Richard M. Friedberg

Richard M. Friedberg is a theoretical physicist who has contributed to a wide variety of problems in mathematics and physics. These include mathematical logic, number theory, solid state physics, general relativity^[1], particle physics, quantum optics, genome research^[2], and the foundations of quantum physics^[3].

Works of Richard Friedberg

Friedberg's most well-known work dates back to mid 1950s, when he was an undergraduate at Harvard. He published several papers over a period of 2-3 years^[4][5][6][7]. The first, Two Recursively Enumerable Sets^[4] introduced a trick called the priority method, which became a fundamental technique in the subject.

In 1968, Friedberg proved independently what became known as Bell’s inequality, not knowing that J. S. Bell had proved it a few years earlier. He showed it to the physicist and historian Max Jammer, who somehow managed to insert it into his book “The Conceptual Development of Quantum Mechanics”^[8], although the latter bears the publication date 1966. This caused Friedberg some embarrassment later when classmates at Harvard, knowing of the result only through Jammer’s book, supposed that Friedberg was the first discoverer. (A letter from Friedberg to Jammer dated May 1971 begins, “It was nice of you to remember what I showed you in 1968. I finally got around to writing it up in 1969, but just then I found out about Bell’s 1964 paper (Physics 1, 195) which had anticipated my ‘discovery’ by three years. So I did not publish.”) For last couple of years, Friedberg and Hohenberg (who passed away on Dec 15, 2017) collaborated on Foundations of Quantum Mechanics ^[9].

Friedberg is also known for his love of music and poetry. He wrote poems in several letters ^{[10] [11] [12] [13]} that he wrote to Douglas Hofstadter in 1989. The last letter contains two sonnets ”The Electromagnetic Spectrum” and "Fermions and Bosons".(Hofstadter replied about two years later.) These letters include a very in-depth critique and analysis of topics in Metamagical Themas – a collection of articles that Hofstadter wrote for the popular science magazine Scientific American during the early 1980s.

Friedberg wrote a popular-level book on Number theory -- "An Adventurer’s Guide to Number Theory" (New York, Mc Graw-Hill, 1968; reissued by Dover Publications, Inc. (1994)}. He writes in the book -- ``The difference between the theory of numbers and arithmetic is like the difference between poetry and grammar".

Early life

Friedberg was born in Manhattan on Oct 8, 1935. His father, Charles K. Friedberg, was a renowned cardiologist whose book “Diseases of the Heart”, published by W.B. Saunders (1949, 1956, 1966), was translated into many languages and became the undisputed ”bible” for its thorough explication of physiologic mechanisms combined with its straightforward clinical advice to physicians, drawn from the author’s own practice. His mother, Gertrude Tonkonogy, wrote a play, “Three-Cornered Moon”, whose success on Broadway in 1933 was felt to have “rescued” a season in which the theatrical world was uncertain whether any play would draw audiences in the depth of the Great Depression.

Selected Published Works

• "Two Recursively Enumerable Sets Not Recursive in Each Other", Richard Friedberg, Proc. Nat. Acad. Sci. vol. 43, p. 236 (1957) [communicated by K. Gödel]. doi:10.1073/pnas.43.2.236
• "A criterion for completeness of degrees of unsolvability", Richard. M. Friedberg, Journal of Symbolic Logic, Volume 22, Issue 2 June 1957, pp. 159-160.
• "A Learning Machine: Part I", R.M. Friedberg, IBM Journal of Research and Development (Volume: 2, Issue: 1, Jan. 1958).
• "Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication", Richard M. Friedberg, Journal of Symbolic Logic, Volume 23, Issue 3 September 1958, pp. 309-316.
• "Dual Trees and Resummation Theorems", R. Friedberg, J. Math. Phys. vol. 16, p 20 (1974). Bibcode: 1975JMP....16...20F
• "The Electrostatics and Magnetostatics of a Conducting Disc", R. Friedberg, Am. J. Phys vol. 61, p.1084 (1993).
• "Path Integrals in Polar Variables with Spontaneously Broken Symmetry", R. Friedberg, J. Math Phys. vol. 36, p. 2675 (1995). doi:10.1063/1.531360
• "Derivation of Regge’s Action from Einstein’s Theory of General Relativity", R. Friedberg and T. D. Lee, Nucl. Phys. B 242, 145 (1984).
• "Frequency Shifts in Emission and Absorption by Resonant Systems of Two-Level Atoms", (with S. R. Hartmann and J. T. Manassah), Phys. Reports 7C, 101 (1973).
• "Efficient Sorting of Genomic Permutation by Translocation, inversion and block interchange" S. Yancopoulos, O. Attie, Friedberg, Bioinformatics vol. 21, pp 3352-59 (2005). doi:10.1093/bioinformatics/bti535

References