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Julia Robinson
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Career
Hilbert's Tenth Problem
Hilbert's tenth problem asks for an algorithm to determine whether a Diophantine equation has any solutions in integers. Robinson began exploring methods for this problem in 1948 while at the RAND Corporation. Her work regarding Diophantine representation for exponentiation and her method of using Pell's equation led to the J.R. hypothesis (named after Robinson) in 1950. Proving this hypothesis would be central in the final solution. Her research publications would lead to collaborations with Martin Davis, Hilary Putnam, and Yuri Matiyasevich.BOOK, The Decision Problem for Exponential Diophantine Equations, Robinson, Julia, Davis, Martin, Putnam, Hilary, 1961, Annals of Mathematics, Princeton University, In 1970, the problem was resolved in the negative; that is, they showed that no such algorithm can exist. Through the 1970's, Robinson continued working with Matiyasevich on one of their solution's corollaries, which stated thatthere is a constant N such that, given a Diophantine equation with any number of parameters and in any number of unknowns, one can effectively transform this equation into another with the same parameters but in only N unknowns such that both equations are solvable or unsolvable for the same values of the parameters.WEB,weblink My Collaboration with JULIA ROBINSON, logic.pdmi.ras.ru, 2018-08-28, At the time the solution was first published, the authors established N = 200. Robinson and Matiyasevich's joint work would produce further reduction to 9 unknowns."Hilbertâ€™s tenth problem asks in essence whether the set D is decidable. The answer is negative. In contrast, we can show that D is Turing-recognizable. Before doing so, letâ€™s consider a simpler problem. It is an analog of Hilbertâ€™s tenth problem for polynomials that have only a single variable, such as 4x3 âˆ’2x2 + x âˆ’ 7. Let D1 = {p| p is a polynomial over x with an integral root}.Here is a TM M1 that recognizes D1: M1 = 'On input âŸ¨pâŸ©: where p is a polynomial over the variable x. '1.' Evaluate p with x set successively to the values 0, 1, âˆ’1, 2, âˆ’2, 3, âˆ’3, . .. If at any point the polynomial evaluates to 0, accept ."BOOK,weblink Introduction to the theory of computation, Michael., Sipser,, 2013, Cengage Learning, 9781133187790, 3rd, Boston, MA, 761858892, George Csicsery produced and directed a one-hour documentary about Robinson titled Julia Robinson and Hilbert's Tenth Problem, that premiered at the Joint Mathematics Meeting in San Diego on January 7, 2008. Notices of the American Mathematical Societyprinted a film reviewJOURNAL, Wood, Carol, Carol S. Wood, May 2008, Film Review: Julia Robinson and Hilbert's Tenth Problem,weblink PDF, Notices of the American Mathematical Society, Providence, RI, American Mathematical Society, 55, 5, 573â€“575, 0002-9920, 2008-06-06, and an interview with the director.JOURNAL, Casselman, Bill, May 2008, Interview with George Csicsery,weblink PDF, Notices of the American Mathematical Society, Providence, RI, American Mathematical Society, 55, 5, 576â€“578, 0002-9920, 2008-06-06, The College Mathematics Journalalso published a film review.JOURNAL, Murray, Margaret A. M., September 2009, A Film of One's Own, College Mathematics Journal, Washington, DC, Mathematical Association of America, 40, 4, 306â€“310, 0746-8342,RAND Corporation
During the late 1940s, Robinson spent a year or so at the RAND Corporation in Santa Monica researching game theory which led to her published paper called "An Interactive Method of Saving a Game" in 1951.ENCYCLOPEDIA, Feferman, Solomon, Solomon Feferman, Biographical Memoirs, Julia Bowman Robinson, 1919â€“1985,weblink PDF, 2008-06-18, 1994, National Academy of Sciences, 63, Washington, DC, 978-0-309-04976-4, 1â€“28, {{Rp|7}} In her paper, she proved that the fictitious play dynamics converges to the mixed strategy Nash equilibrium in two-player zero-sum games. This was posed by George W. Brown as a prize problem at RAND Corporation.{{Rp|59}}Rational Number Theory Thesis
Robinson's Ph.D. thesis, "Definability and Decision Problems in Arithmetic," showed that the theory of the rational numbers was an undecidable problem, by demonstrating that elementary number theory could be defined in terms of the rationals. (Elementary number theory was already known to be undecidable by GÃ¶del's first Incompleteness Theorem.Here is an excerpt from her thesis:"This consequence of our discussion is interesting because of a result of Godel which shows that the variety of relations between integers (and operations on integers) which are arithmetically definable in terms of addition and multiplication of integers is very great. For instance from Theorem 3.2 and Godel's result, we can conclude that the relation which holds between three rationals A, B, and N if and only if N is a positive integer and A=BN is definable in the arithmetic of rationals." Robinson, J. (1949). Definability and decision problems in arithmetic. Journal of Symbolic Logic, 14(2), 98-114. doi:10.2307/2266510Statistical Sequential Analysis
Julia Robinson's very first paper was published in 1948 titled "A Note on Exact Sequential Analysis" which was a product of her time as a statistics lab assistant under Jerzy Neyman at Berkeley.{{Rp|7}}Professorship at UC Berkeley
After marrying Raphael M. Robinson in 1941, she was not allowed to teach at in the Mathematics Department at Berkeley as there was a rule which prevented family members from working together in the same department. Instead, she stayed in the statistics department despite wanting to teach calculus. Although Raphael retired in 1973, it wasn't until 1976 she was offered a full time professorship position at Berkeley only after the department heard of her nomination to the National Academy of Sciences.Eduction
