**Steven Orszag**'s father, Joseph Orszag was a lawyer. The family were Jewish and originally from Hungary with Steven's paternal grandparents Alex and Regina Orszag both being born in Hungary. Alex (born 1876) and Regina (born 1886) emigrated to the United States in 1903 and settled in Manhattan, New York City. Joseph, born in New York on 4 February 1910, was the third of Alex and Regina's children. Joseph married Rose (born 26 July 1909) and their son Steven was born in Manhattan. However, he was brought up in Forest Hills, a residential area of Queens, New York City, where he attended Forest Hills High School. In 1959 he was one of the nine prize winners in the Society of Actuaries' Preliminary Actuarial Examination. When he took the examination, Orszag was still at Forest Hills High School but the other eight winners were all much older and university undergraduates.

Beginning his studies at the Massachusetts Institute of Technology in 1959, when only sixteen years old, he graduated with a B.S. in 1962. Still only nineteen years of age, he set sail for England where he spent the academic year 1962-63 studying at St John's College, Cambridge University. Returning to the United States, he began his graduate studies in 1963 at Princeton University. His thesis advisor was Martin David Kruskal who was Professor of Astronomy at Princeton but, when Orszag began his graduate studies, Kruskal was also a member of Project Matterhorn, which today is known as the Princeton Plasma Physics laboratory. Orszag completed his doctoral thesis *Theory of Turbulence* within three years and was awarded a Ph.D. in 1966. Orszag, in collaboration with his thesis advisor, published a paper in 1966 with the same title as his thesis. Even before he began undertaking research at Princeton he had become engaged to Reba Karp, the announcement of the engagement appearing in the New York Times on 25 August 1963. Reba, the sister of Joel Karp, was the daughter of Gertrude Herskowitz and Jack Karp. Steven and Reba were married on 21 June 1964; they had three sons J Michael Orszag, Peter Richard Orszag and Jonathan Marc Orszag. Peter Orszag became an economist and served as an advisor to President Clinton, then as budget director for President Obama.

In 1967 Orszag was appointed as a professor of applied mathematics at the Massachusetts Institute of Technology. At MIT he was a colleague of Carl M Bender and together they collaborated on a graduate level mathematics course for seven years. Bender said [3]:-

[The lecture notes from the course were published as the textbookThe course]was so popular that a lot of students from Harvard came to take it as well. A course that good really wasn't offered at Harvard.

*Advanced mathematical methods for scientists and engineers*:

*Asymptotic Methods and Perturbation Theory*(1978). Vadim Komkov writes in a review:-

Chambers writes in a review inThis book is not the usual "mathematical methods for engineers" text, which could contain, according to the taste of its author, almost any elementary, or intermediate level topic in analysis, linear algebra, numerical analysis, game theory, systems theory, functional analysis, probability, statistics, or even logic, generally with little cohesion among the different parts of such a mixture. Here the authors intend to introduce the engineering or physics student to asymptotic and perturbation analysis, specifically concentrating on obtaining answers to problems which arise in physics. ... This book contains a wealth of solved problems and of techniques for approximating the exact solutions. It is a suitable text for a "topics" course, but it is a valuable addition to the library of any applied mathematician who is practicing his art by trying to solve physical problems.

*The Mathematical Gazette*[1]:-

Over twenty years after it was first published the book was reprinted in 1999. A D Wood, reviewing the reprint, writes:-The title of this volume is somewhat misleading in that the subjects discussed are approximate analytic solutions of ordinary differential and difference equations, and no other topics are considered. ... This is a very good book. The text reads well and, as the blurb states, "this book stresses care rather than rigor". There are many examples and exercises, and a welcome feature is the large number of diagrams which compare the approximate solutions with the known solutions of some of the problems discussed. The reader will be amused by the quotation at the beginning of every chapter from Sherlock Holmes, although the exact relevance is not always obvious. The book is well produced, and it will surely be of great use to those interested in these matters. It is not only the authors who hope for a similar book on approximate solutions of partial differential equations.

Carl Bender spoke about his former colleague at MIT [3]:-This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic.

In 1984 he returned to Princeton University when he was appointed Forrest E Hamrick Professor of Engineering. He remained there for fourteen years before moving to Yale where he was appointed in 1998. He was Percey F Smith Professor of Mathematics at Yale from 2000 until his death in 2011. Before looking briefly at Orszag's contributions, let us look at his own description of the field in which he worked [4]:-Orszag engaged with students of varying levels of mathematical talent. He was fast-paced. You had to run to keep up with him. But he was also warm and patient and humble at unexpected times.

