Julia Robinson

Julia Hall Bowman Robinson (December 8, 1919 – July 30, 1985) was an American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems. Her work on Hilbert's 10th problem (now known as Matiyasevich's theorem or the MRDP theorem) played a crucial role in its ultimate resolution. Robinson was a 1983 MacArthur Fellow.

Julia Hall Bowman Robinson
Julia Robinson in 1975
BornDecember 8, 1919
St. Louis, Missouri, United States
DiedJuly 30, 1985 (aged 65)
Oakland, California, United States
NationalityUnited States
CitizenshipAmerican
Alma materUniversity of California, Berkeley
Known forDiophantine equations
Decidability
Spouse(s)Raphael M. Robinson
AwardsNoether Lecturer (1982)
MacArthur Fellow
Scientific career
FieldsMathematician
InstitutionsUniversity of California, Berkeley
Doctoral advisorAlfred Tarski
InfluencedYuri Matiyasevich

Early years

Robinson was born in St. Louis, Missouri, the daughter of Ralph Bowers Bowman and Helen (Hall) Bowman.[1]:4 Her father owned a machine equipment company while her mother was a school teacher before marriage.[1]:4 Her mother died when Robinson was 2 years old and her father remarried.[1]:4 Her older sister was the mathematical popularizer and biographer Constance Reid and her younger sister is Billie Comstock.[1]:22

When she was 9 years old, she was diagnosed with scarlet fever which was shortly followed by rheumatic fever.[2]: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.[1]:4 She attended San Diego High School and was given an IQ test which she scored a 98, a couple points below average.[2] Nevertheless, Julia stood out in high school as the only female student taking advanced classes in mathematics and physics.[1]:4 She graduated high school with a Bausch-Lomb award for being overall outstanding in science.[3]

In 1936, Robinson entered San Diego State University at the age of 16.[1]:4 Dissatisfied with the mathematics curriculum at San Diego State University, she transferred to University of California, Berkeley in 1939 for her senior year. Before she was able to transfer to UC Berkeley, her father committed suicide in 1937 due to financial insecurities.[1]:5 She took five mathematics courses in her first year at Berkeley[4], one being a number theory course taught by Raphael M. Robinson. She received her BA degree in 1940,[1]:5 and later married Raphael in 1941.[1]:5

Mathematical contributions

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 as a statistics lab assistant by Jerzy Neyman in the Berkeley Statistical Laboratory, where her work resulted in her first published paper, titled "A Note on Exact Sequential Analysis".[1]:5

Robinson received her Ph.D. degree in 1948 under Alfred Tarski with a dissertation on "Definability and Decision Problems in Arithmetic".[3]:14 Her dissertation 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 Gödel's first Incompleteness Theorem.)[5]

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." [6]

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.[7]

In 1950, Robinson first met Martin Davis, then an instructor at the University of Illinois at Urbana-Champaign, who was trying to show that all sets with listability property were Diophantine in contrast to Robinson's attempt to show that a few special sets — including prime numbers and the powers of 2 — were Diophantine. Robinson and Davis started collaborating in 1959 and were later joined by Hilary Putnam, they then showed that the solutions to a “Goldilocks” equation was key to Hilbert's tenth problem.[8]

In 1970, the problem was resolved in the negative; that is, they showed that no such algorithm can exist. Through the 1970s, Robinson continued working with Matiyasevich on one of their solution's corollaries, which she once stated that

there 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.[3]

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.[3]

Game theory

During the late 1940s, Robinson spent a year or so at the RAND Corporation in Santa Monica researching game theory. Her 1949 technical report, "On the Hamiltonian game (a traveling salesman problem),"[9] is the first publication to use the phrase "traveling salesman problem".[10] Shortly thereafter she published a paper called "An Iterative Method of Solving a Game" in 1951.[1]: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.[5]:59

Professorship at UC Berkeley

Robinson was not allowed to teach in the Mathematics Department at Berkeley as there was a rule which prevented family members from working together in the same department after marrying Raphael M. Robinson in 1941.[1] Robinson then instead 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 after the department heard of her nomination to the National Academy of Sciences.[11]

Honors

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.[11] In 1975, she was the first female mathematician to be elected to the National Academy of Sciences.[1]

Robinson was elected the first female president of the American Mathematical Society. It took time for her to accept the nomination, 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."[3]

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. [12] 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.

