Robert Berger (mathematician)

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.