Emmy Noether – mathematical genius

The subject of today’s post is a true unsung heroine – not only is she unknown among the general public but few scientists have heard of her, even though Albert Einstein called her ‘the most significant and creative female mathematician of all time’, and the mathematical theorem she developed became the basis for many important discoveries in physics, including the Higgs boson.

Amalie ‘Emmy’ Noether was in Erlangen, Germany on March 23, 1882, the daughter of a professor of mathematics. While her brother was encouraged to follow in his father’s footsteps, and later became a renowned applied mathematician, Emmy was encouraged towards more feminine pursuits – English, French, cooking and piano. She went to a finishing school and in 1900 gained a certificate to teach English and French. But Emmy couldn’t suppress her love of maths, and, although she was not allowed to formally enrol, was given permission to audit classes at the University of Erlangen, where her father taught and her brother was a student. She took the final exam and did so well she was given the equivalent of a degree. Emmy went on to gain a postdoctoral degree – only the second woman to do so – and earned the respect of all her colleagues. But the university refused to hire her as a professor and for ten years she worked with her father at the Mathematics Institute in Erlangen, and began to publish her work.

During the First World War – a time that distressed pacifist Emmy – she was invited by leading mathematicians Felix Klein and David Hilbert to help them further define one of Einstein’s theories at the University of Gottingen. Faculty members blocked her appointment as a professor, saying: ‘What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?’ Hibbert fought Emmy’s case, protesting: ‘I do not see that the sex of the candidate is an argument against her. After all, we are a university, not a bathhouse.’ Emmy was eventually appointed as an unpaid guest lecturer, a position that became more or less permanent. Her spontaneous and enthusiastic teaching style didn’t suit everyone but Emmy gained a reputation as a warm and charismatic teacher, who treated her students as family and listened to their personal problems. Her fiercely loyal students, who became known as Noether’s boys, traveled from as far as Russia to study with her.

At this stage, Emmy began formulating what became Noether’s theorem. I won’t bore you with the details – it is maths after all – but it’s to do with energy and momentum. When her findings were published they caused a sensation, matched only by the later discovery that she was a woman.

Emmy lived for maths. She never married and lived modestly with no interest in possessions or personal vanity. A colleague described a lunch in which she became so engrossed in her discussion of her theorem that she gesticulated wildly while eating and spilled her food constantly, wiping it from her dress, completely unperturbed. She was energetic and happy, and is described as laughing often. But her happiness was short-lived. Following the rise of the Nazis in 1933 she was one of the first Jewish scientists to be fired, and was forced to flee Germany. She traveled to the US, where Einstein helped her find a teaching position in the Bryn Mawr College. Here she taught women for the first time, was highly respected and formed a close friendship with Anna Pell Wheeler, another woman mathematician. But only 18 months after arriving in the US, Emmy had an operation for an ovarian cyst and died of an infection a few days later, aged just 53.

Since then, despite remaining relatively unknown, her recognition has extended beyond the world: a crater of the moon and a minor planet have been named after her. And last year Google created one of their lovely doodles to celebrate her 133rd birthday.

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Alice Herz-Sommer: oldest Holocaust survivor

It’s a while since I wrote a blog post, but recently I discovered a story so uplifting I was inspired to restart. Alice Herz-Sommer was born in Prague in 1903, one of five children, including a twin sister. Her childhood was intellectually stimulating: her parents ran a cultural salon and visitors included Franz Kafka, Gustav Mahler, and Sigmund Freud. At the age of six she started learning piano and by her teens was teaching and performing. She met Leopold Somner, a violinist, in 1931 and married him two weeks later. They led a busy and creative life and had one son, Raphael.

After the Nazi invasion of Czechoslovakia, most of Alice’s family emigrated to Palestine but Alice remained to care for her sick mother, Sophie. In 1942, Sophie was arrested and later killed. Alice channeled her grief into her piano playing, practicing endlessly until her own arrest, together with Leopold and Raphael, in 1943. They were sent to Terezin-Theresienstadt camp where Alice’s musical prowess became her saviour. She later told of her experience:

‘We had to play because the Red Cross came three times a year. The Germans wanted to show its representatives that the situation of the Jews in Theresienstadt was good. Whenever I knew that I had a concert, I was happy. Music is magic. We performed in the council hall before an audience of 150 old, hopeless, sick and hungry people. They lived for the music. It was like food to them. If they hadn’t come, they would have died long before. As we would have.’

In the years of her incarceration, she played more than 150 concerts. Raphael also performed in the children’s opera staged by the Nazis to show ‘normal’ life in the camps. Sadly, Alice was separated from her husband and he died in Dachau, six days before the end of the war.

After the war, Alice moved to Palestine and was reunited with her twin, though many of her family, her husband’s family and all her friends had died. But what makes Alice’s story exceptional is she didn’t let this tragedy define her, instead living a fulfilling life. She once said: ‘I am looking for the nice things in life. I know about the bad things, but I look only for the good things.’

In 1962, she attended the Eichmann trial in Jerusalem, commenting: ‘I have to say that I had pity for him. I have pity for the entire German people. They are wonderful people, no worse than others.’

She taught music before moving to London in 1986, to support Raphael in his career as a cellist. Sadly, Raphael died of a heart attack in 2001, aged 64, a devastating blow, but Alice remained positive. She lived alone and for many years had an active daily routine that included swimming, playing the piano for three hours and attending classes at the University of the Third Age.

Alice became the oldest Holocaust survivor and died in 2014, aged 110. She attributed her long life to optimism: ‘I was always ugly. My twin sister was very beautiful. But she was a pessimist and so she died at 74. If you are a pessimist the whole organism is in a tension all the time.’ When asked whether she was afraid of dying, she replied: ‘Not at all. No. I was a good person, I helped people, I was loved, I have a good feeling.’