1.1. The 2001 Prize.

Oswald Veblen (1880-1960), who served as president of the American Mathematical Society in 1923 and 1924, was well known for his work in geometry and topology. In 1961 the trustees of the Society established a fund in memory of Veblen, contributed originally by former students and colleagues and later doubled by his widow. Since 1964 the fund has been used for the award of the Oswald Veblen Prize in Geometry. Subsequent awards were made at five-year intervals. The current amount of the prize is $4,000 (in case of multiple recipients, the amount is divided equally). The 2001 Veblen Prize was awarded by the American Mathematical Society Council on the basis of a recommendation by a selection committee consisting of Mikhael Gromov (chair), Richard S Hamilton, Robion C Kirby, and Gang Tian. At the Joint Mathematics Meetings in New Orleans in January 2001, the 2001 Veblen Prize was presented to Jeff Cheeger, Yakov Eliashberg, and Michael J Hopkins.

1.2. Citation for Yakov Eliashberg.

The 2001 Veblen Prize in Geometry is awarded to Yakov Eliashberg for his work in symplectic and contact topology. In particular the prize is awarded for:

1. His proof of the symplectic rigidity, presented in his International Congress of Mathematicians talk:

"Combinatorial methods in symplectic geometry", Proceedings of the International Congress of Mathematicians, Berkeley, California, 1986 (American Mathematical Society, Providence, RI, 1987), 531-539.

2. The development of 3-dimensional contact topology, presented in the papers:

"Classification of overtwisted contact structures on 3-manifolds", Inventiones Mathematicae 98 (3) (1989), 623-637; and "Invariants in contact topology", Proceedings of the International Congress of Mathematicians II (Berlin, 1998).

1.3. Yakov Eliashberg Biography.

Yakov Eliashberg was born in December 1946 in Leningrad, USSR. He received his Ph.D. from Leningrad University in 1972 under the direction of V A Rokhlin. From 1972 to 1979 he taught at the Syktyvkar University of Komi Republic of Russia and from 1980 to 1987 worked in industry as the head of a computer software group. In 1988 Eliashberg moved to the United States, and since 1989 he has been a professor of mathematics at Stanford University. Eliashberg received the Leningrad Mathematical Society Prize in 1972. In 1986 and in 1998 he was an invited speaker at the International Congress of Mathematicians. He delivered the Porter Lectures at Rice University (1992), the Rademacher Lectures at the University of Pennsylvania (1996), the Marston Morse Lectures at the Institute for Advanced Study (1996), the Frontiers in Mathematics Lectures at Texas A&M University (1997), and the Marker Lectures at Pennsylvania State University (2000). In 1995 Eliashberg was a recipient of the Guggenheim Fellowship.

1.4. Yakov Eliashberg Response.

I am greatly honoured to be a corecipient of the Oswald Veblen Prize of the AMS along with such outstanding mathematicians as Jeff Cheeger and Mike Hopkins. Symplectic geometry and topology has flourished during the last two decades, and I am happy that I was able to contribute to its success. I want first to thank my wife, Ada, for her lifelong support. I am also grateful to N M Mitrofanova, who converted me to mathematics from music when I was in school, and to Professor V A Rokhlin, who shared with me his topological insights when I was a student in Leningrad University. I was greatly influenced by my friend and colleague Misha Gromov. From him I learned about symplectic structures; then I struggled to find a balance between the apparent flexibility and hidden rigidity of the symplectic world. I am grateful to Misha for sharing his vision with me. My gratitude also goes to V I Arnold for many stimulating and critical discussions, and to D B Fuchs, who invested a lot of time to help me clarify the proof of my first result in symplectic geometry, the Arnold conjecture for surfaces. I owe a lot to all my coauthors: R Brooks, M Fraser, A Givental, M Gromov, H Hofer, C McMullen, N M Mishachev, L Polterovich, T Ratiu, D Salamon, and W P Thurston. Finally, I thank my colleagues and students at the Stanford mathematics department for creating a stimulating environment for geometric research.

2.1. The Heinz Hopf Prize.

The Department of Mathematics (D-MATH) at ETH Zurich awards the Prize in honour of mathematics professor Heinz Hopf (1894-1971) who died in 1971. At the age of 37, he assumed the ETH Zurich professorship of the famous mathematician, physicist and philosopher Hermann Weyl (1885-1955). Hopf defined the Hopf invariant, which is named after him, as a topological invariant of the mapping of spheres of different dimensions. He also introduced Hopf algebra, which later became fundamentally significant in the theory of quantum groups, amongst other areas.

