Hilda Geiringer
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Hilda Geiringer (28 September 1893 – 22 March 1973), also known as Hilda von Mises and Hilda Pollaczek-Geiringer, was an
Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...
n mathematician.


Life

Geiringer was born in 1893 in
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
, Austria into a
Jewish Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, rel ...
family. Her father, Ludwig Geiringer, was born in
Hungary Hungary is a landlocked country in Central Europe. Spanning much of the Pannonian Basin, Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia and ...
and her mother, Martha Wertheimer, was from Vienna. Her parents had married while her father was working in Vienna as a textile manufacturer.


University of Vienna

While still in high school, Geiringer showed great mathematical ability. Her parents supported her financially so that she could study mathematics at the
University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...
. After receiving her first degree, Geiringer continued her study of mathematics in Vienna. She received her Ph.D. from the
University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...
in 1917 under the guidance of Wilhelm Wirtinger with a thesis entitled "Trigonometrische Doppelreihen" about
Fourier series A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems ...
in two variables. She spent the following two years as Leon Lichtenstein's assistant editing the Jahrbuch über die Fortschritte der Mathematik, a mathematics review journal.


Berlin Institute of Applied Mathematics

In 1921, Geiringer moved to
Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...
where she was employed as an assistant to
Richard Edler von Mises Richard Martin Edler von Mises (; 19 April 1883 – 14 July 1953) was an Austrian scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of ...
at the Institute of Applied Mathematics. In this same year, she married Felix Pollaczek who, like Geiringer, was born in Vienna into a Jewish family and had studied in Berlin. Pollaczek obtained his doctorate in 1922 and went on to work for the Reichspost (Postal service) in Berlin, applying mathematical methods to telephone connections. Hilda and Felix had a child, Magda, in 1922, but their marriage broke up. After the divorce, Geiringer continued working for von Mises and at the same time raised her child. Although trained as a
pure mathematician Pure may refer to: Computing * Pure function * PureSystems, a family of computer systems introduced by IBM in 2012 * Pure Software, a company founded in 1991 by Reed Hastings to support the Purify tool * Pure-FTPd, FTP server software * Pure ...
, Geiringer moved towards
applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...
to fit in with the work being undertaken at the Institute of Applied Mathematics. Her work at this time was on
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
,
probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, and also on the mathematical theory of
plasticity Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Behavioral plasticity, change in an organism's behavior in response to exposur ...
. She submitted a thesis for her Habilitation to qualify as an instructor at the
University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...
, but it was not immediately accepted. Geiringer lost the right to teach at the university in December 1933. In fact, she had been proposed for appointment to the position of extraordinary professor in 1933 but the proposal had been ”put on hold” once the Civil Service Law came into effect two months after
Adolf Hitler Adolf Hitler (20 April 1889 – 30 April 1945) was an Austrian-born German politician who was the dictator of Nazi Germany from 1933 until Death of Adolf Hitler, his suicide in 1945. Adolf Hitler's rise to power, He rose to power as the lea ...
attained power. This law disqualified
Jew Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly inte ...
s from serving as teachers, professors, judges, or in other government positions. Geiringer left Germany after she was dismissed from the University of Berlin, and, with Magda, she went to
Brussels Brussels, officially the Brussels-Capital Region, (All text and all but one graphic show the English name as Brussels-Capital Region.) is a Communities, regions and language areas of Belgium#Regions, region of Belgium comprising #Municipalit ...
. There she was appointed to the Institute of Mechanics and began to apply mathematics to the theory of vibrations.


