The Life and Work of W H and G C Young

by their son L C Young

Chapters:
I. Background
II. Life Works
III. The Chisholm side
IV. Grace
V. A New Life
VI. Pioneer
VII. Telegram
VIII. Collonge
IX. Thwarted

To explain in part my parents' great drive and unusual thinking, we look into family histories, bearing in mind that in recent events there are no mathematical proofs, and that, further back, the 2n ancestors of the n-stage are, for n exceeding some by no means large value, virtually the same for all Britons...

I. The misty background of the Youngs ups and downs.

Family history soon merges into legend. One of my most vivid early recollections is a tall tale told by my mother. Se non e vero, e ben trovato.

The tale concerns a yeoman, Tom Young, who joined up to fight the Armada and brought the sharp scythe he used to mow his fields of wheat. Arms being in short supply, he was soon using this great scythe with great effect when boarding a Spanish vessel, and the superstitious Spaniards soon fled in panic; only the Spanish Captain stood his ground, but he was made prisoner when one foot was scythed off. All at once, Tom Young felt sorry for the poor man and desperately cried to him to try sticking the foot on again! Years later, a visitor hobbled in at Tom's farm: "Why it's the Spanish Captain," Tom exclaimed," You should have stuck that foot on again!" Perhaps similar stories, passed on from generation to generation, are as important as inherited genes, in the preconditions that help to form mathematicians. What the story brings out, is that in their thinking and doing the Youngs are unusual ,as are, by definition, all mathematicians...

Wheat fields get trampled, and farmers executed in Civil War, but people need their daily bread. At various times (for rural England had not easily forgotten the turbulent past, nor did it soon forget Cromwell's Ironsides), younger brothers of the yeomen Young had chosen to become bakers in Ipswich. One such baker was our ancestor in the 18th century, and 2 of his sons, William and Abraham, settled successively in London. William died in 1767 and his house was taken over by Abraham, our next ancestor, who had established himself as a merchant in corn and seed and so forth, and married Mary French. William and Mary were very popular names in those days: Abraham's eldest daughter was called Mary and married a William (Sawer) and Abraham's youngest sister was also called Mary, but luckily -did not marry a William - she actually married the Rev. Thomas Bolton, and I might mention that a nephew of her husband, also named Thomas Bolton, married Susannah Nelson, sister and heiress of the famous admiral. (How little you need go back in time, to find a well-known figure somehow connected with your own family!)

Coming from the safest of professions, Abraham tried to diversify, but this has risks too, since it is more difficult to be expert at several lines of work than at only one. He had in 1778, a serious setback, perhaps from a loss at sea: the American War of Independence was in full swing and the French Navy had just started an undeclared war on British ships - at any rate the claim Abraham had to settle, included one for supplying a mast. However he was able to arrange to pay in full all his creditors, even - according to his will - after his own death in 1797, and he kept scrupulously to this arrangement. His good name among customers ,associates and fellow merchants caused his other ventures, mainly shared, to prosper, and he died fairly well-off.

One main business, arising from this diversification and then extremely profitable, passed to our next Young ancestor, his eldest son, Abraham II, (born 1768, died 1827): it was a bank of sorts, and funded middlemen, who bought (say) Scottish sheep for resale to London butchers. This Abraham II in his turn had married at age 24 a Mary, in fact a widow with a small son, and he had met her in a stage coach! (Contrary to the wording of a quotation in Grattan-Guinness, Annals of Science 29 (1972), this was not a 2nd marriage of Abraham II!) This Mary was, however, well-connected in the City, which certainly did not hurt his business reputation! In 1821, the "bank" became "Young and Son", having been virtually turned over to Abraham II's eldest living son (not an ancestor), as "associate". It had now grown to such an extent that only big clients were accepted, smaller ones being shunted to a smaller bank. Of course a large cash balance had then to be kept in the till.

The "bank" business was not without risk: the years 1820 to 1830 saw some quite extraordinary fluctuations in values of all kinds, and in prices of things like food in particular. There was also fantastic speculation: thus in Jan. 1825, Brazilian mining shares, worth 10 shillings the preceding Dec. 1824, were listed at 66; however it was soon found that the mines had become full of water during some 14 years of revolution, and could not be worked for profit. As a result, again and again there was panic among depositors; from this "Young and Son" were largely secure, since they accepted only rather large deposits. However, in 1827, the chief client, one Godfrey Kemp, came in one day and withdrew his whole account!

It was not thought urgent to replenish the till, but they might as well send someone, to be made familiar with bank procedure, to cash a cheque that had come in, of some 4000. They probably sent our next Young ancestor, Abraham II's second son, Henry. Unfortunately, by the time this messenger had made his way to the proper building, up the proper steps, to the proper doors, he found the doors closed: that bank had failed. The resulting frantic run on all banks was inevitable, but unforeseen. Without the extra 4000, Young and Son ran out of cash and had to close its doors. Among the businesses that did so, it was one of the few soon to repay its creditors in full, but the damage to its assets and its reputation was never made up. The "bank" resumed half-heartedly until 1840, but it was no place for our ancestor Henry Young (born 1806, died 1883). In 1828, he became a grocer. A few years later (1835) he married Susannah Wright, descended from makers of beautiful coaches, similar to the one used by British Sovereigns to open Parliament. (He remarried some time after his first wife's death, but this does not affect the present account.)

The earlier Wrights, particularly John Wright, invented for these coaches comfortable springs, patented in 1754 based, I am told, on a mathematical idea. Without such springs, in our modern transport, the wear and tear on passengers and conveyances would be uneconomic and unbearable.

(It is a small world! For the 2nd time, going back but a little way from my father's birth, we meet someone of note, but in this case no mere national hero: whole nations depend on the invention of plain John Wright, that benefactor of mankind, and so do billions of money. Ah, but how easy it is to kill the promise of creativity! This too we shall now see...)

II. "La reussité de sa vie manquée."

Susannah and Henry Young had an only child, the later Henry ( born 1837, died 1899), who was in due course sent to the City of London School, where he won mathematical prizes and the friendship of another bright boy, Edwin Abbot. Then at 14, his mother having died or being close to death, he was taken away from school ... For 7 years, interrupted solely by a year of military service, our later Henry, my grandfather, helped as apprentice in his father's grocery. School was forgotten, he fell in love, and eventually, in 1860, he married Hepzipah Jeal, who was very strict and non-comformist, her surname being probably an anglicised form of the Huguenot Gilles. All too soon he realized that he was cut off from what he ought to have been. He retained a very good brain, in fact, in a law case in which he represented himself he was complimented by the judge; however he became, by most accounts, bitter and difficult, with chronic indigestion -- in fact a sullen "Mute Milton". He did what he could to help a son become what he himself had failed to be: that son was our William Henry Young.

The marriage to Hepzibah had first been blessed with a daughter, Susan (Eppie Susannah, born 1861, married Walter Scoles 1887, died 1895). Then, after Will (1863) came George Herbert (born 1865, died 1870), Alfred (Henry Alfred, born 1867, married Ellen Maud Hills 1894, died 1941). May (Mary Ann, born 1869, died 1949), Ethel (Ethel Margaret, born 1878, died 1960).

These were anxious times when in 1870 the two eldest boys contracted meningitis: George Herbert died, Will recovered. That was, no doubt, when Susan was such a help to her mother and acquired a very privileged position in family affairs that Will was apt to resent; for in those days men thought themselves greatly superior to women, and boys to mere girls... On the other hand, Susan and her mother, who ruled the household, disapproved of Will's interest in many things, particularly in foreign lands and languages. They felt that it was bad enough for the father to spend time on travel booklets, and not on something practical. Will liked to be with his father, to see further than the little shop, and to reflect that "there are more things in heaven and earth".

