Monthly Archives: November 2013

‘Encounters of a mathematician’…

For the last few weeks, I have been cataloguing the papers of mathematician, Walter Ledermann (1911-2009).  The collection largely composes of highly mathematical letters from Thomson to Ledermann.  Having the somewhat dubious distinction of failing mathematics twice, its fair to say I had misgivings!

My failure as a young mathematician was due in part to my ready dismissal of mathematics as a dull, dry, monotonous subject (but in the main, a serious lack of talent!).  I remember somewhat haughtily telling my long-suffering teacher that I liked subjects about people.  Mathematics, as far as I was concerned, lacked any humanity and any discernible art.  How wrong I was.

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Ledermann as a young man, from his autobiography

Ledermann, a German-Jewish refugee, was more than used to such criticism being levelled at the subject – the art form – of his choice.  In fact, he opens his autobiography, Encounters of a Mathematician, with the following:

Mathematics is a soulless occupation devoid of feeling and human values.

But that, Ledermann tells us, was never his experience:

I feel strongly that mathematics can and should form part of human relationships.

Ledermann grew up in Berlin, proving himself a talented violinist and mathematician from an early age.  He loved music, and despite growing up in the midst of the depression, attended concerts regularly by any means possible.  By the 1930s, the Berlin that Ledermann called home had changed rapidly, and he and his family were no longer welcome.  It was his love of mathematics that gave him hope – despite the anti-Semitism he encountered, Ledermann’s ability, talent, and enthusiasm could be neither denied nor quashed.  In fact, Ledermann’s talent for mathematics quite literally saved his life.

On completion of his degree at the University of Berlin in 1934, Ledermann won a scholarship created by students and citizens of St Andrews to support a Jewish refugee.  He received a warm welcome from his fellow students, his lecturers, and the local community at St Andrews, and tells us: ‘it is no exaggeration to affirm that I owe my life to the people of St Andrews’ (Encounters of a Mathematician).

Ledermann completed his PhD after just two years, and found himself at the University of Edinburgh.  This would be the start enduring friendships between Ledermann and the brilliant and troubled mathematician, A C Aitken, as well as Professor Godfrey Thomson.

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Professor Sir Godfrey Thomson

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Alexander Craig Aitken

Ledermann quickly became Thomson’s mathematical assistant (or ‘tame mathematician’, as he puts it!), assisting him in writing The Factorial Analysis of Human Ability.  Thomson and his contemporaries used Factorial Analysis to understand human differences (mathematics and humanity again!), and this is still a technique used by psychologists today.  Thomson spoke to Ledermann in fluent German at their first meeting, much to Ledermann’s delight, and the working relationship was a successful one:

My work with Godfrey Thomson was inspiring, creative, and intimate.  We met daily during the morning break at Moray House, where the Department of Education was situated.  After we had briefly surveyed the progress of our research on the previous day, Miss Matthew, his charming and highly efficient secretary, brought in the coffee and some delicious buttered ginger bread.

The very intensity with which he pursued his ideas, was a great stimulus for me to solve the mathematical problems he had passed on to me.  Godfrey Thomson did not claim to be a mathematician.  Although he understood mathematical formulae when they were presented to him, he preferred to verify his ideas by constructing elaborate numeral examples from which the theoretical result could be guessed with some confidence.

Sadly much of Ledermann’s replies to Thomson are absent.  Thomson sends Ledermann pages and pages of calculations with explanatory notes, then his next letter will be one thanking Ledermann for the brief formula he has sent in return (Thomson at one point refers to Ledermann’s formulae as ‘very pretty’!).  The letters also show the warmth of feeling between the two, with Thomson frequently enquiring of Ledermann’s family, many of whom were still in Germany, and telling Ledermann about his own family.

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An example of the small postcards Thomson sent Ledermann

Ledermann treasured the letters.  In a letter to Lady Thomson, who was attempting to write Thomson’s biography, he writes:

I have over a hundred letters from Sir Godfrey, written between 1937 and 1946, some of them short notes, others carefully worked out in the form of a research paper, with many interesting questions and illustrations.  I greatly treasure the correspondence, not merely on account of its considerable scientific, and, may I add, aesthetic value, but also because it contains so many typical examples of that human warmth and sympathy for which Sir Godfrey finds a place even at the beginning or at the end of a mathematical letter.

Letter from Ledermann to Lady Thomson, Coll-1310/1/1/1/17

Ledermann returned to St Andrews after working with Thomson, and would go on to accept teaching positions at the University of Manchester, and the University of Sussex.  His love of mathematics continued to endear him to students and fellow lecturers, and he continued to undertake revision lectures for students for years following his retirement.  His wife, Ruth, was a social worker and therapist, and they retired together to London, where Ledermann passed away in 2009.

For Ledermann, the beauty of the equations passed between himself and Thomson were no different to the music of his violin – each displayed ingenuity and art.  His love of mathematics was the source of the most satisfying ‘human encounters’ he had throughout his lifetime, and the correspondence between himself and Thomson serves as a reminder of the beauty and humanity of mathematics.

Sources: Walter Ledermann’s autobiography, Encounters of a Mathematician

‘Who is that chap with the terrific head?!’

