The present work owes its development and support to my revered teacher, Prof Dr E Hlawka.

... for the following papers: "On simultaneous approximation of two algebraic numbers by rationals (1967)", "T-numbers do exist (1970)", "Simultaneous approximation to algebraic numbers by rationals (1970)" and "On Mahler's T-numbers (1971)".

In view of his origins from Edmund Hlawka's Vienna school of mathematics it seems to be quite natural that a topic of recurrent interest in Schmidt's scientific activities have been problems from the theory of uniform distribution.

Last winter I was able to extend Roth's famous theorem on rational approximation to an algebraic irrational to simultaneous approximations. I hope you will forgive me if I devote the rest of this lecture to this subject; I had not anticipated this result when I gave the title of my talk in the fall of 1969.

Our present methods for estimating the number of solutions of congruences, equations and inequalities have a number of common features. In particular, these methods involve exponential sums.

Vice-Chancellor,

It is a great honour, as well as a great pleasure, to present to you Wolfgang Schmidt, Distinguished Professor Emeritus of Mathematics at the University of Colorado in Boulder. One of the most gifted, creative and influential mathematicians today, he has made profound and far-reaching contributions to number theory.

Professor Schmidt was born in Vienna where he also received his early education. He studied Mathematics and Physics as an undergraduate and in 1955 obtained his PhD from the University of Vienna. His doctoral work was so revolutionary that a chapter was dedicated to its exposition in J W S Cassels', now classic, monograph "An Introduction to the Geometry of Numbers" published in 1959. He took up his Chair at the University of Colorado, Boulder in 1960, just five years after completing his PhD. He has remained there for his entire career not least because of an abiding passion for hiking and skiing. The mountains and snow conditions in Colorado are unrivalled! He has climbed all of the peaks in Colorado of 14,000 feet or more.

Since his PhD, exactly six decades ago, he has published over 200 research articles, many of them containing spectacular results and breakthroughs in various branches of number theory: Diophantine approximation, geometry of numbers, uniform distribution and normality. Most mathematicians would be happy with fifty in a lifetime! Even more outstanding is the fact that in this century alone, when he was past the age at which most of us would consider retiring, he has published 33 articles, some solving a longstanding open problem on recurrence sequences and some developing the new theory of "parametric' geometry of numbers. In short, Professor Schmidt continues to introduce novel ideas and techniques and produce work at the very highest level. He had told me that he is no longer quite the skier he once was, however.

Three examples of his fantastic creativity and vision that are still influencing current research, in particular at York, are the celebrated Schmidt Subspace Theorem; the axiomatic formulation of Schmidt Games, and the unifying aspect of Regular Systems. Apart from solving important, long-standing problems, Professor Schmidt has been widely influential in formulating new and exciting programmes of research. His conjectures have attracted the attention of many world experts, including some located here. This makes it especially appropriate that the University of York recognises his enormous, enriching and beautiful contributions to mathematics by the award of an honorary doctorate. Some of you graduating here today will have come directly into contact with Professor Schmidt's work - two of his books are recommended texts for our fourth year number theory course. He is a strikingly clear thinker and writer.

Professor Schmidt has received many honours including the American Mathematical Society Cole Prize, the Humboldt Prize and a Guggenheim Fellowship. He is the only mathematician to date to have been awarded the Austrian Decoration for Science and Art and is one of only four mathematicians invited to address the International Congress of Mathematicians three times. In addition, he is a fellow of the National Academy of Sciences, the Polish Academy of Sciences and the American Mathematical Society.

She could laugh about almost any situation. She understood people and how to care for them. She made people happy, whether visiting scholars from all over the world or her beloved neighbours on Ithaca Drive. She volunteered for the homeless and causes for underprivileged populations. She was universally loved.

Although he restricted his studies primarily to the subject of number theory, his works have stimulated the evolution of several other branches of mathematics. For example, Schmidt developed the so-called theory of heights of polynomials. In the late 1980s algebraic geometer Bombieri applied Schmidt's results in order to prove effective assertions concerning the number of rational points of elliptic curves. This happened only a short time after Gerd Faltings had been awarded the Fields Medal, which is the highest award for mathematicians, for his very complicated proof of the finiteness of the number of such points. With the help of Schmidt's theory. Bombieri got more - and in an even easier way. As his assistant, I got to know Wolfgang toward the end of my studies in Vienna, when I was working in a very different - nearly opposite - branch of mathematics. Therefore I was quite amazed when I realized that the Wolfgang Schmidt, whom I had encountered in the bibliography of many publications, turned out to be the famous 'geometer of numbers.' His way of giving lectures is very factual, which corresponds well with the subject he is talking about, yet the most elegant wit of a very great thinker often gratifies the audience. Even in his dissertation, after reading several pages of tricky, hard-to-imagine assessment of the derivation of a new result, one comes across his dry comment, "After more precise consideration ... is capable of considerable improvement."