The Prize, which is well-endowed with CHF 30,000, is donated by Dorothee and Alfred Aeppli - the latter being a former student of Heinz Hopf. The committee responsible for awarding the Hopf Prize is proposed by the Conference of Professors at the Department of Mathematics at ETH Zurich and appointed by the ETH President. The Heinz Hopf Prize has been awarded every two years since 2009. In 2009 it went to Robert MacPherson from the Institute for Advanced Study in Princeton and in 2011 to Michael Rapoport from the University of Bonn.

2.2. Yakov Eliashberg's links to Zurich.

Both scientists have a long-standing connection to Zurich as a place of research. Born in 1946, Yakov Matevich Eliashberg regularly visits ETH Zurich as a guest researcher. This Russian mathematician has been working as a professor of mathematics at Stanford University since 1989. He is a fellow of the American Mathematical Society and was awarded the Oswald Veblen Prize in 2001.

2.3. The 2013 Prize.

The Heinz Hopf Prize 2013 is being awarded to two mathematicians Yakov Eliashberg from Stanford University and Helmut Hofer from the Institute for Advanced Study in Princeton. The prize is endowed with CHF 30,000 and is awarded by the Department of Mathematics of ETH Zurich.

2.4. Mathematicians awarded for pioneering research.

Yakov Matevich Eliashberg and Helmut Hofer are amongst the leading researchers in the area of mathematical topology. Their pioneering contributions have expanded this basic research discipline with new research approaches and methods. "Yakov Eliashberg and Helmut Hofer are two leading mathematicians who have made exceptional achievements in what is currently one of the most active areas of research in mathematics", says Gisbert Wüstholz, Chairman of the Committee of the Heinz Hopf Prize and emeritus ETH professor for mathematics. He pays further tribute to the two laureates by maintaining that "without the work of Eliashberg and Hofer, symplectic topology and contact topology would not even exist in their current form".

As a basic mathematical discipline, topology deals with the abstract structures and general features of spaces of all kind. In doing so, it examines space concepts that are more complex than the space of Euclidean geometry, which people are familiar with in their everyday lives given its three dimensions of height, width and depth.

2.5. Lasting influence on further research.

By applying the methods of Eliashberg and Hofer, related questions in research such as are possible for Euclidean space can also be asked and answered appropriately for far more general topological spaces. Their findings and methods have also had a lasting influence on other areas of mathematics and physics far beyond their own specialist field, such as low-dimensional topology, field theory, researching dynamic systems and higher analysis.

The research of Eliashberg and Hofer also offers applications in physics in particular. Symplectic topologies contain structures that are suitable for measuring spaces and with which physical processes can be described, similar to the general theory of relativity. The symplectic field theory developed by Eliashberg and Hofer, which is today one of the key tools of topology, can also be applied to questions of physical field theory.

2.6. Eliashberg and Hofer speak about their prize winning work.

Eliashberg: This prize was awarded to Helmut and myself for our work in symplectic topology and its application to Hamiltonian dynamics. It is not the only topic we have worked on, but we spend a lot of time with it.

So everybody is used to Euclidean geometry. And Euclidean is based on measuring distance and angles with a scalar product. If you have two vectors and want to compute the area of the parallelogram which is spanned by this vectors you need a skew symmetric function.

Turns out that the phase space of any mechanical system has a canonical structure of this type and the evolution equations in mechanics preserve this structure.

This topic was more or less started by Ponicaré's interest in celestial mechanics. He was aware that many problems are not integrable and formulated questions one might be able to answer nonetheless, for example how many periodic solutions a system has.

One particular question is now called the "Last geometric theorem of Poincaré". Not much progress happened after it, until the 1980s.

Hofer: The progress started by including some other fields, that happened at the beginning of the 80s. So if you were working in some of the fields which later came together, which for us was the case, I came from analysis, specifically nonlinear partial differential equations, and Yakov came from geometry, it was interesting to see people coming from different cultures arriving to the same type of problems. The beginning was the merging of ideas from different fields.

Eliashberg: Mathematics at the beginning of 19th century started to branch in more and more fields, but now these branches start converging and some unexpected connection between different fields were found. Good mathematics is always inter-related and the convergence will always bring new results.