Was it this disunity which later prompted Will to repeat so much to his own children the story of a father showing his sons a bundle of sticks which they vainly tried to break, though they broke with ease the separate sticks? Will told them also a story in keeping with his mother's Huguenot background, about a good German Herr Doktor who interviewed candidates for a post, and who would generally be assured, earnestly that the candidate would "do his whole duty", such a candidate, the Herr Doktor would never appoint ... The need for something beyond duty, far beyond, has been expressed more forcibly, but perhaps not more subtly ...

After the usual more elementary establishments, Will was naturally sent to the school his father had been sent to -- and mercifully he was not taken away again at the age of 14! Why not? Because his mother and his elder sister helped in the grocery, they were practical. Thanks to them, he did not end up, like his father, a sullen "Mute Milton". My father became a mathematician: an actual benefit could thus be derived from the financial set-back (of 1827), just as in the case of LaGrange, whose career in mathematics was made possible by financial losses sustained by his father. It therefore gives me particular pleasure that a great-granddaughter of Will's elder sister Susan is now, in her turn, a mathematician.

At his father's old City of London School, Will acquired his still wider interests and his tremendous drive, he "caught fire". The Head was now Abbot, his father's friend, famous as a classicist and as the author of the charming mathematical dream-tale Flatland by "a Square". Will also had the support, even of his grandfather ( the 1st Henry Young), who sent him, for his 16th birthday, Smith's Wealth of Nations. At school, Will was considered the best in mathematics...but he also had a first lesson in set-backs: he came 2nd with the final examination. He laid his head on his desk and all but cried. As if such things matter!

It was the English system at the time and when he won a Peterhouse Scholarship, the school insisted on keeping him another year to do, over and over again, soul-destroying examination problems. At Cambridge, a year later, again with a Peterhouse Scholarship, he found virtually the same thing as he had just had - to us, a century later, it would seem hardly worthy of a University. Will, anticipating the advice given in the better colleges 50 years later, took it all in his stride. He did not devote excessive time and energy to what he later called "sack-racing". He took up tennis and rowing, he ran in a race and won, and he read a great deal. In his 2nd year, when he was being prepared for the all-important Part I of the Tripos, he was also deep in Motley's Dutch Republic, given to him by his grandfather. In Part I he was "merely" 4th, the first 4 being very close together. Still, after a first in Part II the following year, he was elected 1886 to a Peterhouse Fellowship.

Will did not compete for a Smith's Prize. Why not? Let us just say that his enthusiasm for what was then called "mathematics" in Cambridge was not all-entrancing. He was full of Motley's Dutch Republic, and the discussions with his friends, the Westcotts, sons of the Bishop of Durham, decided him to switch from non-Conformism to the Church of England. Instead of the Smith's Prize, he competed for the Peterhouse Theological Prize (the "Butler Prize", awarded on an examination on Butler's Analogy), which he won. He also founded and ran a literary society, the Heywood Society, and he did some travelling, attending incidentally a lecture by Frobenius in Berlin -- a lecture which impressed him deeply, but which led to nothing on his part.

Will did make some half-hearted inquiries about the Smith's Prize. Lord Kelvin suggested two unsuitable problems, Abbot said "Go to Germany" (the most sensible advice), Forsyth (later Professor) said "Write a textbook". Will turned over this last suggestion in his mind, and realized that Cambridge -could do with some life put into mathematics! However, the way to cause this, was not to write an abstruse textbook for the Smith's Prize. Instead, he became a highly successful mathematical coach, so much so that he had dreams of restoring the family fortune...

In a sense, his first pupil had already been his brother Alfred, whom he had coached and coached -ad nauseam, and who hated him as a hard taskmaster. Still Alfred had finally got through Sandhurst, and had also learnt from Will the need I spoke of, for more than mere duty. He ended up as Brigadier-General in India. At Cambridge, Will established his coaching business with extreme efficiency: it was partly conducted with up to 3 pairs of pupils in different rooms, and partly as lecturer at Girton. Of his methods I shall only say that when a young Fellow told him, " I work myself to the point of exhaustion, and still my pupils have bad results!", Will said simply, "They should be doing the work".

Was Will's heart really in this? When J M Keynes, a 7th Wrangler, consulted him, Will, who had read Smith's Wealth of Nations, advised him to take up economics.

III. On the Chisholm side.

Some say the Chisholms were Danes who came in the 5th century and settled in the North of Scotland, others that they came over with William the Conqueror and found it best to be there, far from him. About the year 1730, one of them walked from there to London, and being a great fellow, 6 ft 41 /₂ in height, was given a place in the Royal Household. A grandson of his, Henry Chisholm, after working at a nearby bookseller's and then as secretary and librarian in a country estate, became a private secretary to Lord Grenville and married Gwen Williams, the companion of a sister of Lord G in 1803. Then in 1806 Lord G became Prime Minister, and eventually in 1823, he also used Henry Williams Chisholm, the 14-year-old son of Henry Chisholm, to write out letters, ministerial documents, and a collection of verses in various languages. (Remarkably, this taking HWC from school seems not to have had any ill effects!) The following year, when Lord G. retired, the two Chisholms, father and son, were made, respectively, Senior and Junior Clerks, with salaries of L500 and L100, at the Exchequer.

The rules at the Exchequer were strange (according to HWC's later "RecollectionsÓ, published in Temple Bar 1890), and previous to Lord G's holding the sinecure office of Auditor of the Exchequer, even stranger. Lord G's predecessor, the Duke of Newcastle, when appointed a clerk at the Exchequer, would charge the salary with an annual amount! Lord G's procedure was not very different: he expected, without payment, personal services, such as auditing the accounts of his own landed property. Moreover, in 1807 he appointed Henry Chisholm as King's agent to the colony of Sierra Leone with a salary of L200 a year; but in 1823, when he made the corresponding appointment for the Gold Coast, the L200 salary was somehow omitted and went to someone else. Should one infer that a King's agent was expected to get some benefit from the post itself, by collecting daily interest in the revenues in his charge?

Unfortunately in 1829, Henry Chisholm allowed himself to be duped. along with no doubt many others, by what should surely seem to us one of the most barefaced Stock Exchange swindles of even those extraordinary years (1820 to 1830): India stock, in which he had been persuaded to invest the revenues of Sierra Leone and the Gold Coast, suddenly halved in value. He fled to Paris, where he died in 1832, in the great cholera epidemic. The liabilities left behind were covered by a life insurance, by the compulsory sale of personal effects, by the India Stock he had brought, and by some L300O which Lord G and a Mr Hilditch, as sureties, had to make up. (This was less than Lord G was getting every year for doing nothing as Auditor!)

In the grim years that followed, HWC had to support his mother and 3 sisters on a Junior Clerk's L10 a month. How they managed to survive, I do not know, but I sometimes think there are ties of deep affection, that only those can experience who have survived together great hardship. Such a tie was, in my opinion, established between HWC and his mother, and constitutes the strongest reason why HWC did not marry, for many years, the woman he loved. There were, however, other reasons, as we shall see. How did they survive? I think bravely, even proudly. I think that even HWC, who blames his father, was at the same time proud of him; but he was proud also of his mother, and she, in her turn, kept up the family spirits and pride, by telling her children (what HWC later so painstakingly and conscientiously drew up in the form of a geneaology) of a kinship to Sir Orlando Bridgeman, 1st Lord of the Admiralty under Queen Elzabeth I, and also to the famous "Mother of Wales" ( Mam Cymru), Catherine of Berain.

