Robert Berger (mathematician)
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.
- Darling, David J. (2004). The universal book of mathematics: from Abracadabra to Zeno's paradoxes. John Wiley and Sons. pp. 18–. ISBN 978-0-471-27047-8. Retrieved 29 September 2011.
- Berger, Robert (1966), "The Undecidability of the Domino Problem", Memoirs of the American Mathematical Society 66: 72 pp., doi:10.1090/memo/0066.
- Robert Berger at the Mathematics Genealogy Project.
- Büchi, J. R.. "The undecidability of the domino problem". Mathematical Reviews 36 (49). MR 0216954.
- Author biography from Raffel, J. I.; Mann, J. R.; Berger, R.; Soares, A. M.; Gilbert, S. (1989), "A generic architecture for wafer-scale neuromorphic systems", The Lincoln Laboratory Journal 2 (1): 63–76.
- Awards and Recognition, Lincoln Laboratory Annual Report 2010, p. 50, retrieved 2011-09-30.
- MIT Lincoln Laboratory receives five R&D 100 Awards, Lincoln Laboratory, retrieved 2011-09-30.
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