Marian Boykan Pour-El (April 29, 1928 – June 10, 2009) was an American

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

ian who did pioneering work in

computable analysis In mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with the parts of real analysis and functional analysis that can be carried out in a compu ...

Early life and education

Marian Boykan was born in 1928 in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

; her parents were dentist Joseph Boykan and his wife Matilda (Mattie, née Caspe), a former laboratory technician and housewife. As a young girl, she performed ballet at the Metropolitan Opera House, and this influenced her later life where she was often more comfortable speaking before large audiences than in small groups. Although she wanted to attend the Bronx High School of Science, it was at that time only for boys; instead, she went to a girls' school,

Hunter College High School Hunter College High School is a secondary school located in the Carnegie Hill neighborhood on the Upper East Side of Manhattan. It is administered by Hunter College of the City University of New York (CUNY). Hunter is publicly funded, and there i ...

. Her parents were unwilling to pay the tuition for private college for her, so she went to

Hunter College Hunter College is a public university in New York City. It is one of the constituent colleges of the City University of New York and offers studies in more than one hundred undergraduate and postgraduate fields across five schools. It also admi ...

, an inexpensive local higher-education establishment primarily aimed at training schoolteachers. There she earned a bachelor's degree in physics in 1949. She also completed enough courses in mathematics for a second major but was not allowed to have two majors by Hunter College's rules. She was accepted to

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

for graduate studies in mathematics, with full support, as the only woman in the program. At Harvard, she earned a master's degree in 1951 and a Ph.D. in mathematical logic in 1958. She was very isolated and lonely at Harvard, with few friends and, initially, no other students even willing to sit next to her in her classes. The nearest restroom to her classes was in a different building, and one of the few buildings with air conditioning in the summers was off-limits to women, even when she was assigned as an instructor to a class in that building. Because there were no logicians at Harvard at that time, she spent five years of her time as a visiting student at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. Her doctoral dissertation was ''Computable Functions''.

Career

After finishing her doctorate, Pour-El joined the mathematics faculty at

Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsylvan ...

. She earned her tenure there in 1962. During a sabbatical from 1962 to 1964 at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, she worked with

Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imme ...

. She moved in 1964 to the

University of Minnesota The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Tw ...

, and was promoted to full professor there in 1968. Except for a year from 1969 to 1970 as a visiting professor at the

University of Bristol , mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type ...

, she remained at the University of Minnesota until her retirement in 2000. At Minnesota, her doctoral students included

Jill Zimmerman Jill Loraine Zimmerman (born 23 March 1959) is an American computer scientist and the James M. Beall Professor of Mathematics and Computer Science at Goucher College. Since 2006, she has been the head of the Goucher Robotics Lab. Early life an ...

(Ph.D. 1990), later the James M. Beall Professor of Mathematics and Computer Science at Goucher College, Maryland.

Contributions

Pour-El's early work concerned recursion theory, and included joint work with William Alvin Howard,

Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emerit ...

Donald A. Martin Donald Anthony Martin (born December 24, 1940), also known as Tony Martin, is an American set theorist and philosopher of mathematics at UCLA, where he is an emeritus professor of mathematics and philosophy. Education and career Martin rece ...

, and

Hilary Putnam Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century. He made significant contributions ...

. In a 1974 publication, she studied analogues of computability for analog computers. She proved that, for her formulation of this problem, the functions that can be computed by such computers are the same as the functions that define solutions to

algebraic differential equation In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the concept of differential algebra used. The intention is to in ...

s. This result, a refinement of the work of

Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-o ...

, became known as the Shannon–Pour-El thesis. In the late 1970s Pour-El began working on

. Her "most famous and surprising result", co-authored with Minnesota colleague J. Ian Richards, was that for certain computable

initial condition In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). For ...

s, determining the behavior of the

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...

is an undecidable problem. Their result was later taken up by

Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fello ...

in his book ''

The Emperor's New Mind ''The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics'' is a 1989 book by the mathematical physicist Sir Roger Penrose. Penrose argues that human consciousness is non-algorithmic, and thus is not capable of being modeled ...

''; Penrose used this result as a test case for the

Church–Turing thesis In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of comp ...

, but concluded that the non-

smoothness In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it ...

of the initial conditions makes it implausible that a computational device could use this phenomenon to exceed the limits of conventional computing. Freeman Dyson used the same result to argue for the evolutionary superiority of analog to digital forms of life. With Richards, Pour-El was the author of a book, '' Computability in Analysis and Physics''.

Recognition

Pour-El was elected to the Hunter College Hall of Fame in 1975, and as a Fellow of the

American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is an American international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific respons ...

in 1983. A symposium was held in honor of Pour-El in Japan in 1993.

Personal life

As a student at Berkeley, Pour-El met her husband, Israeli biochemist Akiva Pour-El. They had one daughter, Ina. Her husband followed her to Penn State after completing his doctorate a year later, and he later followed her, again, when she moved to Minnesota. They lived separately for several long intervals, most notably from 1969 to 1975 when her husband taught in Illinois, and Pour-El wrote an article in 1981 on how having a long-distance relationship worked for her. Pour-El's brother is music composer Martin Boykan.

Selected publications

References

{{DEFAULTSORT:Pour-El, Marian 1928 births 2009 deaths 20th-century American mathematicians American women mathematicians Mathematical logicians Women logicians Hunter College alumni Harvard University alumni Pennsylvania State University faculty Fellows of the American Association for the Advancement of Science People from New York City 20th-century American women 21st-century American women