I was born on October 9, 1947 in Elblag, Poland, eight hours before my identical twin brother Tadeusz. We grew up close in a loving family with no academic tradition.

Our interest in mathematics began in a technical high school (which focused on steam turbines) where we were successful in mathematical olympiads. Instead of continuing our education in engineering we entered the Mathematics Department of Warsaw University in 1966. However, we no longer shared our ideas in mathematics as we wished to be more independent intellectually.

At the end of my first undergraduate year I was fortunate to attract the attention of Professor Andrzej Schinzel, who invited me to attend and to give talks in his number theory seminar at the Mathematics Institute of the Polish Academy of Sciences. Early on I was fascinated by analytic number theory because of the large variety of tools, which are used to establish results of an arithmetical flavour. I was particularly impressed by the work of Yu V Linnik. I started alone on sieve methods while Professor Schinzel provided general advice, and also helped with editorial matters.

A year before I graduated in 1971 I had two papers accepted for publication, one of which became my master thesis and the other my PhD thesis, which I defended in the spring of 1972 without entering graduate school (the requirement of passing an exam on Marxism philosophy delayed my thesis defense!).

From 1971 to 1983 (the year I left Poland with my family for the United States) I was employed at the Mathematics Institute of the Polish Academy of Sciences in Warsaw, at which time I was promoted to Professor and elected corresponding member of the Polish Academy of Sciences.

During this period I spent one year in Pisa (1976/77) at the Scuola Normale Superiore where I had the opportunity to expand my interest in sieve methods under the influence of Enrico Bombieri and in collaboration with John Friedlander. Later in the USA my collaboration with John evolved into many other topics in number theory (exponential and character sums, distribution of prime numbers, etc.). Our numerous joint results constitute the essential bulk of my total work.

Next, my time spent at the University of Bordeaux in 1979/80 and the subsequent visits during 1980–82 were critical for directing my interest to the field of automorphic forms. There began my collaboration with Jean-Marc Deshouillers. We developed new estimates for the Fourier coefficients of cusp forms in the spectral aspect and for sums of Kloosterman sums. All of these are basic tools in modern analytic number theory; they open doors for using non-abelian harmonic analysis to study natural numbers.

At the same time in Bordeaux I worked with Étienne Fouvry on primes in arithmetic progressions. We succeeded in establishing equidistribution results over residue classes, which surpass those implied by the Riemann hypothesis. Later we improved the range of these results jointly with Bombieri and Friedlander at the Institute for Advanced Study (AIS) at Princeton.

My first years in the USA (September 1983–December 1986) were spent at the IAS with two semester breaks for visits to the University of Michigan and as a Distinguished Ulam Visiting Professor to the University of Colorado at Boulder. I also made a few trips to Stanford University to work with Peter Sarnak. At the Institute it was like being in paradise to have free time to think of mathematics, to discuss and to share ideas with members of the School of Mathematics, distinguished visitors, as well as with the faculty of Princeton University. Such an atmosphere easily boosts the aspirations of everybody. I was driven to the uncharted waters of the Riemann hypothesis for varieties (Deligne’s result) directing some of it into powerful tools for analytic number theory. Jointly with Friedlander and Fouvry, and with assistance from Birch, Bombieri and Katz, crucial improvements were made in asymptotic formulas for some arithmetic functions, which are fundamental to the theory of prime numbers. The Riemann hypothesis for varieties is also used later in my work on

*L*-functions (jointly with Brian Conrey) and on Hecke eigenvalues (jointly with William Duke). It is gratifying that my mathematical “children”, Étienne Fouvry, Emmanuel Kowalski and Philippe Michel travel much further conceptually in their “Theory of Trace Functions”, and produce very strong results which unify many applications.

I love working in collaboration with others. Peter Sarnak and I established (among many other things) statistical results concerning the central values of families of automorphic

*L*-functions, which shed new light on the Riemann hypothesis. Moreover, we revealed new connections with the notorious exceptional character issues. Brian Conrey, Kannan Soundararajan and I established that a large percentage of zeros of

*L*-functions rest on the critical line. John Friedlander and I developed extra axioms for sieve theory which allows one to break the parity barrier, and hence to produce prime numbers in sparse sequences. Algebraic and analytic number theory coexists beautifully in my recent work with John Friedlander, Barry Mazur and Karl Rubin on the spin of prime ideals.

In January 1987 I moved from the IAS to Rutgers University accepting the position of New Jersey State Professor of Mathematics. Teaching graduate students at Rutgers is a great pleasure; it relaxes me from the more intense pursuit of research, and it convinces me that the future of my beloved subject, analytic number theory, is bright.

24 September 2015 Hong Kong