Istanbul

In 1934, Geiringer followed von Mises to
Istanbul Istanbul is the List of largest cities and towns in Turkey, largest city in Turkey, constituting the country's economic, cultural, and historical heart. With Demographics of Istanbul, a population over , it is home to 18% of the Demographics ...
where she had been appointed as Professor of Mathematics and continued to research in applied mathematics, statistics, and probability theory. While in
Turkey Turkey, officially the Republic of Türkiye, is a country mainly located in Anatolia in West Asia, with a relatively small part called East Thrace in Southeast Europe. It borders the Black Sea to the north; Georgia (country), Georgia, Armen ...
, Geiringer became intrigued with the basic principles of
genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinians, Augustinian ...
formulated by the Augustinian friar
Gregor Mendel Gregor Johann Mendel Order of Saint Augustine, OSA (; ; ; 20 July 1822 – 6 January 1884) was an Austrian Empire, Austrian biologist, meteorologist, mathematician, Augustinians, Augustinian friar and abbot of St Thomas's Abbey, Brno, St. Thom ...
. Between 1935 and 1939, she was preoccupied with uses for the theory of probability to which she and von Mises had made major, early contributions. Arguably Hilda Geiringer was one of the pioneers of what emerged as the burgeoning disciplines bearing such names as
molecular genetics Molecular genetics is a branch of biology that addresses how differences in the structures or expression of DNA molecules manifests as variation among organisms. Molecular genetics often applies an "investigative approach" to determine the st ...
,
human genetics Human genetics is the study of inheritance as it occurs in Human, human beings. Human genetics encompasses a variety of overlapping fields including: classical genetics, cytogenetics, molecular genetics, biochemical genetics, genomics, populatio ...
,
plant genetics Plant genetics is the study of genes, genetic variation, and heredity specifically in plants. It is generally considered a field of biology and botany, but it intersects with numerous life sciences, including molecular biology, evolutionary biolog ...
,
heredity Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic infor ...
in man,
genomics Genomics is an interdisciplinary field of molecular biology focusing on the structure, function, evolution, mapping, and editing of genomes. A genome is an organism's complete set of DNA, including all of its genes as well as its hierarchical, ...
,
bioinformatics Bioinformatics () is an interdisciplinary field of science that develops methods and Bioinformatics software, software tools for understanding biological data, especially when the data sets are large and complex. Bioinformatics uses biology, ...
,
biotechnology Biotechnology is a multidisciplinary field that involves the integration of natural sciences and Engineering Science, engineering sciences in order to achieve the application of organisms and parts thereof for products and services. Specialists ...
,
biomedical engineering Biomedical engineering (BME) or medical engineering is the application of engineering principles and design concepts to medicine and biology for healthcare applications (e.g., diagnostic or therapeutic purposes). BME also integrates the logica ...
, and
genetic engineering Genetic engineering, also called genetic modification or genetic manipulation, is the modification and manipulation of an organism's genes using technology. It is a set of Genetic engineering techniques, technologies used to change the genet ...
, among others. The world has not given sufficient credit to this intelligent woman's pioneering work mainly because it was done in Istanbul and published in Turkish journals.


United States

Following Atatürk’s death in 1938, Geiringer and her daughter went to
Bryn Mawr College Bryn Mawr College ( ; Welsh language, Welsh: ) is a Private college, private Women's colleges in the United States, women's Liberal arts colleges in the United States, liberal arts college in Bryn Mawr, Pennsylvania, United States. Founded as a ...
in
Pennsylvania Pennsylvania, officially the Commonwealth of Pennsylvania, is a U.S. state, state spanning the Mid-Atlantic (United States), Mid-Atlantic, Northeastern United States, Northeastern, Appalachian, and Great Lakes region, Great Lakes regions o ...
in the
United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
, where she was appointed to a lecturer position. In addition to her lecturing duties at Bryn Mawr College, Geiringer undertook, as part of the war effort, classified work for the
United States National Research Council The National Academies of Sciences, Engineering, and Medicine (NASEM), also known as the National Academies, is a congressionally chartered organization that serves as the collective scientific national academy of the United States. The name i ...
. During 1942, she gave an advanced summer course in
mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
at
Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...
in Providence,
Rhode Island Rhode Island ( ) is a state in the New England region of the Northeastern United States. It borders Connecticut to its west; Massachusetts to its north and east; and the Atlantic Ocean to its south via Rhode Island Sound and Block Is ...
, with the aim of raising the American standards of education to the level that had been attained in Germany. She wrote up her outstanding series of lectures on the geometrical foundations of mechanics and, although they were never properly published, these were widely disseminated and used in the United States for many years. To this day, even though Brown University never offered Geiringer permanent employment, the university takes full birthplace credit for these “mimeographed notes.”


Marriage to Richard Edler von Mises

Geiringer and von Mises married in 1943 and, the following year, she left her part-time, low-pay lecturing post at
Bryn Mawr College Bryn Mawr College ( ; Welsh language, Welsh: ) is a Private college, private Women's colleges in the United States, women's Liberal arts colleges in the United States, liberal arts college in Bryn Mawr, Pennsylvania, United States. Founded as a ...
to be nearer to him and because the Wheaton College offered her her first permanent position in the USA. She accepted a post as Professor and Chairman of the Mathematics Department at Wheaton College in
Norton, Massachusetts Norton is a New England town, town in Bristol County, Massachusetts, United States, and contains the villages of Norton Center, Massachusetts, Norton Center and Chartley, Massachusetts, Chartley. The population was 19,202 at the 2020 United Stat ...
. During the week, she taught at the college, then traveled to Cambridge every weekend to be with von Mises. For many reasons, this was not a good arrangement. There were only two members of the mathematics faculty at Wheaton College and Geiringer longed for a situation where she was among mathematicians who were carrying out research.


