a powerful instrument in the study of some important problems in physics and

engineering.

He is one of the creators of modern computational mathematics. As in many other cases, the

theory of numerical methods is a development and extension of the computational methods for

solving the mathematical problems encountered in large-scale problems of physics and engineering,

notably in the field of nuclear and thermonuclear energy.

His pedagogical and organizational work has been very varied. For over half a century he has

taught at Moscow State University, as reader, professor, faculty and department head, and recently,

as deacon of the faculty of computational mathematics and cybernetics, which he was largely

instrumental in founding. Many generations of physicists and mathematicians regard him as their

teacher.

He is director of the Keldysh Institute of Applied Mathematics of the Academy of Sciences

of the USSR. Here, problems of enormous scientific and economic importance have been solved

under his direction, notably in the fields of geophysical prospecting, plasma physics and nuclear

reactors, gas dynamics and electrodynamics, sorption dynamics, the processing and interpretation

of the results of physical experiments, etc. These problems were handIed at all stages, starting with

the physical statement and strict mathematical formulation, and ending with numerical

computations leading to concrete results.

In general, Tikhonov’s work and activity have always been distinguished by the scale of his

understanding, the width of his erudition, the elegance and precision of his mathematical

constructions, and his deep comprehension of the problems of Soviet science. We wish him health

and strength for many years to come, with further valuable results and all success in his varied

undertakings.

Translated b,t D. E. Brown