In 1936, she entered San Diego State University at the age of 16.{{Rp|4}} Dissatisfied with the mathematics curriculum at San Diego State University, she transferred to University of California, Berkeley in 1939 for her senior year and received her BA degree in 1940.{{Rp|5}}After graduating, Robinson continued in graduate studies at Berkeley. As a graduate student, Robinson was employed as a teaching assistant with the Department of Mathematics and later by Jerzy Neyman in the Berkeley Statistical Laboratory, where her work resulted in her first published paper.{{Rp|5}} Robinson received her Ph.D. degree in 1948 under Alfred Tarski with a dissertation on "Definability and Decision Problems in Arithmetic".{{Rp|14}}Honors
U.S. National Academy of Sciences
After Robinson solved Hilbert's tenth problem, Saunders Mac Lane nominated her for the National Academy of Sciences. Alfred Tarski and Jerzy Neyman also flew out to Washington, D.C. to further explain to the NAS why her work is so important and how it tremendously contributed to mathematics. In 1975, she was the first female mathematician to be elected to the National Academy of Sciences.American Mathematical Society
Julia was elected the first female president of the American Mathematical Society. It took time for her to accept the nominated, stated in her autobiography:"In 1982 I was nominated for the presidency of the American Mathematical Society. I realized that I had been chosen because I was a woman and because I had the seal of approval, as it were, of the National Academy. After discussion with Raphael, who thought I should decline and save my energy for mathematics, and other members of my family, who differed with him, I decided that as a woman and a mathematician I had no alternative but to accept. I have always tried to do everything I could to encourage talented women to become research mathematicians. I found my service as president of the Society taxing but very, very satisfying."Julia Robinson Mathematics Festival
The Julia Robinson Mathematics Festival sponsored by the American Institute of Mathematics 2013â€“present and by the Mathematical Sciences Research Institute, 2007â€“2013, was named in her honor.Other notable honors
In 1982, Robinson was given the Noether award through the Association for Women in Mathematics and did a lecture series called Functional Equations in Arithmetic. "Noether Brochure: Julia Robinson, Functional Equations in Arithmetic". Association for Women in Mathematics. Retrieved 2008-06-18 Around this time she also was given the MacArthur Fellowship Prize of $60,000. In 1985, she also became a member of the American Academy of Arts and Sciences.Personal life
Early years
Robinson was born in St. Louis, Missouri, the daughter of Ralph Bowers Bowman and Helen (Hall) Bowman.{{Rp|4}} When she was 9 years old, she was diagnosed with scarlet fever which was shortly followed by rheumatic fever.BOOK,weblink The Autobiography of Julia Robinson, Reid, Constance, 1986, The College Mathematics Journal, 3â€“21, 22 November 2018, {{Rp|4}} This caused her to miss two years of school. When she was well again, she was privately tutored by a retired primary school teacher. In just one year, she was able to complete fifth, sixth, seventh, and eighth year curriculum.{{Rp|4}} She attended San Diego High School and was given an IQ test which she scored a 98, a couple points below average.{{Rp|8}} Despite her below average IQ score, Julia stood out in high school as the only female student taking advanced classes in mathematics and physics.{{Rp|4}} She graduated high school with a Bausch-Lomb award for being overall outstanding in science.Family
Her father owned a machine equipment company while her mother was a school teacher before marriage.{{Rp|4}} Her mother passed away at the age of 2 and her father remarried.{{Rp|4}} Her older sister was the mathematical popularizer and biographer Constance Reid and her younger sister is Billie Comstock.{{Rp|22}}Before Julia was able to transfer to UC Berkeley, her father committed suicide in 1937 due to financial insecurities.{{Rp|5}} During her first year at Berkeley, she took a number theory course taught by Raphael M. Robinson. She later married Raphael in 1941.{{Rp|5}}Death
In 1984, Robinson was diagnosed with leukemia, and she passed away in Oakland, California, on July 30, 1985.Political work
In the 1950s Robinson was active in local Democratic party activities. She was Alan Cranston's campaign manager in Contra Costa County when he ran for his first political office, state controller.BOOK, Julia: A life in mathematics, Reid, Constance, Mathematical Association of America, 1996, 0-88385-520-8, Washington, DC, BOOK, Being Julia Robinson's Sister, Reid, Constance, Notices of the American Mathematical Society, 1996, Providence, RI, 1486â€“1492,Notes
{{Reflist}}References
- {{DSB |first=Martin |last=Davis |title=Robinson, Julia Bowman |volume=24 |pages=265â€“268}}
- JOURNAL, Matijasevich, Yuri, My collaboration with Julia Robinson,weblink 10.1007/BF03024472, 1992, The Mathematical Intelligencer, 0343-6993, 14, 4, 38â€“45, 1188142, .,
External links
- "Julia Bowman Robinson", Biographies of Women Mathematicians, Agnes Scott College
- {{MacTutor Biography|id=Robinson_Julia}}
- {{MathGenealogy|id=32658}}
- Julia Bowman Robinson on the Internet (weblink" title="web.archive.org/web/20050319230207weblink">mirror)
- {{YouTube |e4x9XKNAYjU | Trailer for Julia Robinson and Hilbert's Tenth Problem}}
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