The city was much smaller then and still retained some rural character: small wooden houses with gardens, an occasional horse-driven cart. After the joy of early childhood, going to school was a setback. After 7th grade I went to mathematical school no. 2. It was a true change: lectures and seminars on advanced mathematical topics taught by professors and students from the University, the shining classes on literature and on history.

During the preseminar dozens of people congregated near the auditorium entrance, chatting and exchanging books and texts of all kinds. The seminar typically began with Gelfand telling some anecdotes and mathematical news, after which would come a talk by an invited speaker. Often there was not enough time to finish, and the talk continued serially, each time beginning from scratch and covering about half of the material from the week before, the speaker gradually fading away and being replaced by a student assigned by Gelfand to explain what the talk was, or should have been, about. Any speaker deemed not to have understood the subject, or to have explained it badly (or if the writing was too small and the voice not clear) was harshly reprimanded.

Gelfand gave a talk about his work, mentioning that I had obtained a similar theorem. After the talk I approached Gelfand, and he at once ordered me to leave Yuri Ivanovich Manin, who was my supervisor, and be his student. I refused. When I told Manin about the accolade, he said this had happened to many, e.g., to himself and to Shafarevich. Thereafter I stayed in an outer orbit of Gelfand's influence, and our relationship was excellent.

Sasha's very first mathematical paper - a note on coherent sheaves on $\mathbb{P}^{n}$, written in 1977, opened a new direction in algebraic geometry. Together with the paper of Bernstein-Gelfand-Gelfand on the same topic (which appeared simultaneously with Sasha's), it revealed the role of the derived category of coherent sheaves as an invariant of an algebraic variety, and started the theory of exceptional collections, which now became an indispensable part of algebraic geometry, especially in connection with homological mirror symmetry. One of the significant impacts of these papers, amplified by the subsequent one of Beilinson-Bernstein-Deligne on perverse sheaves, was that they brought derived categories within the field of vision of mathematicians working in many different fields, and they started to play an increasingly pivotal role in areas well beyond algebraic geometry: representation theory, non-commutative geometry, symplectic topology, mathematical physics, etc. The fact that the two approaches to coherent sheaves on $\mathbb{P}^{n}$ (by Beilinson and by Bernstein-Gelfand-Gelfand) appeared at the same time was providential for the birth of the theory of Koszul duality. Even though Koszul algebras had been known for some time, the connection of the symmetric and exterior algebras to derived categories of sheaves on $\mathbb{P}^{n}$ showed that Koszul duality can be stated as an equivalence of derived categories of modules. This picture was developed in Beilinson's later works.

No one at the seminar could replace them.

The authors show how to construct a localization functor for certain noncommutative rings related to a reductive Lie algebra g. This functor identifies g-modules with sheaves of modules over a ring of (twisted) differential operators on a suitable flag manifold. As an application a new classification of irreducible Harish-Chandra modules and a proof of the Kazhdan-Lusztig conjecture are sketched. Other proofs of the latter conjecture (in one form or another) have been given by Brylinski and Kashiwara and by Vogan.

The Moscow Mathematical Society Prize for young mathematicians carried a considerable prestige, especially with the mathematical community at-large, as opposed to the official authorities. It was awarded by the elected Society Council which represented the cream-of-the-crop of the community in terms of research achievements and international reputation. The prize was awarded for a specific body of, work, jointly if the recognised work was joint, and was subject to the upper age restriction of thirty years for all nominees. The prize usually was given for really outstanding work which produced a strong and lasting impact and was also a good predictor of the winner's long-term success. Usually two prizes were awarded every year.

At the end of the 80s "perestroika" brought onto Moscow streets immense crowds calling for changes. These arrived: the country was split and pillaged by the robber barons, the life losses on a par with those in the Civil War 74 years earlier.

At 41, Beilinson no longer is eligible for the Fields Medal. Nevertheless, "his mathematical achievements are on the level of those of the most renowned Fields Medalists," Manin said. The influence of Beilinson's work extends into representation theory, arithmetical geometry and modern mathematical physics, said Manin. Beilinson holds the prestigious first David and Mary Winton Green University Professorship in Mathematics. Since 1989, Beilinson largely has spent fall semesters teaching at the Massachusetts Institute of Technology as a professor of mathematics and working the rest of the year as a researcher at the Landau Institute of Theoretical Physics in Chernogolovka, Russia.