Slowly, very slowly, things improved, although time and again HWC failed to get a promotion, expected and hoped for. In 1834 he became Assistant Clerk, and at last in 1843, after 2 years of unending work (necessitated each day by a major fraud of 1841, in the Exchequer itself), Senior Clerk. He was then 34, it was 20 years since he had been taken from school, except for a few months in 1824, when he had been sent back there prior to his appointment as Junior Clerk at the Exchequer. However in those 20 years his education had not, in effect, stopped: when will people realise that a school, a university, and so forth, provide only a beginning? HWC did much more than continue what was started at school, and he also, with the traditional Welsh love of music, inherited, no doubt, from his mother, and encouraged by his great school-friends, learned to play the violin and joined Quartets, an Orchestra, the Civil Service Band, besides attending (free, thanks to relatives or friends) the Opera at the Haymarket or at Covent Garden.

It was probably through his music that he met, about 1840, his future wife Anna, or in full, Anna Louisa Bell, one of the 13 children of William and Elizabeth Bell. Her mother had herself been one of 12 children of George and Fearne Kinnear, whose portraits by Raeburn are in the Scottish National Gallery, together with Dr. John Gardiner, President of the Royal College of Physicians of Edinburgh. I said earlier that there were reasons for HWC not to marry Anna for many years, besides his deep affection for his mother: we now see what they were! Even for a Chisholm, whose motto is Ferios Ferio, marrying into so exalted prolific a family, might well seem alarming!

The Bells were originally a Scottish Border Clan, going back at least to a William Bell of Kirkconnel in Annandale, who was granted his land by Charter in 1424. The branch we are concerned with, migrated to Ulster in the 16th century and became very Irish, so much so, that our William Bell's father, Hugh, born in Dublin but settled in London, was once arrested for High Treason! He had had to dinner two well-known Irishmen... Fortunately he was vouched for by the Undersecretary of State, the famous George Canning... William Bell's father had established in the City a business mainly concerned with Irish trade and wine, and with part-victualling the Royal Navy. This business became Bell Brothers, and William Bell shared in it. Unfortunately it failed in 1842. However William bell had a marvellous tenor voice, and therefore influential friends; in 1845 he was appointed to the lucrative position of Official Assignee in the Court of Bankruptcy. Did this make things any easier for HWC? Not at all: he threw himself into his work.

He finally proposed in 1857; his mother had died, aged 83, and his sisters had long ceased to be dependent on him. The marriage took place in 1859. He prospered. From then on, he received much official commendation, culminating in his being thanked by Parliament in 1868, for 3 large volumes (affectionately known for many years as "the Chisholms" at the Board of Trade) on the subject nearest to his heart -- after his heroic fight against private penury and debt -- the National Debt, which covers the period 1688 to 1868. Later, he was put in charge of the Weights and Measures Department and he erected in Trafalgar Square, on the North Side, public standards of length. He became Warden of the Standards, a position subsequently abolished. Parliament also asked him to report on a proposed metric system in Britain: his report was favourable, but the proposal was deferred. His services were not confined to his own country in this context: he received fine gifts from the Republic of France and from the Czar of all Russias.

Some years before his retirement, the family moved to Church Lane House, Haslemere, and he commuted to his London office. The house was a large one near the station, with 6 acres of garden and farm, but this meant much more than merely living in the country. Haslemere was a little haven of Art, Poetry, Music: people like the Tennysons and William Morris were fellow-residents and many leading creative artists visited the town. To Anna, it was the intellectual atmosphere she had been used to before her marriage, and she and her husband soon contributed to the spirit of the place-- they gave recitals together in the Haslemere Town Hall; he had remained a good violinist, and she was a pianist with every advantage that contact with great musicians can bring. For Anna's parents, except in the few years when bankruptcy hit, were well-known music lovers, patrons of the Royal Academy of Music, and of the Arts generally.

HWC and Anna had 3 children: Helen (or Helen Augusta, born 1863, died 1909), intelligent and charming, but a semi-invalid from polio; Hugh (born 1866, married Eliza Beatrix Harrison 1893, died 1922), who did conventional things very well and ended up by editing the Encyclopedia Britannica (11th edition); and my mother, Grace (in full Grace Emily, born 1868). (I do not count a 1st child, who had accidental brain damage and had been kept, until her death at age 20, in a suitable nursing home.) Helen and Grace at one time experimented with thought transfer in different rooms, and agreed that the first to die would try to appear to the other. Many years later, when my mother was on the Continent, she told us that she saw Helen come into the room, and that the next morning a telegram arrived to say that Helen had died. My mother was unusually unprejudiced, even in matters that a conventional scientific outlook is apt to frown on. However, if questioned on thought transfer, she would undoubtedly have pointed out that her own little Irish terrier always knew when she was approaching the house ...

IV. Unusual Grace.

Grace's upbringing was not the conventional one. In her early years she was much troubled by headaches and by screaming and walking in her sleep: the doctor at Haslemere said she was to have no lessons except those "for which she herself asked". He had been called in when she was about 5 years old and the family had just moved to Haslemere, and when he asked who she was, she replied "I'm John of Gaunt, time-honoured Lancaster!" Clearly she would not lack things she wanted to learn... What she did ask for was music and mental arithmetic, which her mother taught her, and when she was 10 years old she had regular lessons from a governess. It was not so bad as it sounds! Indeed for her, judging by the results, it was perhaps fully as good, to say the least, as being at the best school in England. Under this system, she grew into a tall and strong young woman, unafraid and eager to learn more, whereas few schools, and even few universities at the time, least of all in England, realized that the education they provided was only a beginning...

After all, Grace was in a haven of the highest form of intellectual life: contact with the great ones in Art, Poetry, Music and yet to live in fresh air of the hills, and to eat fresh country food, what more could a child ask? She would never forget, she once said, how she had sat with the great violinist Joachim, on the shore of Frensham pond. She was then aged 17. It was also the year in which, in spite of her lack of a conventional education, she passed the Cambridge Examination.Her ambition was to take medicine: like so many young women, she was inspired by the example of Florence Nightingale, and charitable duties had taken her, unafraid, into the most dreadful districts of London. However, her mother being totally against her taking medicine, Grace decided on mathematics and surprised everyone by winning the Sir Francis Goldsmith Scholarship at Girton College, Cambridge. Her father doubled its value for her, and in April 1889 she went up to Cambridge to pass the Little-go examination which included Greek: she obtained a First Class and was cross at the unnecessary effort! Little did she know how she would later love Greek... (not having had, as aid, the customary use of the birch.) At Girton, she chose as mathematical coach a Mr. Berry, who quoted: "Six hours work is six, seven hours work is six, eight hours work is five." (Difficult to get across in women's colleges, but there most true). Grace took it to heart. She had to work hard at straightening out her mathematics, for her coach took her along at a rapid rate and she was also attending, in Cambridge itself, lectures delivered at an equally hurried pace. But she also took part in college debates, she read a paper to the Girton Mathematical Club on her father's standard weights and measures, she observed on the College telescope the big sunspot of 1891, and she helped produce a representation of Tennyson's Princess. She made friends, specially with Frances de G. Evans ( later godmother of my eldest brother) and with Isabel Maddison (later on the staff of Bryn Mawr College, Pennsylvania).