Robert Heriot Westwater’s most famous portrait is probably that of Christopher Murray Grieve (more widely known by his nom de plume,  Hugh McDiarmid!).  But Westwater also painted two very different portraits of Sir Godfrey Thomson in honour of his retirement in 1951:

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Formal presentation of Thomson’s portrait at Moray House, 1951, with Lady Thomson on the right

Westwater’s first encounter with Thomson was as a student training as a teacher of art at Moray House:

I remember very clearly my first sight of Professor Thomson as he passed a group of us students in the corridor.  “Who”, I demanded, “Who is that chap with the terrific head?”.  For the rest of my course at the training college I vainly tried to screw up courage to approach him – the art students, alas, had no class under him – to ask him if he would sit for me.  But I never quite succeeded.  And in the intervening years I lamented this somewhat uncharacteristic lack of “brass neck”

Moray House Magazine, March 1951

Westwater was delighted several years later on being commissioned to paint the-chap-with-the-terrific-head’s portrait!  The main portrait was to be a formal one in the striking red and white academic dress of the University of Durham DSc:

Thomson's formal portrait by Westwater

Westwater had some concern with regards to Thomson’s clothing outshining him in the painting:

With most other sitters such a garb would almost inevitably lead to a “portrait of robes with head attached.”  But in Godfrey’s case, not so.  When he arranged himself in the chair set ready, with complete dignity and composure, it was obvious at once that even such a gown could not compete.  The “terrific head” easily subdued it to its proper and subordinate place. 

Moray House Magazine, March 1951

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Page with Thomson’s photograph from the Moray House Magazine, 1950

Westwater commented on the many and varied conversations he and Thomson had during Thomson’s sittings, informing the reader that they were even prone to a sing song now and again (Thomson’s secretary and students were quite used to him playing, singing, and humming Gilbert and Sullivan whenever the notion took him!).  But my favourite passage by far is when Westwater gets rather verbose for his own good and waxes lyrical about the shape of Thomson’s head!:

The very bone structure of his skull begins the puzzle, for it is at once positive, virile, and yet almost frail in its delicacy.  The eyes have an imperious authority and penetration, but the mouth under the forceful nose astonishes by its nearly feminine gentleness.  it would be easy to cite another score of complexities, more subtle and more difficult from the painters point of view.

Moray House Magazine, March 1951

Quite!  Westwater’s second portrait of Thomson was more informal, and was Thomson’s gift from Moray House :

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This remained with the Thomson family for many years after Thomson’s death, eventually being donated to the University.  Ever keen to see paintings around the university rather than in store, we are delighted that Thomson now hangs proud in the office of his greatest advocator!  He is frequently seen and admired by a host of students and visitors.

Westwater clearly enjoyed painting Thomson, and likely he and Thomson would derive great pleasure from knowing his other portrait hangs in Moray House to to this day, reminding everyone, as Westwater put it, ‘of he whom they and I will always think of from different angles as “A Terrific Head”‘!

A few of my favourite things…III

In his mid 20s, Thomson found himself studying for a PhD under the formidable talents of Nobel Prize winining physicist, Karl Ferdinand Braun, at the University of Strasburg.  Today’s object is from this period, and likely held a great deal of sentimental value to Thomson:

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Thomson’s watch fob

The watch fob bears the initials of Thomson’s student ‘verein’ or club, the M.N.St.V, (the mathematical and natural science student verein), which he described as a humble version of the expensive ‘Burschenschaften’, elite student clubs which exist to this day and often involve duals (or Mensur):

In the Mensur…the fighters are protected by goggles and nose-piece, by mattress-like chest and arm protection, must not move or flinch, hold the straight pointed rapiers above the head, touching and at the word…strike at each other’s head and faces.  Two seconds crouch with drawn swords and at the first touch they strike up the combatant’s swords.  this is repeated until the referee gives a decision, or for a given number of rounds.  Often one man gets all the cuts, and the other none.  they are mostly on the head, but also on the forehead and cheek and chin, a ‘Durch-zieher’ cutting across both cheeks almost horizontally.  Then senior medical students give hasty and not very sterile assistance and stitchings, and the heroes drink beer and swagger (if well enough) through the next few days.

The Education of an Englishman, p.53

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Physikalisches Institut, Strasburg, March 1906

The scarring resulting from the dual was, and is, seen as a badge of honour, and students often deliberately irritated the wound, packing it to ensure it was widened.  In Thomson’s humbler club, duals were rare and usually in response to an insult or wrong doing.  No uniforms were required, but members wore a watch fob with the verein’s arms.  Thomson’s Leibbursch*, Carl Andriessen (whose name is engraved on the watch fob with Thomson’s) gave him his.

After World War I, Thomson lost contact with many of his German friends, many of whom were killed or missing.  However, the inscription of one book in his collection, Das Deutschland Buch, shows he kept in touch with Andriessen:

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Inscription from Das Deutschland-Buch

The book is inscribed with a message to Thomson and his wife Jennie, thanking them for their hospitality, and dated June 1931 – 25 years after Thomson left Strasburg.  The more fluent among you might notice he refers to them as ‘Aunt’ and ‘Uncle’, which made me wonder if the giver was in fact Andriessen’s son, though he refers to them as old friends, which would suggest otherwise.  It contains many beautiful images of Germany, a country Thomson loved his whole life, despite the ravages of two World Wars:

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I found the book rather touching – despite the remaining animosity of their prospective nations after World War I, the two clearly have a strong friendship, and Andriessen is able to give Thomson a book about the beauty of his own country, a country Thomson also loved.

For Thomson, the time he spent in Strasburg was one of the happiest periods of his life.  It allowed him to indulge in his passion for research, undertaking intensive work on Herzian waves. His German became fluent, and he immersed himself in German culture.  The watch fob, which he treasured for all those years, perhaps served as the perfect reminder of his life there, and a reminder of enduring friendship.

*’A second year student who adopts a freshman, shows him the ropes, and can claim services in return’

With many thanks to Sarah Noble, LHSA Conservation Intern, who patiently spent a morning showing me how to make bespoke museum boxes and made the lovely box for Thomson’s watch fob!