"There are several people here whose research is very close to mine and who inspired it in a sense, and so I wish to work with them," Beilinson said. He was referring to Spencer Bloch, the Robert Maynard Hutchins Distinguished Service Professor in Mathematics, and Victor Ginzburg, Robert Kottwitz and Madhav Nori, Professors in Mathematics. "People here would like to create something new," Beilinson said. "It's very nice to come to a place that hopefully will create something wonderful when everything is moving." Beilinson also collaborates with Drinfeld, whom he has known for more than two decades.

Science comes naturally to Helen Beilinson. She was born in Moscow and grew up in academia; her father is a mathematician and her mother is a biologist. Her family left Russia when she was a young child and led a nomadic academic life until settling at the University of Chicago. Beilinson's baby-sitters were postdocs and grad students and she spent her childhood roaming her mom's biology lab.

... for achievements in the areas of representation theory, arithmetic geometry, and modern mathematical physics.

Alexander Beilinson's outstanding achievements include proofs of the Kazhdan-Lusztig and Jantzen conjectures, which play a key role in the representation theory, the development of important conjectures ("Beilinson's Conjectures") in algebraic geometry, and a significant contribution to the interface between geometry and mathematical physics. The joint work of Beilinson and Vladimir Drinfeld on the Langlands Program - a woven fabric of theorems and conjectures designed to link key areas of mathematics - has led to impressive progress in implementing the program in important areas of physics, such as quantum field theory and string theory.

Alexander Beilinson and David Kazhdan are two mathematicians who have made profound contributions to the branch of mathematics known as representation theory, but who are also famous for the fundamental influence they have had on many other areas, such as arithmetic geometry, K-theory, conformal field theory, number theory, algebraic and complex geometry, group theory, and algebra more generally. As well as proving remarkable theorems themselves, they have created conceptual tools that have been essential to many breakthroughs of other mathematicians. Thanks to their work and its exceptionally broad reach, large areas of mathematics are significantly more advanced than they would otherwise have been.

Group theory is intimately related to the notion of symmetry and one can think of a representation of a group as a "description" of it as a group of transformations, or symmetries, of some mathematical object, usually linear transformations of a vector space. Representations of groups are important as they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well understood. They are also important in physics because, for example, they describe how the symmetry group of a physical system affects the solutions of equations describing that system and the representations also make the symmetry group better understood. In loose terms, representation theory is the study of the basic symmetries of mathematics and physics. Symmetry groups are of many different kinds: finite groups, Lie groups, algebraic groups, p-adic groups, loop groups, adelic groups. This may partly explain how Beilinson and Kazhdan have been able to contribute to so many different fields.

... NSA destroyed the security of the Internet and privacy of communications for the whole planet. But if any healing is possible, it would probably start with making the NSA and its ilk socially unacceptable - just as, in the days of my youth, working for the KGB was socially unacceptable for many in the Soviet Union. ... NSA needs mathematicians for its tasks, and the AMS has an interest in increasing research funding. But any relationship with an organisation whose activity is so harmful for the fabric of human society is unhealthy. For the sake of integrity, the AMS should shun all contacts with the NSA.

Sasha Beilinson has been a source of light and inspiration for all of us around him - in mathematics and in life in general. As Sasha himself put it on multiple occasions describing other people, a person's ability to produce beautiful mathematics stems from this person's inner freedom. This is exactly the quality that Sasha is amply endowed with, and his unique vision and perception of mathematics is a manifestation of this freedom.

Sasha continues to surprise and delight us by his amazing insight. For example, a couple of years ago he solved the long-standing problem of defining the notion of singular support for étale sheaves. In a sense, his solution is completely elementary; it uses Radon transform as its main tool. Yet, this is something that has eluded experts for decades.

Mathematics is simple, but to perceive this your vision must not be rigid and fixed in one direction. Also appreciation of mathematics is virtually impossible without actively doing it - like Nature, it is reality you have to be part of in order to see it. Remarkably, mathematics shares these traits with our common life. ... To me, understanding ourselves as tiny parts no more important than other living beings, of the great flow of Unknown is of key importance both for everyone's normal life and for our common survival.