Robert Berger (born 1938) is known for inventing the first aperiodic tiling using a set of 20,426 distinct tile shapes.
The unexpected existence of aperiodic tilings, although not Berger's explicit construction of them, follows from another result proved by Berger: that the so-called domino problem is undecidable. This disproves a conjecture of Hao Wang, Berger's advisor, and was published as "The Undecidability of the Domino Problem" in the Memoirs of the AMS in 1966. This paper is essentially a reprint of Berger's 1964 dissertation at Harvard University. Berger's other two committee members were Patrick Carl Fischer and Marvin Minsky. The result is analogous to a 1962 construction used by Kahr, Moore, and Wang, to show that a more constrained version of the domino problem was undecidable.
Berger did his undergraduate studies at Rensselaer Polytechnic Institute, and studied applied physics at Harvard, earning a masters degree, before shifting to applied mathematics for his doctorate. Later, he has worked in the Digital Integrated Circuits Group of the Lincoln Laboratory. In 2009, a paper by Berger and other Lincoln Laboratories researchers, "Wafer-scale 3D integration of InGaAs image sensors with Si readout circuits", won the best paper award at the IEEE International 3D System Integration Conference (3DIC). In 2010, a CMOS infrared imaging device with an analog-to-digital converter in each pixel, coinvented by Berger, was one of R&D Magazine's R&D 100 Award recipients.
Famous quotes containing the word berger:
“When we read a story, we inhabit it. The covers of the book are like a roof and four walls. What is to happen next will take place within the four walls of the story. And this is possible because the story’s voice makes everything its own.”
—John Berger (b. 1926)