When appointed to the Percey F Smith Professorship, his research achievements were described as follows [7]:-Understanding turbulent flows is a "grand challenge" comparable to other prominent scientific problems such as the large-scale structure of the universe and the nature of subatomic particles. In contrast to many of the other grand challenges, progress on the basic theory of turbulence translates nearly immediately into a wide range of engineering applications and technological advances that affect many aspects of everyday life. Numerical prediction of fluid flows is at the heart of understanding and modelling turbulence. However, such computational fluid dynamics simulations challenge the capabilities of both algorithms and the fastest available supercomputers.

We have already given details of his bookSteven A Orszag, the new Percey F Smith Professor of Mathematics, specializes in the areas of computational fluid dynamics, turbulence theory and numerical analysis. He is also noted for his work in applied mathematics, and his research has had an impact on aeronautics, weather forecasting and the electronic chip manufacturing industry. In the areas of computational fluid dynamics, he achieved the first successful computer simulations of three-dimensional turbulent flows. He also developed methods that provide a fundamental theory of turbulence. Another primary research interest has been the development of techniques for the simulation of electronic chip manufacturing processes, some of which have been applied extensively throughout the industry.

*Advanced Mathematical Methods for Scientists and Engineers*(1978) but around the same time he also published, in collaboration with David Gottlieb,

*Numerical Analysis of Spectral Methods: Theory and applications*(1977). In this the authors presented:-

Orszag's contributions to this area are put into perspective in [5]:-... a unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

In addition to these books, Orszag was an editor of a number of books: (editor with K Kuwahara and Raul Mendez)"Spectral methods are great fun," observes Michel Deville, a professor at l'École Polytechnique Fédérale de Lausanne, Switzerland. "It's always a numerical nirvana when - for the first time - one observes that adding one or two polynomials to a basis makes the error for smooth problems drop by a factor of50or even100." Spectral methods have not always come in for such high praise. Although originating in early-201950^{th}-century work of Galerkin and Lanczos, and put to limited use by meteorologists in thes, spectral methods came into their own as a powerful tool for scientific computing only with the advent of the fast Fourier transform. In the early1970s, in a series of landmark papers, Steven Orszag showed that spectral methods, and the closely related pseudospectral methods, could be used to simulate incompressible turbulence withN^{3}Fourier modes at a cost of only O(N^{3}logN)operations per timestep with zero numerical dispersion and dissipation. In a historic computation, Orszag and his colleague G S Patterson undertook the first calculation of homogeneous isotropic turbulence at laboratory Reynolds numbers with a32^{3}pseudospectral discretization. ... In the1977SIAM monograph 'Numerical Analysis of Spectral Methods: Theory and Applications', Gottlieb and Orszag presented the first unified description of the field, with an emphasis on numerical analysis and algorithmic considerations.

*Supercomputers and Fluid Dynamics*(1986); (editor with Raul H Mendez)

*Japanese Supercomputing: Architecture, Algorithms, and Applications*(1988); and (editor with Boris Galperin)

*Large Eddy Simulation of Complex Engineering and Geophysical Flows*(1993). The publisher, Cambridge University Press, describes this last work as follows:-

Orszag published over 400 papers in his career as well as making six successful patent applications. Among the honours he received for his contributions we mention the American Institute of Aeronautics and Astronautics Fluids and Plasmadynamics Prize he received in 1986. He was a John Simon Guggenheim Fellow in 1989 and received the Otto Laporte Award from the American Physical Society in 1991. The Society of Engineering Science awarded him their G I Taylor Medal in 1995. He was named an ISI Highly Cited Author by the ISI Web of Knowledge.... this book was the first to offer a comprehensive review of large eddy simulations(LES)- the history, state of the art, and promising directions for research. Among topics covered are fundamentals of LES; LES of incompressible, compressible, and reacting flows; LES of atmospheric, oceanic, and environmental flows; and LES and massively parallel computing. The book grew out of an international workshop that, for the first time, brought together leading researchers in engineering and geophysics to discuss developments and applications of LES models in their respective fields. It will be of value to anyone with an interest in turbulence modelling.

He died of chronic lymphomic leukaemia at the age of sixty-eight. His colleague at Yale, John Wettlaufer, paid him this tribute [2]:-

Wettlaufer also paid this tribute to Orszag [3]:-Steve was a pioneer in applied and computational mathematics high-performance computing and more recently novel approaches to mathematics education. Vast areas of the landscape of thought have lost a brilliant thinker and a wise adviser.

He was an incredibly talented mathematician. But he was simultaneously probably one of the most generous people I've ever worked with.

**Article by:** *J J O'Connor* and *E F Robertson*