Escher and the Droste effect

A public lecture

Hendrik Lenstra, Mathematics Institute, Leiden University
October 25, 2005 at 7pm
Science Center, Harvard University
One Oxford Street, Cambridge

In 1956, the Dutch graphic artist M.C. Escher made an unusual lithograph with the title `Print Gallery'. It shows a young man viewing a print in an exhibition gallery. Amongst the buildings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden `Droste effect', or infinite repetition; but this is brought to light by a mathematical analysis of the studies used by Escher. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank.

Hendrik W. Lenstra jr. received his Ph.D. in mathematics from the Universiteit van Amsterdam in 1977. He was a full Professor at Amsterdam from 1978 until 1986, at Berkeley from 1987 until 2003, and since 1998 at the Universiteit Leiden in the Netherlands. Lenstra is active in number theory and algebra. He is best known for introducing advanced techniques in the area of number-theoretic algorithms. These have important applications in the areas of cryptography and computer security. Lenstra has been a member of the Royal Dutch Academy of Science since 1984, and a fellow of the American Academy of Arts and Sciences since 1996. He is a recipient of the Fulkerson Prize of the American Mathematical Society and the Mathematical Programming Society (1985). During the academic year 1990/1991, he was Distinguished Visiting Professor at the Institute for Advanced Study in Princeton, and in 2000/2001 he held the Hewlett-Packard Visiting Research Professorship at the Mathematical Sciences Research Institute in Berkeley. In 1998 he won the Spinoza Award, which constitutes the highest scientific honor in the Netherlands.

Clay Public Lectures

The aim of this lecture series is to increase the awareness and understanding of mathematics — in the public at large as well as in the business, scientific and university communities.

Past Lectures:

The Music of the Primes Marcus du Sautoy of Oxford University, MIT, Compton Laboratories, May 8, 2008

Technology-driven Statistics Terry Speed of UC Berkeley, and WEHI, Harvard University Science Center, October 30, 2007

Surfing with Wavelets Ingrid Daubechies of Princeton University, MIT, Stata Center, April 10, 2007

Beyond Computation Michael Sipser of MIT. Harvard University, October 3, 2006

Mathematics and Magic Tricks Persi Diaconis of Stanford University. MIT, April 25, 2006

Escher and the Droste effect Hendrik Lenstra of Leiden University. Harvard, October 25, 2005

Are there unsolved problems about numbers? Barry Mazur, Harvard University. May 3, 2005

Four thousand years of mathematics in images Bill Casselman, University of British Columbia. April 26, 2005

Is there such a thing as infinity? Timothy Gowers, Cambridge University. March 22, 2004.
Lecture notes