Biografia
Geiringer was born in Vienna in 1893. It was a time were women were expected to choose marriage over studying. Her parents were of a different opinion and promoted their daughter's education. They sent her to an advanced secondary school and paid for her studies in mathematics and physics at the University of Vienna.
Geiringer obtained her PhD in mathematics in 1917. The year after she published her thesis, in which she tackled advanced trigonometry and developed a general theory for a Fourier series in two variables. It was published on Monatshefte für Mathematik und Physik (Monthly mathematics and physics).
The country gave her few opportunities because she was a Jewish mathematician; luckily, Wirtinger, her mentor during her doctorate, secured her a job in Berlin as a subeditor in the mathematics magazine Jahrbuch über die Fortschritte der Mathematik (Almanac for the progress of mathematics).
In 1921, she became an assistant to Richard von Mises, the new director of the recently inaugurated Institute of Applied Mathematics at the University of Berlin (today's Humboldt University). Six years later, when she was 34, Geiringer was more than an assistant: she was the first "Privadozent" professor at this university. She was the first woman in Germany to hold that position in applied mathematics.
Not long later, at the age of 37, she achieved one of her most relevant contributions in the field of applied mathematics. Although she had been educated in pure mathematics, Geiringer, under von Mises tutelage, became interested in applied mathematics, in particular in the fields of statistics, probability and plasticity.
Von Mises was looking for ways of simplifying differential equations that would determine plastic deformation in metals. Geiringer found a way of combining two conditions into a sole equation, thus simplifying and accelerating the process to calculate the deformation. They are known as the Geiringer equations. With them, Geiringer became a co-developer of the lineal movement theory, a series of simplification techniques that analyse the conditions of metal deformation.
In 1933, Geiringer's talent was finally recognized: she was appointed teaching assistant. That same year, however, the Nazi party took over German politics. The party put into force a series of laws to deprive Jews from their rights. One of these laws forbid "non-Aryan" people from holding jobs at a government institution. Geiringer, just as many other Jews, lost her position at the University.
She moved to Istanbul with her daughter Magda, offspring of her marriage to another mathematician. During that time, the president of Turkey, Mustafa Kemal Ataturk, was introducing national reforms to modernize the country and the education in the period after the independence of the Ottoman Empire. This meant welcoming around 200 German intellectuals, like von Mises and Geiringer. Von Mises was appointed chair of mathematics in the newly founded University of Istanbul. Geiringer became a teacher with a five-year contract. Geiringer prospered in Istanbul. There, she investigated many fields, published 19 articles in English and even a calculus manual in Turkish.
Turkish professors started to replace Jewish refugees in the University, and Geiringer was one of the teachers replaced.
Her contract was not renewed and von Mises did not want to stay at the University without her. Her situation became more precarious when Ataturk died in 1938 and many of the protections and reforms that were given to Jews disappeared. Geiringer and von Mises left the country because they felt they were not safe any more.
They intended to move to the United States, were scientists like Albert Einstein and Oswald Veblen tried to find a place for their colleagues. But emigrating to the United States was not an easy task: they had a strict annual quota and in 1939, they had already fulfilled it. However, people that could secure a job in an American university, could emigrate with a visa not bound to the immigration quota. These visas were specially hard to get for women, and Geiringer was not an exception. Von Mises secured himself a job at Harvard University and, therefore, a visa; but she did not.
With no job or place to stay and with a German passport, Geiringer was left stranded. Von Mises, along with Einstein and Veblen, got Bryn Mawr, Pennsylvania school for women, to offer her a teaching job. It was unpaid, but Geiringer accepted nonetheless. In doing so, her daughter and her were given a visa.
In 1943, she married Richard von Mises, who was then a Harvard professor. Geiringer worked at Bryn Mawr for five years. During that time, she looked for a job at a university, but despite being a skilled professional and the fact that there was a high demand for applied mathematics in the United States, she did not find a job because she was a woman.
The reply she received after applying for a job at Tufts University evidences the reason why she could not find a job: "It is not only that there is prejudice against women, but it is partially, because we do not want to bring in more women until there are no men."
In 1944, Geiringer was appointed chair of the mathematics department at Wheaton College, another college for women in Norton, Massachusetts. "Women were more likely to be hired by colleges for women and not by universities", Leff claims. Colleges for women offered essential opportunities to women, both professors and students.
But, as Leff points out: "They were colleges", which meant that they did not conduct the complex investigations that Geiringer was carrying out in universities. Her research projects were outside her college obligations and, generally, unpaid.
Geiringer never found an American university that would give her a position similar to the ones she held in Germany or Turkey. After taking the job at Wheaton, Geiringer wrote to von Mises: "I hope that future generations of women are given better conditions. Meanwhile, I will carry on the best I can". And so she did. She stayed at Wheaton, where she was offered an honorary PhD in mathematics, until she retired in 1959. That same year, she was appointed member of the American Academy of Arts and Sciences.
She continued investigating in her free time, but her most significant project was compiling, editing and publishing two editions of the book that von Mises left unfinished after his death in 1953: "Probability, Statistics, and Truth" (1964) and "Mathematical Theory of Probability and Statistics" (1957).
However, Geiringer did not exactly get what she expected. In 1953, she wrote: "I have to do my scientific research on top of my job at the university. It is something that I need to do and that I have never stopped doing since I was a student", she never gave up that profound need she had in her life.
McNeil, Leila (2019). “La turbulenta vida de Hilda Geiringer, la olvidada y genial mujer que revolucionó las matemáticas”, in BBC News. Retrieved on 01/02/2022, https://www.bbc.com/mundo/vert-fut-50503128
