Are there unsolved problems about numbers?
A public lecture
Barry Mazur, Harvard University
May 3, 2005 at 7pm
Stata Center, MIT
32 Vassar Street, Cambridge
Are there unsolved problems about numbers? The answer is yes, and we will discuss one of the most famous of these open problems, the Riemann hypothesis, which is about the hidden structure of the prime numbers 2, 3, 5, 7, ... . Primes are the "building blocks" of all numbers, and are key actors in a subject, central to mathematics, initiated two millennia ago by the Greeks.
Primes seem to be, at the same time very irregularly distributed among all numbers, and yet— if squinted at from a sufficiently far distance—they reveal an astoundingly elegant pattern. In 1859 the German mathematician Bernard Riemann proposed a way of understanding and refining that pattern. His hypothesis (announced in the manuscript pictured on the right) has wide-ranging implications, but to this day we don't know if it is correct. The Riemann Hypothesis, is one of the Clay Mathematics Institute's $1 million Millennium Prize Problems.
Prof. Mazur's lecture will be accessible to the general interested public. No calculus is required.
Photos of Riemann's 1859 manuscript courtesy of of the Niedersächsische Staats- und Universitätsbibliothek Göttingen. Go here for the full facsimilie.