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 words robert and/or berger:
“You can’t build life the way you put blocks together, Toddy.... Did Knox teach you what makes the blood flow? Did he tell you how thoughts come and how they go, and why things are remembered and forgot?... What makes a thought start?... You don’t know and you’ll never know or understand.... Look, look at yourself. Could you be a doctor, a healing man, with the things those eyes have seen? There’s a lot of knowledge in those eyes, but no understanding.”
—Philip MacDonald, and Robert Wise. Gray (Boris Karloff)
“The heart of Paris is like nothing so much as the unending interior of a house. Buildings become furniture, courtyards become carpets and arrases, the streets are like galleries, the boulevards conservatories. It is a house, one or two centuries old, rich, bourgeois, distinguished. The only way of going out, or shutting the door behind you, is to leave the centre.”
—John Berger (b. 1926)