3.1. About the Crafoord Prize.

The Crafoord Prize in Mathematics is awarded by the Royal Swedish Academy of Sciences approximately every three years. It is intended to promote international basic research in several disciplines of science, including astronomy, geosciences, biosciences (particularly ecology), and polyarthritis, as well as mathematics. These disciplines were chosen to complement those for which Nobel Prizes are awarded. The prize carries a cash award of 6 million Swedish krona (approximately US$700,000). The prize is awarded at a ceremony in Stockholm.

3.2. The 2016 Crafoord Prizes.

The Royal Swedish Academy of Sciences has decided to award the Crafoord Prize in Mathematics 2016 to Yakov Eliashberg, Stanford University, Stanford, California, USA:-

... for the development of contact and symplectic topology and ground-breaking discoveries of rigidity and flexibility phenomena,

and the Crafoord Prize in Astronomy 2016 to Roy Kerr, University of Canterbury, Christchurch, New Zealand, and Roger Blandford, Stanford University, CA, USA,:-

... for fundamental work concerning rotating black holes and their astrophysical consequences.

3.3. The 2016 Crafoord Prize in Mathematics.

Yakov Eliashberg is one of the leading mathematicians of our time. For more than thirty years he has helped to shape and research a field of mathematics known as symplectic geometry, and one of its branches in particular - symplectic topology.

Yakov Eliashberg has solved many of the most important problems in the field and found new and surprising results. He has further developed the techniques he used in contact geometry, a twin theory to symplectic geometry. While symplectic geometry deals with spaces with two, four, or other even dimensions, contact theory describes spaces with odd dimensions. Both theories are closely related to current developments in modern physics, such as string theory and quantum field theory.

Symplectic geometry's link to physics has old roots. For example, it describes the geometry of a space in a mechanical system, the space phase. For a moving object, its trajectory is determined each moment by its position and velocity. Together, they determine a surface element that is the basic structure of symplectic geometry. The geometry describes the directions in which the system can develop; it describes movement. Physics becomes geometry.

One of Yakov Eliashberg's first and perhaps most surprising results was the discovery that there are regions where symplectic geometry is rigid and other regions where it is completely flexible. But where the boundary is between the flexible and the rigid regions, and how it can be described mathematically, is still a question that is awaiting an answer.

3.4. There is no royal road to geometry (Euclid).

Yakov Eliashberg is one of the leading mathematicians of our time. For more than thirty years he has helped to shape and research a field of mathematics known as symplectic geometry, solving many of its most important problems and finding new and surprising results. He has further developed the techniques he used in contact geometry, a twin theory to symplectic geometry. Both theories are closely related to current developments in modern physics.

The universe is geometric. Albert Einstein presented this revolutionary idea one hundred years ago, in his general theory of relativity. In this theory, gravity is no longer described as a Newtonian attraction force that acts on different masses, instead it is the curvature of the geometry of space and time. The foundations of this geometry were laid in the mid-1800s by the German mathematician Bernhard Riemann. His aim was to develop geometry that described the very large and the very small - which was exactly what then happened.

However, geometry is much older than this. It is one of the oldest sciences, with roots in ancient Egypt and Babylonia around 5,000 years ago. The word geometry originates from the Greek: geo, which means earth, and metria - measure. Indeed, geometry was originally about practical needs such as measuring and distributing land, constructing buildings or calculating astronomical numbers. It dealt with surfaces, figures and shapes, with quadrants and cubes, circles and spheres. With parallel lines that never meet and triangles where the angles add up to 180 degrees. The Greek Euclid collected and formulated around 300 B.C. all the Antique geometric knowledge in one work, Elementa, and his Euclidean geometry is still taught in schools.

Geometry can come in many different forms; simply drawing a triangle on the curved surface of the Earth is sufficient to realise that there must be other types of geometry. For example, in a triangle with one corner on the North Pole and two on the equator, all the angles can be 90 degrees and then add up to 270 degrees.

Bernhard Riemann did not just investigate curved two-dimensional surfaces, but broadened the concept to multi-dimensional spaces, called manifolds, and presented his discoveries in a famous lecture in Göttingen in 1854. The Riemannian geometry of curved space was an invaluable tool for Albert Einstein when he described, in his general theory of relativity, how empty space is curved by the mass of stars, galaxies and galaxy groups.

In addition to Euclidean and Riemannian geometries, there is also a lesser known type of geometry that has even deeper roots in physics: symplectic geometry. Somewhat simplified, Riemannian geometry can be said to be the expansion of Euclidean geometry to curved space with several dimensions. Symplectic geometry can be described in the same way - as a curvilinear expansion of the well-known Euclidean geometry.