She was not so popular, at first, with the Headmistress, having been induced, in her inexperience, to act as opposer to a motion on women's suffrage, when no one else would undertake this task! She was then also ridiculed by the proposer as "the sort of girl who got married and lived happily ever after". Her academic successes soon made up for this. Isabel was top of the 2nd Class and Grace next below her, in the 2nd year "Mays" examinations. Then, in their 3rd year, both were Wranglers (1st class), with Grace between 23rd and 24th, and Isabel equal to 27th. Directly after, they were allowed to take, unofficially, the Oxford equivalent of the Tripos, and while they were sitting these examinations the Cambridge results came out. Grace was so happy about them that she outdid herself and scored higher in Oxford than anyone else that year. (Isabel got only a 2nd Class.) Grace's high score was in response to a challenge from her brother Hugh: naturally she went all out, she represented womanhood and Cambridge! In the Tripos she had only wanted to do creditably -- she regarded it with somewhat supercilious interest, and after all, what was it really worth? Heavy bets were made on the results, church bells were rung in the Senior Wrangler's home-town, but the rumours!!!

It was said of one Senior Wrangler that what made the difference was that he wrote clearly twice as fast as others could only scribble, and of another that he must have been well primed with brown sherry ...) The Oxford success, not entered on the University record, was important in suggesting to Grace a possible future in mathematics. She returned to Cambridge for the academic year 1892-93 and completed the Tripos Part II. She then went Göttingen, where Felix Klein was precisely looking for young women like her: he had been authorized to try out a PhD program for foreign women. Two American girls (Mary Winston and Isobel Maltby) were in the program already. One cannot imagine a more complete contrast to what Grace had experienced at Cambridge. "Students are gentlemen", she wrote home, and "Klein has the frankest, pleasantest smile, and his whole face lights up with it. He spoke very slowly and distinctly and used the blackboard very judiciously. Mr. Woods (an American student) said he never heard anyone lecture so well and neither had I." Those were superficial differences: more important is that mathematics itself had a wholly different character, being now dominated by concepts and not by shorthand tricks. One such concept, particularly stressed by Klein, was that of groups: it was almost totally ignored by Cambridge for another 40 years, until I myself, as a student, founded the "Group group". Yet the concept of group, more perhaps than any other, had revolutionized mathematics in most of the 19th century. Grace was not slow to grasp the illuminating nature of the concept of group. Her thesis is its application to one of the most formulae-ridden topics in mathematics, spherical trigonometry. For this she was awarded "Magna cum laude" the degree of Doctor of Philosophy in 1895, incidentally becoming the 1st woman to obtain an official doctorate in Germany. (As I mention in my "Mathematicians and their Times," even the famous Sonia Kowalevskaya did not receive an official doctorate.) One consequence of all this is that copies of Grace's thesis were sent to various people, including Will, who had substituted for Grace's coach, Mr. Berry, during one term. Will replied, suggesting a joint book on astronomy, a subject he had treated with her, and in which the methods of her thesis had applications. The book was never written: instead Will and Grace got married on the 11th June 1896. The wedding was attended by Felix Klein himself - not at all embarrassed, incidentally, by my mother's ignorance of German sartorial terms, which caused him to be dressed like a waiter.

V. The New Life

On their honeymoon in Switzerland and Italy, my parents felt deeply the lines Dante puts at the beginning of his Vita Nuova:

In that part of the book of my memory, before the which is little that can be read, there is a rubric saying Incipit Vita Nova.

It was partly to reflect on what the New Life should be, that they went back for one year to the familiar routine of Cambridge: there Frankie (Francis Chisholm Young) was born, his naming linking them to their chosen dedication, which seemed to them like that of St. Francis of Assisi, when he discarded wealth and fine clothes to enter his New Life. A visit to Cambridge by Felix Klein, who was awarded an honorary degree there, decided them. In the Autumn my parents left for Göttingen. To most friends and relatives, this came as a shock; to those of England's money-making class as a matter of course; but still more to many members of the mathematical community in Cambridge! This, at least, has long changed: now one is greeted in the Cambridge Mathematical Library by great photographs of Felix Klein and David Hilbert. As for money, this was of course a problem, my father's savings having had partly to be used for the final years of his father's life and for the starting of my uncle Alfred on a military career; however my father was able to settle L6000 in a trust fund for my mother. Apart from that, what made my parents' scheme financially feasible, was the relatively low cost of living on the Continent, for those possessing an engaging and friendly manner, and absolutely refusing to submit to obvious overcharges, even if this meant going to Court, as my mother had to a few times, not unsuccessfully. The move to Göttingen was at first only for a semester. In that time, under the encouragement of Felix Klein, my father started writing his first paper, which appeared the following year, On systems of n-vectors in n dimensions. However the centre for n-dimensional geometry was really in Turin, in the school of Corrado Segre, and my parents had in any case set their hearts on Italy. So to Italy it was, mainly Turin, for the next 18 months. Soon they made friends with their Italian fellow-mathematicians, and of course little Frankie, who acquired the name of Bimbo, made friends everywhere in spite of some occasional roguish tricks, like throwing bits of coal from the balcony at whoever was below...

My parents took all this, and the learning of Italian and so on, as well as attending lectures and seminars, taking part in discussions, in their stride. For my mother, there was one, quite unexpected, great joy, about which she wrote home to her parents. At first she had taken for granted, as my father had, that her ideas would dominate the joint work. But now, she could see that he was getting ideas, beyond her own and those of their Italian friends.

The stay in Turin ended hurriedly: they had to rush back to London, on account of a serious illness of my grandfather Chisholm. Fortunately, his health greatly improved when he was got away into the country and put in the care of a competent doctor. In Turin my father had written three more papers on n dimensions, one paper being in Italian; my mother, who had less time for her research, had nevertheless managed to write 1 paper, also in Italian. They could now be considered proper mathematicians, at the start of a promising career of creativity, and that was, in effect, what Felix Klein told my mother, who had been placed next to him at the celebration of his 50th birthday. Felix Klein was then visiting Turin in connection with a project, very much in the Göttingen tradition of the unity of every kind of mathematics, the production of the Encyclopaedie (or in full the Encyclopaedie der mathematischen Wissenschaften). This great project of course interested by parents, and they learnt a great deal from it-- so did I, incidentally, when the German edition was still going strong in the early 1920's. A French version ended in 1914. An English edition had also been suggested, but after my parents and other enthusiasts had spent much time and effort on it, any such venture had to be given up because people like Forsyth were against it. At any rate, as a result of Felix Klein's visit to Turin, it was to Göttingen that my parents and little Frankie returned in the Autumn of 1899, after their trip to London on account of the illness of grandfather Chisholm. There, until 1908, the family made its home, and the remaining 5 children, Cecily, Janet, Marion, Laurie (myself), Pat, were born: Rosalind Cecilia Hildegard, born 1900, married Bernard Tanner 1953, died 1992; Janet Dorothea Ernestine, born 1901, married Stephen Michael 1932; Helen Marion Kinnear, born 1903, married Jean Canu 1929, died 1947; Laurence Chisholm, born 1905, married Elizabeth Dunnett 1934; Patrick Chisholm, born 1908, married Marjorie Sargent 1950. There was again a family trip to London in 1900, when my grandmother Chisholm died suddenly (6 months prior to my grandfather Chisholm); it cut short a Summer holiday in Scandinavia intended to avoid a Göttingen epidemic of smallpox. That was also when my father decided it was time again to earn some money: already he had cut expenses by not attending international mathematical congresses. The family's return to Göttingen was therefore without him, he went back to Peterhouse. For many years after that, he travelled to and from the family home, being away for several months at a time. My mother's tasks were no less demanding: in addition to bringing up the family, she was taking University medical courses; this she had always wanted, and now it was my father's insistence, as a kind of an insurance...

