My aim

Fields Medallist W. T. Gowers in his essay THE IMPORTANCE OF MATHEMATICS (see References) - the keynote address at a Clay-funded millennium meeting in Paris - wrote: The percentage of the world's population, or even of the world's university-educated polulation, who could accurately state a single mathematical theorem proved in the past fifty years, is small, and smaller still if Fermat's last theorem [proved by Andrew Wiles] is excluded.

W.T.G.'s comment echoes a rebuke of Robert L. Devaney to the mathematical community. In the Preface to his Chaos, Fractals, and Dynamics (Computer Experiments in Mathematics) Devaney wrote: There are a number of reasons why I have written this book. By far the most important is my conviction that we in mathematics education - whether on the secondary or collegiate level - fail miserably to communicate the vitality of contemporary mathematics to out students. Let's face it: most high school and college mathematics courses emphasize centuries-old mathematics. As a consequence, many students think that mathematics is a dead discipline...

My modest aim this evening is that all in my audience, besides coming to know something of the origins and subsequent development of the theory of transcendental numbers (and the related fields of Diophantine approximations and equations), can accurately state several mathematical theorems proved in the past fifty years (possibly previously unknown to them; don't worry, I won't be giving a test!), and, more importantly, have some notion with respect to the significance of those theorems.