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The woman who reshaped maths, Hacker News

The woman who reshaped maths, Hacker News


When 46 – year-old Hilda Geiringer arrived in New York with her daughter Magda, she must have felt relieved. The year was 1939. And Geiringer, as well as a talented mathematician, was a Jewish woman from Vienna.

For six years, she’d been seeking an escape from the Nazi threat in Europe. In that time, she’d fled to Turkey, been stranded in Lisbon and narrowly escaped internment at a Nazi camp. Her arrival in the US should have opened a new, and far better, chapter.

But it brought other challenges.

The first woman to teach applied mathematics at a German university, Geiringer was known as an innovative thinker who applied her mathematical insight to other sciences. But in the US, she struggled for decades to regain her status in the field.

This wasn’t because of Geiringer’s talent, or lack thereof: she was part of an early vanguard in 20 th-Century applied mathematics at a time when the field was trying to find institutional legitimacy and independence from pure mathematics. With crucial contributions to mathematical theories of plasticity and to probability genetics, Geiringer helped advance the field of applied mathematics, laying fundamental groundwork which many parts of science and engineering rely upon today.

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But Geiringer’s work was more than her livelihood. It was her calling. “I must work scientifically,” she wrote in a 1953 letter to the president of Wheaton College in Massachusetts. “It is perhaps the deepest need in my life.”

Whether she would be allowed to fulfil that need – and under what circumstances – was, after how she would manage to flee the Nazis, one of the biggest questions of her life.

Different beginnings

Geiringer was born in Vienna in 1893. In a time when women were largely expected to pursue marriage over scholarship, Geiringer’s parents took a different view and encouraged their daughter’s education. They sent her to advanced secondary school, then paid for her study of mathematics and physics at the University of Vienna.

While there, Geiringer studied under some of the most prestigious European mathematicians of the early 20 th Century, including (Ernst Mach) thinkMach speed) and her doctoral mentorWilhelm Wirtinger(known forWirtinger derivatives). She received her doctoral degree in mathematics in 1917; the next year her dissertation, in which she tackled advanced trigonometry and developed a generalized theory for a Fourier series in two variables, was published inMonatshefte für Mathematik und Physik(Mathematics and Physics Monthly).

Despite having nurtured Geiringer’s burgeoning skill and love for mathematics, Vienna held few opportunities for a female Jewish mathematician, so Wirtinger secured a position for her in Berlin as assistant editor of the mathematics journalJarhbuch über die Fortschritte der Mathematik(Almanac for the Progress of Mathematics). In 1921 she became assistant toRichard von Mises, the director of the recently established Institute for Applied Mathematics at the University of Berlin (now Humboldt University of Berlin). And six years later, at the age of 34, Geiringer became more than an assistant: she became the first female lecturer (“Privadozent”) at the university. She was the first woman in Germany to hold such a role in applied mathematics.

Hilda Geiringer, shown here during her time at Wheaton College in Massachusetts, was Germany’s first female lecturer in applied mathematics (Credit: Wheaton College)

It was shortly after, at age 37, that Geiringer made one of her most significant contributions to applied mathematics. Although she was trained as a pure mathematician, Geiringer had become increasingly focused on applied mathematics under von Mises – specifically in the areas of statistics, probability, and plasticity.

Plastic deformation occurs when forces cause an object to be permanently distorted. Von Mises was looking for ways to simplify differential equations that determine plastic deformation in metals.

Geiringer found a way to combine two conditions into a single equation, greatly simplifying and speeding up the process of calculating deformation. This is known now as the Geiringer equations. With her equations, Geiringer became a co-developer of the slip-line theory, a set of simplification techniques that analizes the conditions in metal deformation.

Even today, slip-line theory plays a central role in science and engineering. In safety engineering for bridges, for instance, application of this theory ensures that metals don’t strain beyond their deformation point, preventing bends and breaks.

In 1933, Geiringer’s talent was recognized further when she was nominated for an assistant professor position.

But the Nazi party took over German politics the same year.

Refugee status

The party enacted a flurry of legislation to disenfranchise Jews. One was theLaw for the Restoration of the Professional Civil Service Act, which barred “non-Aryans” from holding positions in government institutions. Along with hundreds of other Jewish intellectuals, Geiringer lost her university position.

Along with her daughter Magda, born from Geiringer’s marriage to a fellow mathematician which had ended in divorce, she needed to leave. After a brief stay in Brussels, she and Magda moved to Istanbul.

At the time, Turkey’s president Mustafa Kemal Ataturk was instituting nationwide reforms to modernize the country and higher education post-independence from the Ottoman Empire. This included welcoming nearly 200 German scholars, among them von Mises and Geiringer. Von Mises was appointed chair of mathematics at the newly founded Istanbul University while Geiringer became professor with a five-year contract.

Mustafa Kemal Ataturk, shown here in 1926, led reforms that included welcoming nearly 200 German scholars to Turkey – including Geiringer (Credit: Getty Images)

Geiringer thrived in Istanbul. She pursued multiple avenues of research,publishing18 articles in English and even a calculus textbook in Turkish.

She also conducted innovative research in probability theory and Mendelian genetics by configuring recursive equations to study the distribution of genotypes and blood types.

But this work, too, came crashing down. Turkish professors began to replace the Jewish refugees at the university, and Geiringer was one of those replaced. Her contract wasn’t renewed, and von Mises wouldn’t stay at the university without her. Making their situation more precarious, Ataturk died in 1938. Along with him went many of the protections and reforms that Jewish refugees enjoyed. Feeling it was no longer safe, Geiringer and von Mises left.