Yet both she and my father were working primarily on mathematical research. What made it less impossible than it sounds, was the family help my mother had from one of my aunts. Frankie and my two eldest sisters were a little too much for my poor Aunt Ethel, who first came to help, but ended by having a breakdown; in 1903, Auntie May came instead, staying for many years, and we all liked her very much. My mother was thus able, in her turn, to be of great assistance to my father. My mother understood, perhaps even better than my father, how much they were giving up by their decision to go deeper into mathematics than seemed then possible in the tradition-bound air of England. The spirit of dedication, which can be strong in a young woman, had at first directed her to welfare and medicine, and then had shifted to marriage and mathematics. Now it inspired then both, but it came, perhaps, from her. She felt that it was up to her to do all she could to ensure that neither of them would ever regret the decision they had taken.

VI. Limited means and unabated endeavour.

What was so wrong with my father? A farmer, hearing how in the Continent the hay was being stuck on props to save it being ruined by rain, replied with a sneer, as his own hay lay soaking on the ground, "Oh! sir, we don't go to foreigners to learn our business." My father had done just that: an uncle of my mother's quotes this reply in his reminiscences, and may even have told my parents what to expect...Like Burns' heroes, they had "dared to be poor for all that". Paradoxically, this relative penury forced the family to make do with a better preparation for the future years, than would have been the case in the tradition-bound schools of the England that we all longed for. There we might have had, besides the much greater expense, an unhealthy atmosphere of recurring black fog. I well remember, when I was only about 3 years old, the family meeting at which we had to decide where to go next. International tensions had escalated, and Göttingen was no longer possible. I was the first the shout, "to ENGLAND!" All the family, except my father, whom I had interrupted, echoed my cry, even my baby brother, who could not yet speak and had no idea what the excitement was about, but who wanted to join in it. My father waited till we were quiet again, and then reminded us that he had been interrupted and still had something to say... In the end, we all changed our minds: I forgot what made me change mine, I think someone mentioned that in Switzerland there were EAGLES...

For the next 7 years, we lived at "La Nonette de la Foret" in Geneva, a house with a large veranda, where my parents had occasional informal mathematical gatherings, with formulae and so on written large, on makeshift "blackboards" consisting of sheets of paper stuck or pinned to the wall. We lived much in the extensive grounds of several acres at least, perhaps much more if childhood memories have not magnified dimensions. I am told that people thought we must be quite rich, for indeed millionaires could have no better home in which to bring up a family! Yet we were not charged for the privilege of roaming in the grounds or climbing trees. Nor were we charged much for medical expenses, when my mother's almost completed medical studies proved, from time to time, insufficient for some minor infection or mishap. Finally, our education, supplemented by books -- of which we had a houseful by no means exclusively in English-- was, I now think, the best in the world for us, yet comparatively inexpensive. All in all, our limited resources were no handicap, and we were fluent from early childhood in several modern languages.

For 4¹/₂ more years the flood of my parents' papers still continued, unabated and uninterrupted: 1 by my mother alone, 73 by my father or joint, as well as my father's Cambridge tract on the fundamental theorems of the differential Calculus. I should mention here specially my father's generalization of the Stieltjes integral, which created quite a stir. My father had become Special Lecturer at Liverpool (part time) and supplemented his income by examinerships. Later the Liverpool position became Professorship of the Philosophy and History of Mathematics, but the salary was only increased by L50. In August 1913, he was appointed for 4 years, the first Hardinge Professor of Mathematics at the University of Calcutta, a visiting position with a generous travel allowance, requiring residence for a few months on the year. For 3 years this greatly slowed the production of papers, as he threw his great energy into the many problems of his new appointment, and proposed making a report in mathematical education in various countries to help such matters. This was further complicated by the outbreak of World War I, and by his undertaking certain secret service duties for the British government, or for his brother who was in charge of the arsenals and small arms manufactories of India, I do not know which. Finally there were the worries and anxieties of a parent, with a son approaching military age, at a time of what we now see as senseless destruction, and yet self-sacrifice and heroism. Between September 1913 and June 1916 my father produced only 3 research papers, one of them joint with my mother, and she produced in her own name alone, 3 research papers herself, one of which won the Gamble Prize at Girton. Their other papers between the same dates comprised 3 lecture summaries (2 of them my mother's), 2 Calcutta expository papers ( 1 of then the inaugural lecture), and an essay on "Mathematics as an arts subject". I had occasion, however, to hear from the mouth of the teacher of one of my own doctoral students from India, how greatly that country's mathematical education benefited from what my father had done. Of all this, I was, of course, in the years at " La Nonette", much too young to have an inkling, but already my personal experiences throw some light on the nature of my parents, and the way they were, perhaps, taken advantage of, in this competitive world. Please do no be too severe on me for my part in these experiences, as I was very young.

I was perhaps 7 years old, when I discovered the honey jar: it had a spoon in it, which I felt sure was wrong. So of course I removed the spoon and I felt fully justified in licking it. Now, however, there was the further problem of where to put the spoon - where indeed except back in the jar? We are then in the original position, and the former procedure is repeated ... My father may not have realised that I had thus discovered mathematical induction, but instead of punishing me, he explained, not very convincingly, that he needed the honey for his health, and that we couldn't afford honey for the rest of the family. However, soon after this he started taking me for walks and talking to me about Sets. It was probably no more difficult than the New Math people tried to bring in later, but I reasoned that what grown men were working on, must be beyond a mere child, and I only pretended to be following. At the right moment, realising that the pretence could not last forever, I would suddenly say, just as he was getting argumentative, "No, I don't see that at all!" My father would get quite angry, and would go off. But the next day he would tell me, "You were quite right!" Of course I now realise that this could have been a tactful way of resuming the talks, but at the time, little imp that I was, I quietly gloated over my father's gullibility. Nor shall I ever know whether or not he saw through my little game on sundry earlier occasions, confident that I would grow out of such childish tricks...

Grow out of them I did and so did we all. Everything was changing very fast. We lost Auntie May, she had to look after Aunt Ethel; we lost our German governess, who had been with us 12 years and was in tears; we had to move from "La Nonette", the rent having been raised, to a house in Lausanne, to fit with my brother Frank's engineering studies; at the same time, the mighty British L having dropped from 25 Swiss FRs to about 16, we dispensed with domestic help, except for an occasional seamstress, who mainly used discarded clothing of older members of the family, to fit as well as possible younger ones. Further, as advised by the Swiss government, we bred rabbits and we grew potatoes: they were kept on our balconies in specially designed boxes, and we also supplemented our diet by puddings, made from starch, and used nettles and dandelions in place of spinach. All this. my mother supervised, and each of us, except of course my father and my eldest brother, had our appointed domestic tasks to fit in outside our school hours. My father meanwhile, awarded Honorary Doctorates in 1913 by the universities of Geneva and Calcutta, had, as I explained, by no means rested on his laurels. In particular, in connection with the report he was planning under the auspices of the University of Calcutta, he visited Japan in 1915, and he then spent several months in the U.S.A. He also worried very much about my eldest brother. But my mother wrote reminding him of St. Francis of Assisi, and there was no possible reply. Frankie left, straight after graduating at the top of his class, as an engineer, at the early age of 19. He was joining the Royal Flying Corps.

The flood of my parents' papers started again, continuing what was, perhaps, for both of them, their best work. In my mother's case, the work resulted in the "Denjoy and Mrs Young" theorems on derivatives, later completed and extended by a number of mathematicians. In my father's case, the main topic had now become trigonometric series, more particularly Fourier series and their allied series. The important Young- Hausdorff inequalities are among the results to which this work led. Now between early June 1916 and mid February 1917, my parents published a further 19 papers, 4 of them joint and 1 of them by my mother alone. In the first of these papers ( "On the convergence of the derived series of Fourier series"), my father introduced "Restricted Fourier series" and obtained, in this and subsequent papers, results now better understood with the help of Laurent Schwartz's theory of distributions. The joint papers I have spoken of earlier; they deal with "crystalline symmetry". This work too, may be regarded as leading to generalisations of the concepts of ordinary analysis and Sets of Points. It established for such a set, properties of symmetry locally, except in the vicinity of relatively rare points. Logically, the set does not have the complete freedom that is thinkable. This suggests the need for wider concepts, and in fact these have subsequently found their way into Analysis.