However, there are significant differences between Riemannian and symplectic geometry; these have not yet been completely investigated, even though the roots of symplectic geometry go back several hundred years. Symplectic geometry was first used to study the classical mechanics that originated in Isaac Newton's laws of motion in the late 1600s. It thus comprises the very foundation of classical physics.

A classical mechanical system could be a planet orbiting the sun, an electron moving in an electromagnetic field, a swinging pendulum or a falling apple. In the 19th century, developments in classical physics led to the simplification of the often complicated calculations that used Newton's differential equations. Instead, methods were introduced to describe and understand motion in terms of symplectic geometry. Physics became geometry.

For example, symplectic geometry describes the geometry of a space that consists of the position and momentum values of a mechanical system, the phase space. For a moving object, its trajectory is determined each moment by its position and velocity, a pair of parameters. Together, they determine a surface element that is the basic structure of symplectic geometry. The geometry describes the directions in which the system can develop; it describes movement.

In the 1800s, mathematicians demonstrated that these surface elements are preserved, i.e. remain constant over time, which has become an important characteristic of symplectic geometry. The surface element has also received a quantum physics interpretation in Heisenberg's uncertainty principle, which says that it is not possible to exactly measure the position and the velocity of a particle simultaneously. This means you can think of a symplectic surface element as a measure of the combined values of position and momentum.

These two values lead to a plane, two-dimensional geometry. However, it can be generalised to geometries in four, six or more even dimensions, which have become interesting objects of study for both mathematicians and physicists in recent decades.

The modern development of symplectic geometry originates in the works of the Russian mathematician Vladimir Arnold in the late 1970s. He was awarded the very first Crafoord Prize for Mathematics in 1982.

Arnold formulated a number of central problems for which solutions were needed. Yakov Eliashberg was among those who were inspired; it is not easy to do his efforts complete justice in such a short text. He has been a leading figure in the field since the 1980s, and his ground-breaking research has both expanded and deepened symplectic geometry and its related areas, some of which he developed himself.

One of his first and perhaps most surprising results was the discovery that there are regions where symplectic geometry is rigid and other regions where it is completely flexible. Flexibility is studied in a branch of mathematics called topology. Here, geometric objects can be arbitrarily stretched, twisted, and bent without losing their properties. In contrast, deformations of rigid geometric objects are much more constrained and are determined by more refined properties than merely their topology.

In symplectic geometry, rigidity and flexibility live side by side and one of the challenges was to find the decisive properties of geometric objects that determine whether they are flexible or rigid. Time and again, the work of Eliashberg has showed that the borderline between the two regions is not where it first appears to be.

One of the characteristic properties of symplectic geometry is that on a small scale, i.e. locally, all symplectic spaces look the same despite being different globally. This is in contrast to ordinary geometry, where there are important local differences: if you have a ball, all you have to do is to draw a small triangle on its surface to discover that it is curved. This is not the case for symplectic geometry.

Yakov Eliashberg has identified the smallest building blocks, the atoms of flexibility. The presence of such an atom guarantees that everything is the same, even on a larger scale, and that you are in the flexible region. Eliashberg's flexibility theory says that a rigid region can be transformed into a flexible one if you introduce a single such tiny building block. For example, a construction that is as stiff and stable as the Eiffel Tower would lose its rigidity if a tiny flexible building block was added; the tower would become limp and collapse.

However, if there is no such flexible building block, you are in our rigid world in which things retain their shape. This world is built from tiny strings according to string theory, which tries to unify the two most successful physics theories of the twentieth century - quantum mechanics and the general theory of relativity. String theory has long had an intensive exchange of ideas with symplectic geometry, where in particular symplectic rigidity plays an important role.

A now classic example of symplectic rigidity is the non-squeezing theorem, which Vladimir Arnold also named the principle of the symplectic camel after a reformulated biblical quote: "It is easier for a rich man to enter the kingdom of heaven than it is for a symplectic camel to pass through the eye of a needle".

It was the Russian-French mathematician and Eliashberg's colleague Mikhail Gromov who demonstrated that symplectic geometry does not permit the circus trick of pulling a camel through a needle's eye. If the issue was just the volume, the camel could be stretched out into a long thin thread. But symplectic geometry does not allow this; rigidity is what applies here.

The answer to the camel problem was obtained using Gromov's theory of holomorphic curves, which was later related to both string theory and the quantum field theory of high energy physics. It also became the central tool in the new field of symplectic topology.