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.[5][11]

"I don’t remember exactly what happened, but the end result was that Julia involved herself during those years in the nitty-gritty of Democratic Party politics—she registered voters, stuffed envelopes, rang door- bells in neighborhoods where people expected to be paid for their vote. She even served as Alan Cranston’s campaign manager for Contra Costa County when he successfully ran for state controller—his first political office."

— Constance Reid [11]

Robinson was also a volunteer for Adlai Stevenson’s presidential campaigns.[13]

Death and legacy

In 1984, Robinson was diagnosed with leukemia, and she died in Oakland, California, on July 30, 1985.[1][5]

"One of Julia’s last requests was that there be no funeral service and that those wishing to make a gift in her memory contribute to the Alfred Tarski Fund, which she had been instrumental in setting up in honor of her late teacher, friend, and colleague. Modest to the end, she let her character and achievements speak for themselves."

— Solomon Feferman [1]

The Julia Robinson Mathematics Festival sponsored by the American Institute of Mathematics 2013–present and by the Mathematical Sciences Research Institute, 2007–2013, was named in her honor.

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 Society printed a film review[14] and an interview with the director.[15] The College Mathematics Journal also published a film review.[16]

Notes
  1. Feferman, Solomon (1994). "Julia Bowman Robinson, 1919–1985" (PDF). Biographical Memoirs. 63. Washington, DC: National Academy of Sciences. pp. 1–28. ISBN 978-0-309-04976-4. Retrieved 2008-06-18.
  2. Reid, Constance (1986). The Autobiography of Julia Robinson (PDF). The College Mathematics Journal. pp. 3–21. Retrieved 22 November 2018.
  3. "My Collaboration with JULIA ROBINSON". logic.pdmi.ras.ru. Retrieved 2018-08-28.
  4. https://www.nap.edu/read/4560/chapter/21#455
  5. Reid, Constance (1996). Julia: A life in mathematics. Washington, DC: Mathematical Association of America. ISBN 0-88385-520-8.
  6. Robinson, J. (1949). Definability and decision problems in arithmetic. Journal of Symbolic Logic, 14(2), 98-114. doi:10.2307/2266510
  7. Robinson, Julia; Davis, Martin; Putnam, Hilary (1961). The Decision Problem for Exponential Diophantine Equations. Princeton University: Annals of Mathematics.
  8. https://www.sciencenews.org/article/how-julia-robinson-helped-define-limits-mathematical-knowledge
  9. Robinson, Julia (5 December 1949). "On the Hamiltonian game (a traveling salesman problem)" (RM-303). Santa Monica, CA: The Rand Corporation. Retrieved 2 May 2020. Cite journal requires |journal= (help)
  10. Alexander Schrijver's 2005 paper "On the history of combinatorial optimization (till 1960). Handbook of Discrete Optimization (K. Aardal, G.L. Nemhauser, R. Weismantel, eds.), Elsevier, Amsterdam, 2005, pp. 1–68.PS,PDF
  11. Reid, Constance (1996). Being Julia Robinson's Sister. Providence, RI: Notices of the American Mathematical Society. pp. 1486–1492.
  12. "Noether Brochure: Julia Robinson, Functional Equations in Arithmetic". Association for Women in Mathematics. Retrieved 2008-06-18
  13. https://www.sciencenews.org/article/how-julia-robinson-helped-define-limits-mathematical-knowledge
  14. Wood, Carol (May 2008). "Film Review: Julia Robinson and Hilbert's Tenth Problem" (PDF). Notices of the American Mathematical Society. Providence, RI: American Mathematical Society. 55 (5): 573–575. ISSN 0002-9920. Retrieved 2008-06-06.
  15. Casselman, Bill (May 2008). "Interview with George Csicsery" (PDF). Notices of the American Mathematical Society. Providence, RI: American Mathematical Society. 55 (5): 576–578. ISSN 0002-9920. Retrieved 2008-06-06.
  16. Murray, Margaret A. M. (September 2009). "A Film of One's Own". College Mathematics Journal. Washington, DC: Mathematical Association of America. 40 (4): 306–310. ISSN 0746-8342.
gollark: Maybe I need more `ASSERT`s.
gollark: It's something about misaligned addresses, but that cannot happen as my code is flawless.
gollark: no.
gollark: Wow, I've *never* seen a SIGBUS before.
gollark: I don't know why. I'm not even calling `malloc`.

References
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