VII. The telegram.

It came early on a Sunday and could only mean one thing. My mother rushed to the front door. Yes, it was from the War Office... Moments later she was upstairs, and I heard what I have never heard again, my father crying. Frankie had been killed... "You hundreds of thousands," my mother wrote later," who have gone through what we went through, you will have a vision of those awful hours of agony! Then, 10 days after the news, the calm came-- a wonderful calm, no words of resignation taken from books, no colouring of religious fervour or affectation of feelings, caught at second hand. The calm was as truthful as the storm had been."

The flood of papers started again, but fitfully, and for quite a while all by my father: one note of April 1917, 9 papers from October to March 1918, then no paper for a year, and then, in 2 months, 4 papers on area and multiple integrals. The truth is that the main ideas had mostly accumulated in my father's mind during the previous long absences; the delays were due to my mother's difficulty in finding time to write up the final versions. She was struggling with them while having to run a household on a very tight budget and without outside domestic help. This last was an impossible task when the landlord raised the rent, as he wanted the property for himself.

We moved. Housing was scarce because of the war, but we were lucky. We found a much smaller house in what was unofficially known as the "village of postmen". The name of the house, "Chalet la denteliere", was appropriate, if you regard as lace (dentelle) the tiny garden's giant dandelions (dents-de-lion). To see where our belongings could go, my mother had to make a scale plan of the rooms and of our furniture. Also, to minimize moving costs and breakages, she herself carted, in an old conveyance that I shall not dignify by the name of perambulator, smaller items such as books and china, on many trips. Doubtless the rest of us helped similarly in the move.

The day we were due to move in, my mother and I had gone in advance to put some order into the items thus piled up in the various rooms and on the stairs of our new home. This was when two well-known and influential mathematicians called: I think they were de la Vallee Poussin from Belgium and Mittag-Leffler from Sweden. They had done so some years before, when I was alone at home and had told them nobody was in - I was then 11 years old and didn't know any better. This time my mother rose to the occasion, she was magnificent, she received them on the doorstep like a queen and explained that we were moving and that my father and eldest sister were away. She excused herself for a few minutes, and then again half an hour later when she brought her best china and tea, together with the famous family rock cakes, freshly baked, and I proudly assisted.

My father, meanwhile, had been far from idle. As a result of Frank's death, which he had been helpless to prevent, he had, for a time, been throwing his great energy into things for which he really needed a whole army of secretaries and assistants. In the previous months, after that day in June when Frank left to join up in England, he had tried hard to use what influence his friends might have, to get Frank transferred to more valuable and less dangerous work. In fact, for both my parents, even their mathematics had become secondary, compared with his news, and with their hopes. When these hopes were shattered, my father did make a great effort to complete the report he had undertaken for Calcutta: it got no further than about 100 badly printed gallery pages, though some of the sections were excellent. His visiting professorship at Calcutta was at an end, and he terminated his long association with Liverpool. He had ambitious projects: like many Swiss friends, he desired a reconciliation of the opposing forces, saving the best cultural traditions of the pre-war Germany. I cannot say that he was unsuccessful: his ideas and those of his Swiss friends have made at least a partial come-back since then, in what is now a different world, not without new problems. There was also his attempt to alter the British educational system-- he was unhappy, as I am, with its constant examinations, and with many other things, which have, perhaps, not improved. Finally, as the War ended, and his former advisee, J M Keynes, sent him a copy of the now famous "Economic consequences of the Treaty of Versailles", my father spent much time on economics, which was then, for a mathematician, in an unsatisfactory state. It was like a revelation to my father to come across the writings of the great 'Pareto', who had just died, and had been professor right in the local university.

Forces were, however, afoot for bringing my father back into mathematics proper. For one thing, we were hard up. For another, he was getting well-known, even in his own England, where the most absurd stories about him were still being circulated. In 1917 the London Mathematical Society awarded him its de Morgan medal. Hardy and Littlewood had become strong supporters, particularly after an annoying comment of my father's, at a London lecture by Littlewood, had turned out most helpful! This support might have been ineffective, since Hardy was also supporting the pacifist Bertram Russell, but the death of my eldest brother was proof enough of the family's patriotism. At any rate the word got around that an important mathematician (just think of it, a 4th WRANGLER!) was available, and the University of Wales at Aberystwyth offered him the post of Professor of Pure Mathematics, which he accepted, starting in the academic year 1919-20.

In the Swiss Canton de Vaud, we had our friends, in particular my eldest sister's mathematics teacher, Monsieur Jaccottet, who had been, 25 years previously, one of "the pentagon" of fellow-students of my mother's under Felix Klein. Otherwise my father's reputation, and his belated recognition in Britain, had made little or no impression in that part of Switzerland, which has its own way of looking at things. As an example of the strength of local tradition at the portion of our XXth century, I might mention that in November 1925, at a lakeside municipality among the vineyards, near Lausanne, someone was fined three FRs -for wheeling a wheelbarrow during sermon-time.

Not all local traditions were as sanctimonious, but it does remind us of the time when learned theologians from that area were leading the Protestant cause, and the words of their sermons were firing the hearts of many ardent followers in Scotland and in parts of England, and also those of my father's Huguenot ancestors on his mother's side. Since that time, classical learning, supported by theology, had been the pride of the Canton. The school I went to, because of its fine reputation, was even exempt from federal examinations.

The shock of my brother Frankie's death mainly made me realise that I must take on new responsibilities. My conscience smote me for sundry misdeeds and deceptions that I had got away with. The Bishop, who confirmed me about that time in the Church of England, must have mistaken my pangs of conscience for religious fervour! He said to me, " Why not choose a career in the Church ?" I seemed surprised, so he added, what would have killed any religious zeal, "There's money in it!" I made a different choice: I was eager to learn-- so were we all, in the family. I persuaded the School authorities to let me skip a year, to avoid the 1st year of English, and a trimester later to allow me to switch to the Greek section. I wanted a difficult task. I found in the section some boys, like me, keen. Soon we were all reading Homer, far ahead of the others. For us, the words of Goethe still rang true:

When we stand face to face with antiquity and gaze earnestly at her with the object of taking her as a model, we get the feeling of becoming for the first time human beings.

My interest in Greek-- my passion for it-- was infectious, not only among my classmates, but also in my own family. My mother began to spend what time she had on Plato and she made notes of ideas that might help my father's projects. Soon I too was an avid reader of Plato, and I obtained a School Prize for reading the Theaetetus. My two eldest sisters started Greek too, and they sent me postcards in Greek whenever we were apart. My other sister (Marion) and my young brother (Pat) did not join in this. Pat, my little playmate and the family darling who had -"kissed the Blarney Stone" had just been admitted to my school; there, to our shocked surprise, he proved to be, for 3 years, irrepressible. Marion --one of a few girls allowed, on a trial basis, to attend my School, where she joined the section "mathematiques speciales" in the class above mine and was 2nd -- had no time for things like Greek and was soon earning money from Tutoring and using it to pay for her own clothes, she was anxious to be financially independent.