They set their sights on the US, where scientists like Albert Einstein andOswald Veblenwere attempting to place their colleagues. But immigrating to America, with its strict annual quotas, wasn’t easy, especially in 1939. AsLaurel Leff, creator of theRediscovering the Refugee Scholars of the Nazi Era project, explains, by the time Geiringer was trying to immigrate, the quota for that year had already been met.

“The reason that 1939 was the year that the quota was filled was because that was after Kristallnacht, ”says Leff. Kristallnacht, also called the Night of Broken Glass, was a clear indication to the world that the Nazi party was intensifying its violence against Jewish people. For two days and nights, Nazis swept through Germany, burning more than 1, 000 synagogues, vandalising Jewish homes and businesses and killing nearly 100 Jews.

Germans pass by the broken windows of a shop in the aftermath of Kristallnacht, a night which showed the world how dangerous Germany was becoming for Jews (Credit: Getty Images)

US immigration law had a small non-quota loophole – a provision called Section 4-D. “This is the one that is relevant when you’re talking about scientists and scholars,” Leff says. “It was basically for people [who] were getting jobs at American universities; they could immigrate on a non-quota visa. ”For the entirety of the war, Leff says, only 900 people were granted non-quota visas.

Non-quota visas posed unique challenges for women, who often were unable to find professorial positions – usually the reserve of men – whether in their home country or the US.

Geiringer was no different. Von Mises secured a position at Harvard University and, thus, a visa.

But without a home or job, Geiringer was quite literally cut adrift. While she and Magda were en route to the Mediterranean from London, World War Two officially began, stranding them in Lisbon as their German passports were denied for entry back to England. Without permission to stay in Lisbon, Geiringer and Magda were faced with deportation to Germany and internment in a Nazi camp.

Geiringer’s correspondence to von Mises, and her mentor’s journals from the time, reflect a tangible sense of desperation. On the day he learned of Geiringer’s abandonment in Lisbon, von Mises wrote in his journal (reproduced in the bookMathematicians Fleeing From Nazi Germany) that he “immediately decided to undertake steps”.

Together with Einstein and Veblen, he reached out to women’s colleges Bryn Mawr and Smith College, hoping to secure Geiringer a job – and with it a visa. Geiringer even suggested that they marry to hurry the immigration process. On days when von Mises didn’t receive any word from Geiringer, he vented his panic, at one point writing, “worn out and almost desperate”.

While Geiringer’s mentor Richard von Mises secured a position at Harvard – and a visa – Geiringer’s gender disqualified her from many jobs (Credit: Getty Images)

But Bryn Mawr, a women’s college in Pennsylvania, came through. Even though the position they offered was unpaid, Geiringer took it, and she and Magda received their visas. After six years of uncertainty, they could settle. Von Mises and Geiringer even married soon after, in 1943.

The imminent threat of the Holocaust had passed for Geiringer, but her troubles weren’t over.

Math demand

When Geiringer was looking for positions during World War Two, applied mathematics was in demand in the United States. “The growth of applied mathematics in the US has to do with war-related research,” says Alma Steingart, historian of applied mathematics at Columbia University in New York. “A lot of it comes from the fact that this is war preparation and there’s mobilization on many fronts.”

Even after the war, the field grew. “Funding starts coming into applied mathematics. And this recognition by the American mathematical community itself, that they need to start making sure that applied mathematics is well-developed in the US ”grows, she says.

But despite demand and Geiringer’s qualifications, her gender disqualified her for many jobs.

“Mathematics is one of the worst fields in terms of women’s participation,” Steingart says. Even Brown University, which Steingart says was one of the two main sites for applied mathematics and where Geiringer developed a series of acclaimed lectures on the geometrical foundation of mechanics, did not offer her employment.

One response to her inquiries for employment at Tufts College near Boston left little room for speculation about why she couldn’t find a job: “… 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 ”.

After five years at Bryn Mawr and searching for a university position, Geiringer became head of the mathematics department at Wheaton College, another women’s college in Norton, Massachusetts. “The places where women were most likely to get hired would be women’s colleges as opposed to universities,” Leff says. “[Hilda] was able to get a job at a women’s college, because women’s colleges would hire women.”

Eventually, Geiringer became head of the mathematics department at Wheaton College, Massachusetts (Credit: Wheaton College)

Women’s colleges provided essential opportunities for women as both professors and students. But, as Leff points out, “women’s colleges were colleges”, so they didn’t support the same type of sophisticated research that Geiringer had been doing in universities. Any research she did would be outside of her college duties and typically unpaid.

Geiringer never found in a US university a position equal to what she had in Germany and Turkey.

After accepting her post at Wheaton, Geiringer wrote to von Mises, “I hope there will be better conditions for the next generations of women. In the meantime, one has to go on as well as possible. ”

And Geiringer did go on. She stayed at Wheaton, which granted her an honorary doctorate in mathematics, until her retirement in 1959, that same year, she was elected a fellow of the American Academy of Arts and Sciences. She still did research when she found the time, but her most significant project post-immigration was compiling, editing, and publishing von Mises’ unfinished book in two editions after his death in 1953: Probably, Statistics, and Truth in 1964 and Mathematical Theory of Probability and Statistics in 1957.

Even if Geiringer didn’t get exactly what she wanted, she never gave up on chasing that deepest need in her life.

Missed Genius

Ask people to imagine a scientist, and many of us will picture the same thing – a heterosexual white male. Historically, a number of challenges have made it much more difficult for those who don’t fit that stereotype to enter fields like science, math or engineering.

There are, however, many individuals from diverse backgrounds who have shaped our understanding of life and the Universe, but whose stories have gone untold – until now. With our new BBC Future column, we are celebrating the “missed geniuses” who made the world what it is today.

Portrait of Hilda Geiringer by Emmanuel Lafont.

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