Eliashberg has transferred much of this mathematics to contact geometry, a sister theory to symplectic geometry which lives in odd dimensions. An odd dimension can be achieved when the total energy in a mechanical system is constant (according to the principle that energy in a closed system can neither be created nor destroyed). This means that the system cannot move freely in its two degrees of freedom, so one dimension can be removed.

If, for example, this constant energy determines the distance from the centre of a plane, contact geometry will apply to the one-dimensional circle around the centre, while symplectic geometry applies in the two dimensional plane surrounding it. The two geometries are thus very closely related, and contact geometry in one or more odd dimensions has been another of Yakov Eliashberg's specialist areas.

In the intersection between contact geometry and mathematical knot theory there are Legendre knots. These are knots that must follow special limitations dictated by contact geometry. Using the same type of technique as for the camel, Eliashberg demonstrated that it is not always possible to transform two Legendre knots into each other, even if there are no purely topological barriers. The knots are rigid.

The large mathematical machinery developed by Eliashberg for studies of rigidity led to a new field - symplectic field theory - which, in turn, became a source of numerous new insights, discoveries and links to other areas.

Time and again, Yakov Eliashberg has found new areas and problems that are of particular interest to explore. But where the boundary is between the flexible and the rigid regions, and how it can be described mathematically, is still a question that is awaiting an answer.

3.5. Yakov Eliashberg biography.

Yakov Eliashberg is the Herald L and Caroline L Ritch Professor of Mathematics at Stanford University. Born in Russia in 1946, he received his PhD from Leningrad University in 1972 under the direction of Vladimir Rokhlin. He moved to the United States in 1988 and has been at Stanford since 1989. He received the Leningrad Mathematical Prize in 1972 and a Guggenheim Fellowship in 1995. He has been an invited speaker at the International Congress of Mathematicians in 1986 and 1998 and has been the recipient of a number of lectureships. He was awarded the AMS Veblen Prize in Geometry in 2001 and the Heinz Hopf Prize in 2013. Eliashberg was elected to the US National Academy of Sciences in 2003 and became an AMS Fellow in 2012.

4.1. About the Wolf Prize.

The Wolf Prize carries a cash award of US$100,000. The science prizes are given annually in the areas of agriculture, chemistry, mathematics, medicine, and physics. Laureates receive their awards from the President of the State of Israel in a special ceremony at the Knesset Building (Israel's Parliament) in Jerusalem.

4.2. Yakov Eliashberg wins 2020 Wolf Prize in Mathematics.

Professor Yakov Eliashberg is awarded the Wolf Prize:-

... for his foundational work on symplectic and contact topology changing the face of these fields, and for his ground-breaking contribution to homotopy principles for partial differential relations and to topological foundations of multi-dimensional complex analysis.

4.3. Yakov Eliashberg Wolf Prize Laureate in Mathematics 2020.

Yakov Eliashberg is one of the founders of symplectic and contact topology, a discipline originated as mathematical language for qualitative problems of classical mechanics, and having deep connections with modern physics. The emergence of symplectic and contact topology has been one of the most striking long-term advances in mathematical research over the past four decades. Eliashberg is among the main exponents of this development.

In the 1980s Eliashberg developed a highly ingenious and very visual combinatorial technique that led him to the first manifestation of symplectic rigidity: the group of symplectomorphisms is closed in the group of all diffeomorphisms in the uniform topology. This fundamental result, proved in a different way also by Gromov and called nowadays the Eliashberg-Gromov theorem, is considered as one of the wonders and cornerstones of symplectic topology. In a series of papers (1989-1992), Eliashberg introduced and explored a fundamental dichotomy "tight vs overtwisted" contact structure that shaped the face of modern contact topology. Using this dichotomy, he gave the complete classification of contact structures on the 3-sphere (1992). In these papers Eliashberg laid foundations of modern contact topology and introduced mathematical language which is widely used by researchers in this rapidly developing field.

In a seminal 2000 paper Eliashberg (with Givental and Hofer) pioneered foundations of symplectic field theory, a powerful, rich and notoriously sophisticated algebraic structure behind Gromov's pseudo-holomorphic curves. It had a huge impact and became one of the most central and exciting directions in symplectic and contact topology. It has led to a significant progress on numerous areas including topology of Lagrangian submanifolds and geometry and dynamics of contact transformations, and it exhibited surprising links with classical and quantum integrable systems.