To me it seems as if Pat resented inwardly those who had stayed neutral, while Marion, who had specially admired Frankie, as all of us had, resented rather those who allowed useless slaughter. Like the rest of us, they were really reacting, in their different ways, to the same tragic shock as us all; and they were doing so all the more strongly, because Swiss tradition is so different from British and because Frankie fitted in with either.

VIII. Collonge and Aberystwyth.

At Aberystwyth my father made great efforts to build up an up-to-date mathematics department, taking advantage of the hardships experienced by mathematicians in post-war Europe. It was not difficult to persuade the financially embarrassed to give visiting courses: the difficulty was in persuading people in Britain to let them come and to pay the modest honorarium. This difficulty reappeared in many places in the 1930's and hardly need be explained more fully. Let me just mention that, in some cases, my mother, bless her heart, sent the prospective lecturer money to buy decent clothes and that one such person stayed at our house for quite a while. We had moved again, this time to a place 5 minutes by train from Lausanne, having bought a large house "Collonge".

My father was in term-time in lodgings at or near Aberystwyth, with one of my sisters (Cecily in 1919-20 and in 1921-22, Janet in 1920-21), or my mother (1922-23). At Collonge we had quite a fair-sized garden, and we had bought a vineyard and various pieces of land, to help preserve the fine view. We looked onto Lake Leman, over the picturesque roofs of Lutry, and to the mountains of the French coast opposite, rising out of the Lake. Our carrier pigeons and our bees used to fly straight across. Our white Pekinese ducks, as big as geese, were quite content, in the absence of a near stretch of water, to go weeding among the vines. Our rabbits -- descendants of our prize silver-fur pet-- mowed our grass when we placed them in specially devised roly-polys of wire netting. Our population of pets also included a huge black cock and his 8 or 9 hens and at times a couple of guinea fowls and one or more great turkeys. My brother Pat and I, aided or impeded by our great mongrel dog and a pair of tiny cheeky bantams, were in charge of the daily show and of its pandemonium of protests and excitement. We attended to the daily needs of our protŽgŽs, and they in turn supplied much of the family food, not much more expensively than in the local shops. We also had virtually limitless crops of strawberries, cherries, pears and apples, and even some quince, at the appropriate times of the year, for our own consumption, and of course grapes, though the birds and wasps etc. had their share too. We continued with all this, long after the post-war shortages and rationing had ended, and to make up for what Pat and I thus took on outside, my sisters had a corresponding bigger share of the daily chores inside the house. However all this had to be fitted in, most of the year, between school or university hours, and in the vacations between my father's requirements when he was at home, so that the bulk of the work was still done by my mother, and generally with her characteristic look of intelligent sympathy, as if she was always ready to help someone else.

This may sound hectic if we add that, twice a week, milk had to be fetched between 5 and 6 o'clock in the morning after a steep 20 minute climb, and that the train to Lausanne, that we caught to go to school, left at about half past 6, six days a week. It almost goes without saying that the train might sometimes be missed. In that case it was still possible to scramble down and up steep slopes of prickly bushes and to run all the way after that. The temptation to avoid much of the prickly scrambling was very strong: this meant a forbidden crossing by an electrified railway bridge. I regret to say that I was not the only one in our family to risk my life in this foolhardy way. Even so, though I was unaware of such things at the time, living in Aberystwyth in the 1st few post-war years, was, by comparison, grim indeed. For one thing, ex-soldiers, returning from insanitary trenches, had brought back most unpleasant infections, quite apart from the terrible 'flu that killed as many people as the war itself. After extremely trying experiences, my father had to institute most drastic precautions. For another, the milk and butter were hardly of the quality we had got accustomed to in Switzerland, and the food generally was not precisely as delectable as my mother's home cooking; moreover, even fish was of poor quality, the best being sent straight to London. Living conditions were a little better at the start of my father's 2nd year, as he now had lodgings some 8 miles away and came in by train to Aberystwyth daily with my sister Janet, who was with him that year: they were now able to bathe in the Gulf Stream. However a rail strike spoilt it all, as there was now only one train a day each way, at an unpredictable time, and they were sometimes obliged to walk. On one occasion when they were waiting for the train, Janet strolled to the other platform, and the train arrived before she had time to get back. What could she do? The train only stopped at their station for a moment. She got into the train from the wrong side, crossing the live rail. My father nearly had a fit: he was terrified. He had lost Frank and now he was about to lose Janet... When she entered the train unhurt, he gave her a long lecture and dictated a letter, full of reproaches to my mother, on the way she had brought up, first Frankie, and then Janet, perhaps others: (He little knew of earlier transgressions on the Swiss railway bridge!) The letter, mercifully, was never posted: Janet had destroyed it as soon as written. We never heard of this episode-- I learnt of it only 60 years later! All Janet posted was the usual brave little postcard to me in Greek. My father, having relieved his feelings, never mentioned the subject again.

There was, however, at the end of the academic year, one most worrying incident. My father had to stay a little longer in Aberystwyth, so he arranged for Janet to travel as far as Paris with a mathematician, who was going there after giving a course of lectures as visitor in my father's department. Janet was shown Paris and duly put into her train to Lausanne, and my father had written to tell us when she would arrive. We met the train, she was not on it. My mother, all of us, were terribly anxious; I well remember that day: hour after hour , and no Janet. Finally she arrived, 12 hours late: she had been put into the wrong part of her train at Paris and had gone to sleep. When she woke up, it was at a little place where there was no train back for hours: what's more, she had been robbed. One consequence of all this, is that Marion, who finished school that year, absolutely refused to take her turn and accompany my father for one year at Aberystwyth. She had become a rebel, convinced that Swiss ways were best, and the family, particularly my father, all wrong. She wanted to study for a University certificate in mathematics at Lausanne.

I am not saying that she was wrong to want this: it was presumably just what the mathematician de Rham did at that time, after making a remarkable contribution in a totally different field. But of course, as my father's helper. she would have learnt plenty of mathematics too! She could hardly expect him, the professor, to admit that she would learn more, in the time, at Lausanne? It would be different if she were to register in a different subject : in that case Lausanne might well be better- for instance in medicine.

My father could be very persuasive; he once persuaded Professor Hobson to vote Conservative -- Professor Hobson remained a friend, but never really forgave him. Marion never really forgave my father when he got her to register in medicine: she complained of the hard work it was, to make up the semester thus lost, and eventually it led to her break with the family in June 1924. There were of course by then other matters involved, but I doubt that they would have occurred but for her resentment of my father's well-meant persuasiveness. Actually medicine was a good thing to study, both because of its great progress in the war years, particularly in surgery, and because of the post-war epidemics. Also, if she had done more medicine, it might have spared her in 1948, at least from a painful useless treatment, when she was dying of Cancer in Paris. In any case, the break only lasted a few years, and was entirely in character. Both before and after the few years of her break, she could be at times impossible, and at times quite charming. Also she would tackle great domestic tasks, long neglected because of urgent matters, though in her hurry to make it seem in order, she was not above "sweeping dust under the rug". On the whole my mother loved her dearly, and spoke of her " starry eyes", and we all shared my mother's feelings. All too soon any strains within the family seemed insignificant compared with events outside; and for my part, I had for some time similarly realised the insignificance of the little imperfections I had thought to have discovered in the various people around me. From about 1919, I learnt to appreciate more and more my parents and also my teachers at school. Mine was thus not an uncritical admiration, which breeds fanatics who see only one side of a question. In the final years at school, when I was learning ( at long last) what many of the subjects taught, history in particular, really should be, I realised, among other things, what a wonderful library my father had collected. I was able to consult, for instance, the many volumes of Lavisse, History of France: need I say more? His interests and his knowledge were encyclopedic.I gather that in his Aberystwyth lectures my father was similarly encyclopedic: his was a department of mathematics as a whole, not one of algebra, or geometry, or analysis, etc., nor of still more specialised fields. His lectures covered many mathematical topics, including some of his own contributions, and giving enough information --barely enough-- to make it all exciting, challenging, puzzling and yet accessible, thus forcing his auditors to read in the library, and to think hard and cooperate among themselves. It was hard work for my father as well, and to provide perspective, it needed supplementing by his scheme of visiting foreign lecturers. That was precisely where there was opposition: the University President wanted lecturers to be Welsh! Surely "University" implies some universality? My father won, but the wear and tear, and the self-imposed load of teaching affected his health. In his 4th year at Aberystwyth he applied for leave for the Summer term of at least the following academic year. This was refused and he resigned.

