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Professor Bernhard Neumann was interviewed in 1998 for the Interviews with Australian scientists series. By viewing the interviews in this series, or reading the transcripts and extracts, your students can begin to appreciate Australia's contribution to the growth of scientific knowledge.
The following summary of Neumann's career sets the context for the extract chosen for these teachers notes. The extract covers the geometrical ideas behind a talk that Neumann gave to general audiences. Use the focus questions that accompany the extract to promote discussion among your students.
Bernhard Neumann was born in Germany in 1909. He showed a precocious mathematical talent as a youngster, teaching himself calculus by the age of 12 and in Year 10 inventing three-dimensional analytical geometry. He earned a D Phil from Friedrich-Wilhelms Universität in Berlin in 1932, one of the youngest ever to receive this award in mathematics from Berlin.
Due to the growing political and economic difficulties, Neumann left Germany for Britain in 1933. He completed a PhD in mathematics at Cambridge University in 1935. Although obviously a talented mathematician, he had difficulty finding work. In 1937 he took up a three-year temporary position as assistant lecturer at University College, Cardiff. He married fellow German mathematician Hanna von Caemmerer in 1938 after a long and secret engagement.
At the onset of World War II, Neumann was briefly interned as a German alien and on his release volunteered for the army. From1940 to 1945 he served initially with the Pioneer Corps, then the Royal Artillery and finally the Intelligence Corps. In 1946 he became a lecturer at University College, Hull, where his wife Hanna joined him on staff as an assistant lecturer in the same department.
Neumann moved to the University of Manchester in 1948 and spent the next 14 years there. Appointed as lecturer, he was promoted to senior lecturer and then Reader. During these years he was awarded many honours for his work. He received the Wiskundig Genootschapte Amsterdam Prize in 1949 for his solution of a problem on infinite groups and the Adams Prize from Cambridge University in 1952 for his work published as ‘An essay on free products of groups with amalgamations’. In 1954 he received a DSc from the University. He was elected to Fellowship of the Royal Society in 1959.
In 1962 Neumann arrived in Australia to take up the appointment of Foundation Chair of the Department of Mathematics within the Institute of Advanced Studies of the Australian National University (ANU). He served as Head of the Department until retiring in 1974. On retirement, he was made Emeritus Professor and Honorary Fellow at the ANU. In addition he was a Senior Research Fellow at the CSIRO Division of Mathematics and Statistics from 1975 to 1977 and then Honorary Research Fellow from 1978 until his death in 2002.
Neumann played a dominant role in mathematics in Australia from the time of his arrival in the country. He had long associations with organisations involved with the encouragement of mathematics at many levels. These included the Australian Mathematical Society, the Australian Mathematics Trust, the Australian Association of Mathematics Teachers and the Australian Mathematical Olympiads Committee. In appreciation for his work, a number of these organisations present prizes or awards named in his honour.
He was elected to the Fellowship of the Australian Academy of Science in 1964. An active member of the Academy, he served on Council (1968-71), and as Vice-President (1969-71). Through the Academy he initiated the Australian Subcommission of the International Commission on Mathematical Instruction and was on Australian delegations to many meetings of the International Mathematical Union. He was active in getting the Academy involved in providing material for schools; after a long gestation period, six volumes of Mathematics at Work appeared in 1980-81.
Neumann authored over 100 research papers and two books in mathematics. He wrote numerous reviews and essays about famous mathematicians including a six-volume series, The Selected Works of BH Neumann and Hanna Neumann.
He was made a Companion of the Order of Australia in 1994 for service to the advancement of research and teaching in mathematics. He was a strong supporter of all endeavours in mathematics and helped develop Australia’s significant international mathematical profile.
He was also an accomplished musician and chess player, and was well-known in Canberra for riding his bicycle in all weathers! He died on 21 October 2002.
When you arrived in Australia, weren't you already a Fellow of the Royal Society?
Yes. I had been elected in 1959, on a Thursday, and left on the Sunday afterwards for my first visit to Australia.
It wasn't long before you were elected to this Academy, in 1964, and Hanna was elected in 1970. You served on Council and were Vice-President between 1969 and 1971, and in 1984 you were invited to give the Matthew Flinders Lecture. I have often wondered how you selected a subject and a title in such a theoretical subject as yours for presentation to a general audience of scientists, many of whom would scarcely know what a group was.
I had for years had a number of talks for general audiences. Two of them were geometrical – very elementary, all two-dimensional geometry – and those I developed and gave again and again. And one on women in mathematics I have also given quite a number of times. I chose one of the geometrical ones but I had an audience response of nil. The Academy never published it; it was published later elsewhere. But the other one I gave often, under the title 'Napoleon, My Father and I'.
What was the theme there?
It comes from triangle geometry. If you take an arbitrary triangle – all in the plane – and erect equilateral triangles on the three sides, then take their centres and join them, you get another equilateral triangle, whatever you started with. This theorem my father had discovered when he was working on some transformer for three-phase electrical current, which had been invented in the '70s by Tesla and had developed into the natural way of transmitting electrical power. If you look at the high-tension power lines anywhere, you find they come in multiples of three except for the thin earth-wires on top, which shouldn't carry anything.
My father had published this theorem in two mathematical articles in an engineering journal before the war. At that time one still got an honorarium for publishing an article. In fact, he got an honorarium for each, and from that he had built for him a music cupboard and a music stand, both of which I still have. I knew about this theorem of his but didn't do anything about it until he wrote a book on polyphase electric currents. He had found a book by a Scottish author – in English – and asked the Springer-Verlag whether they wanted a translation of it, because it seemed interesting to engineers. They said, 'No, we want an original book. Will you write it?' So he wrote it. But this was already in the 1930s so they said, 'Sorry, we can't publish a book from a Jew. But you can have it. Do with the manuscript as you like.'
So he brought the manuscript with him to Wales when he and my mother came, translated it into English and offered it to a publisher. It was published late in '39, in English. I read the proofs of it, just to help him, and that reminded me of this theorem, which I thought surely must be capable of generalisation to other polygons in the plane. I found that generalisation, wrote it up as a paper and then, much later, after I'd already given some talks on it – it's very suitable for a popular talk – I found that somebody had called it Napoleon's Theorem. Since then, many historians of mathematics have been trying to trace it back to Napoleon, without success. It is known that Napoleon was very mathematically inclined and had many mathematicians round him, and it is entirely possible that he knew about the theorem and may even have found it, but there's no proof of that. The first reference that I now know of dates from 1826 but the first ascription to Napoleon dates from about the turn of the century. So that is why I call the lecture 'Napoleon, My Father and I'.
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