Discrimination

Geiringer applied for positions at other
New England New England is a region consisting of six states in the Northeastern United States: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont. It is bordered by the state of New York (state), New York to the west and by the ...
universities, but these applications failed due to fairly open discrimination against women. Discrimination against Jewish mathematicians was also a factor. However, she took it all remarkably calmly, believing that if she could do something for future generations of women then she would have achieved something positive. She also never gave up her research while at Wheaton College. In 1953 she wrote: :''"have to work scientifically, besides my college work. This is a necessity for me; I never stopped it since my student days, it is the deepest need of my life."'' One response to a job application she received was quite typical: :''"I am sure that our President would not approve of a woman. We have some women on our staff, so it is not merely prejudice against women, yet it is partly that, for we do not want to bring in more if we can get men."'' On 23 June 1939,
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
’s astronomy professor
Harlow Shapley Harlow Shapley (November 2, 1885 – October 20, 1972) was an American astronomer, who served as head of the Harvard College Observatory from 1921–1952, and political activist during the latter New Deal and Fair Deal. Shapley used Cepheid var ...
wrote on her behalf to
Radcliffe College Radcliffe College was a Women's colleges in the United States, women's Liberal arts colleges in the United States, liberal arts college in Cambridge, Massachusetts, that was founded in 1879. In 1999, it was fully incorporated into Harvard Colle ...
which operated as Harvard’s sister school. Though it drew instructors and other resources from Harvard, Radcliffe graduates were not granted Harvard degrees until 1963. Even though Geiringer was a better mathematician and a better teacher than Harvard could provide to the women at Radcliffe, Geiringer was never offered a real job by either. In a letter dated 7 March 1941,
Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lo ...
, writing in her behalf, stated: ''"You know of course that there is more and more demand for knowledge of statistics in several sciences. It is very desirable that when possible the courses in statistics should be given by people who are well-grounded mathematically as well as interested in its applications. Teachers who satisfy both of these conditions are by no means common."'' He concluded that thought with ''"Mrs. Geiringer is perhaps the only woman who satisfies both conditions."'' Three days later,
Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...
wrote: ''"In her field of applied mathematics, and especially in mathematical statistics, she is a first-rate scholar of great experience and accomplishment."'' He then added, ''"in my opinion applied mathematics, which forms the bridge from abstract mathematics to the more concrete neighbor sciences, has up to now been unduly neglected in this country; that in the present circumstances its importance has increased considerably."'' As late as 28 May 1943 she wrote to Hermann Weyl at the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
at Princeton. “I am certainly conscious of the fact that it is hard for a refugee + woman to find something. Nevertheless I have not quite given up hope. I need not say that a research position would be just as welcome to me as teaching.” “I hope there will be better conditions for the next generations of women,” she wrote. “In the meantime, one has to go on as well as possible.”


Work at Harvard

In 1953,
Richard von Mises Richard Martin Edler von Mises (; 19 April 1883 – 14 July 1953) was an Austrian scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of ...
died and the following year Geiringer, although retaining her job at Wheaton College, began to work at Harvard, completing and editing many of von Mises’ unfinished works, with the help of von Mises' student Geoffrey S. S. Ludford. To do this, however, she had to secure a grant from the
Office of Naval Research The Office of Naval Research (ONR) is an organization within the United States Department of the Navy responsible for the science and technology programs of the U.S. Navy and Marine Corps. Established by Congress in 1946, its mission is to plan ...
and it was then that Harvard offered her a temporary position as a Research Fellow in Mathematics. In the archives at Harvard University, there are eight boxes bearing the caption “MISES, HILDA VON ( Mrs. Richard von Mises, known professionally as Hilda Geiringer ) (Applied Mathematics)” HUG 4574.142. The contents of these boxes involve only professional matters such as her “speeches and variants of published works…a few related letters and two notebooks. Boxes 2 and 3 contain manuscripts relating to published items and have numbers referring to the bibliography in HUG 4574.160.” In 1959, Geiringer was elected a Fellow of the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
. In 1956, the University of Berlin, perhaps to assuage group guilt, perhaps to add a luminary name to its roster, elected her Professor
Emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...
and placed her on full salary. In 1959, she formally retired from Wheaton College and, in the following year, that College honored her with the award of an honorary Doctorate of Science. She was also a Fellow of the
Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts ...
.


See also

* Geiringer–Laman theorem


Footnotes


References

* * *


External links


"The woman who reshaped maths: She fled the Nazis, only to face a new challenge: being accepted in academia", Leila McNeill, October 31, 2019
BBC

Agnes Scott College Agnes Scott College is a Private university, private Women's Colleges in the Southern United States, women's Liberal arts colleges in the United States, liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergra ...
{{DEFAULTSORT:Geiringer, Hilda 1893 births 1973 deaths 20th-century American mathematicians 20th-century Austrian mathematicians 20th-century American women mathematicians 20th-century American women scientists American people of Austrian-Jewish descent American statisticians Austrian Jews Austrian statisticians Austrian women scientists Mathematicians from Austria-Hungary Brown University faculty Fellows of the American Academy of Arts and Sciences Fellows of the Institute of Mathematical Statistics Harvard University people Austrian expatriates in Turkey Expatriate academics in Turkey Academic staff of Istanbul University Jewish scientists Jewish women scientists Scientists from Vienna Wheaton College (Massachusetts) faculty Women statisticians