IX. Honours and thwarted efforts.

A few months after Janet's experience on the trains, my mother and I had a similar experience in Italy. I had had a number of illnesses, and the famous Swiss doctor consulted on my behalf had said simply that I should do what I liked! So there we were on our way to Florence and thence to the seaside in the month of October of 1921, and I was armed with a heavy suitcase of books, to make up by reading what I was missing at school. We had to change trains at Milan, and a great crowd was there on the platform waiting for our next train. When that train finally arrived, everyone rushed to get a seat and we thought ourselves lucky to have found 1st class seats for which we paid the supplementary charge. Unfortunately we were not told that that part of the train would be separated off to go to Rimini and Ancona... We had otherwise a most pleasant month in Italy, and I particularly remember the last week and the friendly cordiality of Bianchi in Pisa and of Pincherle, Enriquez and Tonelli at Bologna: at this last city, we saw briefly, from a gallery, Einstein giving a lecture , and vainly trying to explain to a protesting audience that the universe is finite but unbounded, finito ma illimitato. The great Vollera, who had known my parents in their early days at Turin, was similarly extremely friendly and cordial some 16 months later to my sister Cecily and myself, when we had a day in Rome on our way home from Sicily after a winter we had passed, for medical reasons, in the South. Clearly Italy, even under Mussolini, was a land where my parents had many mathematical friends. The same could be said of Poland, where, more than anywhere else, Set Theory had been taken up, and where the great Sierpinski always sent my parents his famous journal, Fundamenta Mathematicae, "a titre gratuit". There was another link between Sierpinski and us: he had lost his collaborator Janiszewski, and we had lost our Frank. Years later, at the Edinburgh congress of 1958, when I met Sierpinski his eyes had tears in them and I was deeply moved.

When my father left Aberystwyth, he was just under 60 years of age and he had written, in his 4 years as professor there, under his name, 17 research papers ( 1 of them joint with my mother), and also accounts of 2 lectures and an obituary. My mother had managed to produce further an account of a lecture of her own together with 4 papers. It was some help, having my 2 eldest sisters take turns at Aberystwyth, but even so I cannot imagine how she managed those papers, and reading Plato, and resuming her playing of beautiful piano music, as if there was nothing much to do, without outside help, at Collonge, in our big house and in our vineyard and grounds! Then, in the Spring of 1922, both Cecily and I contracted appendicitis - (Cecily mildly). My mother began to feel the strain, just as my father did. In the Summer they both went to Bad Nauheim for a cure. while they were in Germany, they arranged with Bolza, who had retired from Chicago, that Janet should study medicine the following academic year at Freiburg, and that he would see her properly installed and registered.

The following April, my parents again were at Bad Nauheim, that was when the decision to give up Aberystwyth was made. I well remember being consulted, and so were others of the family. I was for resigning - health should come first. My parents wrote a few papers after that, but mostly they embarked on projects of a different kind. One such project, which was most certainly not of his seeking, and in a sense a thankless one, arose from the high reputation and affection, in which, by contrast to his early years as pioneer, he was now mostly regarded. He had been nominated in 1920 as England's representative to the International Mathematical Union, formed for the organisation of the Strasbourg Congress of that year. Then in 1922 he was elected president of the London Mathematical Society, which refused to recognize that Union, because it was now organising at Toronto the next congress and German mathematicians were excluded.

My father was thus placed in a difficult position: telegram after telegram was received at Collonge, urging him to take part in the Toronto Congress of 1924. In the end my parents went, as private persons, and as guests of the French delegation. A very special cabin was assigned to them on the Suffren, and after the Congress my mother went on to Bryn Mawr, Pennsylvania, to see her College friend Miss Maddison, and to give a lecture on "The taming of infinity". My father of course gave a major address to the Congress, but it was of the nature of a survey, as such addresses usually are. The same may be said of his retiring presidential address to the London Mathematical Society, except that it was read in his absence, and that it ended with a quotation from Shakespeare's "The Tempest", the famous lines beginning with "This rough magic I here abjure". I do not think that his powers were declining, but rather that he felt that others, particularly my sister Cecily and myself, who were developing promise in mathematics, should now take over.

I was then in good hands, studying in Munich and running the Seminar of Caratheodory and Perron in Analysis. My sister Cecily had impressed our friend Professor Hobson, by questions about Relativity when on her way to the Hospital for an appendictomy! Eventually we both obtained Research Fellowships at our respective Colleges. Also Marion obtained eventually a Scholarship in Mathematics at Bryn Mawr - she was by then quite reconciled with the rest of the family. Moreover we were all, Janet and Pat too, on our way to financial independence.

My father was, meanwhile, receiving further honours. He was nominated by the University of Lausanne as Honorary Professor, but this met with some local opposition and came to nothing. (He was not a resident (for tax purposes) and this may have had something to do with it.) There was also some talk of his possible return to Liverpool, but this again went no further. However he became Honorary Council Member of the French Mathematical Society, and Corresponding Member of the Institute of Coimbra. ( He gave a lecture at Coimbra in 1927, and a quarter of a century later a research student from Coimbra came to Cambridge to work under W.H. Young, who had then been dead some 10 years.)

In 1928 my father was awarded the Sylvester Medal of the Royal Society and an Honorary Doctorate of the University of Strasbourg. That same year he attended the Bologna Mathematical Congress with my mother and with Cecily and Pat, and he was elected a vice-president of the Congress. He gave an address "On the mathematical method and its limitations". The Bologna Congress was the first after the 1st World War at which the German mathematicians were invited, and there was general applause when they appeared led by Hilbert, in spite of the boycott urged by L E J Brouwer from Holland. Unfortunately, this did not mean that Germans were now admitted to the International Mathematicians Union. My father was made President of that Union in 1929, and he worked hard at trying to bring the Germans into it, and generally at transforming the Union into a really international one.

During 1929-30 he visited some 16 countries and saw ministers and leading mathematicians; he also lectured in various languages on the aims and ideals of his Union, and he prepared revised statutes. It all came to nought. Red tape and the anti-German feelings of the President (now Emile Picard) of the International Research Council (to which all International Scientists Unions were then subject) so delayed any change, that in the next Congress, held in 1932 at Zurich, nobody had the slightest interest in the International Mathematicians Union, and it was the same in 1936, at the Congress in Oslo. My mother, as "provisional private secretary", had typed hundreds of useless letters and assisted in the preparation of proposed new statutes and so forth. She had also done many things on her own, for instance she wrote to Gohring, when Hilbert had been arrested and was in due course released. There was further no scarcity of projects, that she, or my father, began work on: in particular she worked on various versions of an Elizabethan novel of some 400 pages that she found no publisher for.

In 1939 my father was elected to an honorary fellowship at his old College, Peterhouse. My mother was similarly proposed for an honorary fellowship at Girton in March 1944, but she died before it could be awarded. By then my father had died, in July 1942, separated from her since May 1940 by the events of the War.