In recent years (2013-2015), Eliashberg found a number of astonishing appearances of homotopy principle in symplectic and contact topology leading him to a solution of a number of outstanding open problems and leading to a "mentality shift" in the field. Before these developments the consensus among experts was that the symplectic world is governed by rigidity coming from Gromov's theory of pseudo-holomorphic curves or, equivalently, by Morse theory on the loop spaces of symplectic manifolds. The current impression based on Eliashberg's discoveries is that rigidity is just a drop in the ocean of flexible phenomena.

4.4. Stanford's Yakov Eliashberg awarded Wolf Prize in Mathematics.

Stanford mathematics Professor Yakov "Yasha" Eliashberg is a recipient of the 2020 Wolf Prize in Mathematics. Along with the Fields Medal and Abel Prize, the Wolf Prize is considered one of the most prestigious awards in mathematics.

Stanford mathematics professor Yakov "Yasha" Eliashberg has been jointly awarded the 2020 Wolf Prize in Mathematics for his contributions to differential geometry and topology.

Awarded since 1978, the Wolf Prize recognises "outstanding scientists and artists from around the world ... for achievements in the interest of mankind and friendly relations among peoples." Along with the Fields Medal and Abel Prize, it is considered the closest equivalent to a Nobel Prize in mathematics.

Eliashberg is the third Stanford math professor to receive the Wolf Prize in Mathematics: Joseph Keller was the prize's 1996-1997 recipient and Richard Schoen received the prize in 2017.

"When I learned of the news, I was surprised and very excited because this is a very famous prize and one that many of my mathematical heroes have received," said Eliashberg, who is the Herald L and Caroline L Ritch Professor in the School of Humanities and Sciences.

One of those mathematical heroes is Sir Simon Donaldson, a mathematician at Stony Brook University in New York and Imperial College London in the UK, with whom Eliashberg shares this year's $100,000 prize. "I'm extremely honoured to be recognized together with Simon," Eliashberg said.

Eliashberg is one of the founders of symplectic and contact topology, a field that arose in part from the study of various classical phenomena in physics that involve the evolution of mechanical systems, such as springs and planetary systems. "The emergence of symplectic and contact topology has been one of the most striking long-term advances in mathematical research over the past four decades," the Wolf Foundation said in a statement.

"Yasha's work played a key role in this evolution," said Rafe Mazzeo, chair of Stanford's Department of Mathematics. "His influence across mathematics is extraordinary. The Wolf Prize is one of the most prestigious awards in mathematics, and it is a richly deserved honour for Yasha to be a recipient of this prize. The Mathematics Department is very proud to see him receive this distinction."

Eliashberg says that, at the most elementary level, he specialises in bringing a geometer's perspective to problems in math and physics. "Geometry is essentially a way of thinking," he said. "Every person chooses a way of thinking that is best suited for them, and I happen to have found that in order to answer questions, I must visualise them and think about them in geometric terms."

Eliashberg has been a professor at Stanford since 1989 and has helped 35 graduate students earn their PhDs. He says that interacting with students is one of the most rewarding aspects of his position. "It takes a lot of time but it is extremely uplifting and also very helpful to my own work," he said.

Eliashberg will receive his award certificate on 11 June in Jerusalem during a special meeting of Israel's parliament. It will, in fact, be his second time attending the ceremony: In 1993 Eliashberg was invited to attend the award ceremony for his friend and collaborator Mikhael Gromov, who was a co-recipient of that year's prize.

Eliashberg said he never imagined he would be a recipient of the same prize himself someday. "Of course, you're always pleased when other people see your work as interesting and important," he said, "but you never think of yourself or your work in that way."

4.5. Yakov Eliashberg biography.

Professor Eliashberg was born in 1946 in Leningrad (now St. Petersburg), Russia. He received his doctoral degree in Leningrad University in 1972 under the direction of V A Rokhlin, and in the same year he joined Syktyvkar University in northern Soviet Union. Eliashberg's route passed through the refusenik years in Leningrad (1980-1987) where he had to do software engineering in order to feed his family, and where he was virtually cut off from normal mathematical life. In 1988 he emigrated to the United States and in 1989 became a Professor at Stanford University. He is a Member of U.S. National Academy of Sciences. For his contributions, Eliashberg has received a number of prestigious awards, including the Guggenheim Fellowship in 1995, the Oswald Veblen Prize in 2001, the Heinz Hopf Prize in 2013 and the Crafoord Prize in 2016. Eliashberg is currently the Herald L and Caroline L Ritch Professor at Stanford University.