Dorothy Maharam Stone (July 1, 1917 – September 27, 2014) was an American mathematician born in

Parkersburg, West Virginia Parkersburg is a city in and the county seat of Wood County, West Virginia, Wood County, West Virginia. Located at the confluence of the Ohio River, Ohio and Little Kanawha River, Little Kanawha rivers, it is the state's fourth-largest city and ...

, who made important contributions to

measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...

and became the namesake of Maharam's theorem and Maharam algebra.

Life

Maharam earned her B.S. degree at

Carnegie Institute of Technology Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

in 1937 and her Ph.D. in 1940 under Anna Johnson Pell Wheeler from

Bryn Mawr College Bryn Mawr College ( ; Welsh: ) is a women's liberal arts college in Bryn Mawr, Pennsylvania. Founded as a Quaker institution in 1885, Bryn Mawr is one of the Seven Sister colleges, a group of elite, historically women's colleges in the United St ...

with a dissertation entitled ''On measure in abstract sets''. Part of her thesis was published in the

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...

. Then she went on to a postdoc 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 ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

, where she first met fellow mathematician

Arthur Harold Stone Arthur Harold Stone (30 September 1916 – 6 August 2000) was a British mathematician born in London, who worked at the universities of Manchester and Rochester, mostly in topology. His wife was American mathematician Dorothy Maharam. Stone s ...

. They married in April 1942. Stone and Maharam both lectured at various universities in the US and the United Kingdom and were faculty at the

University of Rochester The University of Rochester (U of R, UR, or U of Rochester) is a private research university in Rochester, New York. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The University of Roc ...

for many years. She was an invited speaker at a

conference at

Northern Illinois University Northern Illinois University (NIU) is a public research university in DeKalb, Illinois. It was founded as Northern Illinois State Normal School on May 22, 1895, by Illinois Governor John P. Altgeld as part of an expansion of the state's system ...

in 1980. Their two children, David and Ellen, both became mathematicians as well. She retired in 2001. Her husband, Arthur Stone, died August 6, 2000, and her son, David Stone, died August 27, 2014. She died a month later in

Brookline, Massachusetts Brookline is a town in Norfolk County, Massachusetts, Norfolk County, Massachusetts, in the United States, and part of the Greater Boston, Boston metropolitan area. Brookline borders six of Boston's neighborhoods: Brighton, Boston, Brighton, A ...

and was buried at Kehillath Jacob Cemetery in

West Roxbury West Roxbury is a neighborhood in Boston, Massachusetts bordered by Roslindale and Jamaica Plain to the northeast, the town of Brookline to the north, the cities and towns of Newton and Needham to the northwest and the town of Dedham to the ...

Contributions

Maharam pioneered the research of

finitely additive In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, \mu(A \cup B) = \mu(A) + \mu(B). If this additivity ...

measures on integers. Maharam's theorem about the decomposability of complete measure spaces plays an important role in the theory of

Banach space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...

s. Maharam published it in the ''

Proceedings of the National Academy of Sciences of the United States of America ''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Scien ...

'' in 1942. Another paper of Maharam, in 1947 in the ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...

'', introduced Maharam algebras, which are complete Boolean algebras with continuous submeasures.

Recognition

Maharam was named 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 1976.

References

{{DEFAULTSORT:Maharam, Dorothy 1917 births 2014 deaths 20th-century American mathematicians 21st-century American mathematicians American women mathematicians 20th-century American women scientists 20th-century women mathematicians 21st-century women mathematicians Institute for Advanced Study people Carnegie Mellon University alumni Bryn Mawr College alumni University of Rochester faculty People from Parkersburg, West Virginia Mathematicians from West Virginia Fellows of the American Association for the Advancement of Science 21st-century American women