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Home , David Cox (statistician), Dennis Lindley, Egon Pearson, Frank Anscombe, Frank Yates, Harold Jeffreys

“I didn’t want to be a ” Making mathematical in the Second World War

John Aldrich University of Southampton

Seminar Durham January 2018

1 The individual before the event

 “I was interested in . I wanted to be either an analyst or possibly a mathematical physicist—I didn't want to be a statistician.”

David Cox Interview 1994

A generation after the event

 “There was a large increase in the number of people who knew that was an interesting subject. They had been given an excellent training free of charge.”

George Barnard & Robin Plackett (1985) Statistics in the ,1939-45 Cox, Barnard and Plackett were among the people who became mathematical statisticians

2 The people, born around 1920 and with a ‘name’ by the 60s : the 20/60s

Robin Plackett was typical  Born in 1920  Cambridge mathematics undergraduate 1940  Off the conveyor belt from Cambridge mathematics to statistics war-work at SR17 1942  Lecturer in Statistics at Liverpool in 1946  Professor of Statistics King’s College, Durham 1962

3 Some 20/60s (in 1968)

4 “It is interesting to note that a number of these men now hold statistical chairs in this country”*

Egon Pearson on SR17 in 1973 In 1939 he was the UK’s only professor of statistics

* Including  Aberystwyth 1960  School of Hygiene 1961  Robin Plackett Durham/Newcastle 1962  H. J. Godwin Royal Holloway 1968  Maurice Walker Sheffield 1972

5 SR 17 women in statistical chairs? None

Few women in SR17: small skills pool—in 30s Cambridge graduated 5 times more men than women

Post-war careers—not in statistics or universities

 Christine Stockman (1923-2015) Maths at Cambridge. She had started a PhD in astronomy and returned to complete it. She married astronomer .

 Florence Rigg (1917-2010) had a career in computing at the National Physical Laboratory and Atomic Weapons Research Establishment

 Vanessa Allinson (1921-2011) maths at Cambridge and career at GCHQ

6 Outline of talk

 Background  Experience of the First World War  Mathematical statistics in the 30s

 The Second World War  The old unplanned continued  The planned war—arrangements in Cambridge

 A major destination—SR17

 Afterwards

7 A glance at the Great War Interesting because  By comparison the Great War had no significant educational effects for statistics  Some of the institutional changes that contributed to WW II’s positive effects on statistics had their origins in the Great War

8 In 1914 mathematical statistics had one centre in UK: at UCL Over 20 years KP had built up a team researching and teaching biometry/statistics He and his team of computers could produce tables like

9 ‘System’ in the Great War  Before  No concept of manpower planning  No expectation of a long war

 During  before conscription: scientists, including students, volunteered for armed forces  after conscription: immediate needs of forces had priority  Scientists made a contribution by improvising + exploiting connections

10 A V Hill (1886-1977) improvisation & connections

 Pre-war Cambridge fellow and member of Officers’ Training Corps

 Joined infantry in 1914

 In 1916 transferred to Ministry of Munitions to assemble a team to work on anti-aircraft defence

 Through contacts recruited Karl Pearson’s band of computers to work on ballistics

11 1917, KP’s year of ballistics computing

 The work Hill wanted belonged to KP’s past as prof of applied maths not to his present as prof of eugenics  So why do it?  KP wanted to contribute to the war effort and there was no demand for biometrics/eugenics  KP wanted to preserve his team—perhaps enlarge it  Staff were leaving—Herbert Soper (1865-1931) joined the Labour Corps  KP had up to 20 people working but none stayed

12 Pearson’s old students— Greenwood & Yule, good war, bad war (1871-1952) lecturer in School of Agriculture Cambridge. Worked as statistician to the Army Contracts Department and Director of Requirements in the Ministry of Food. (1880-1949 He “never spoke to me of these years with any At Ministry of Munitions which affection” recalled Maurice ran the factories supplying the Kendall army. Work played to his Did some joint work with strengths: studied sickness in Greenwood on accident factories proneness

13 Mathematical statistics did little for war and war did little for stats

 The only demand for math stats came through medical stats  KP and Yule applied their general skills elsewhere on work unconnected with their main interest  For 4 years nobody was taught—the universities were open but empty—and little research was done  Losses were heavy—2000 Cambridge men killed and 3000 wounded though no ‘name’ mathematical statisticians were killed.

14 The late 30s: math stats had spread

 UCL still dominant. After KP’s retirement: at the Galton Lab, at Applied Statistics and J B S Haldane as Professor of Biometry  London School of Hygiene (Greenwood and Irwin)  Cambridge University mathematics (Wishart and Bartlett)  Research bodies: Rothamsted (), Shirley Institute (L H C Tippett), Wool Industries Research Institute ()

I focus on Cambridge because it was the main centre for mathematics and would supply most of the 20/60s

15 Cambridge was producing 30% of UK mathematics graduates Historically the source of mathematical statisticians

 Karl Pearson graduated in 1879

 Ronald Fisher graduated in 1912

graduated in 1913

 Egon Pearson graduated in 1921

 Frank Yates graduated in 1924

A course on the theory of errors (usually taught by an astronomer) was the closest they came to statistics

16 Statistics in Cambridge mathematics

 Yule retired from the School of Agriculture in 1931

 Replacement John Wishart (1898-1956) came from Fisher’s Rothamsted to teach maths students as well as agricultural students

 Maurice Bartlett (1910-2002) came as Mathematics lecturer in 1938. A Wishart student he had worked in ESP’s department and at an ICI research establishment

 And not exactly statistics: Arthur Eddington taught theory of errors and Harold Jeffreys his theory of

17 Wishart’s pre-war course: leading somewhere or nowhere Kempthorne  “I got turned off pure mathematics because it did not seem to be going anywhere. A course in statistics seemed to lead somewhere.”

Barnard (aspiring mathematical logician)  “I started going to it but it was so bad that I gave it up. He never got beyond moments … And I decided it was not for me.” K and a few like him had planned careers in statistics B and more like him had unplanned careers

18 Planning the scientific war—A V Hill

As Secretary of Royal Society initiates Register of Scientific Personnel

Besides efficiency a personal dimension reflecting his own experience in Great War:

 Nobel Prize for “I was aware that there were physiology other tasks I could undertake which were really more essential,  From 20s UCL professor but that was not the sort of thing  In 30s advises one talked about when other government on air chaps were being killed.” defence

19 The new planning

 Perspective  Universal conscription  Comprehensive manpower planning  Expectation of a long, science-based war making universities part of the war machine

 Details  University teachers exempt from conscription  Special treatment for medical and science students  Shorter degrees

 Uni committee assigns finishing students to war 20 k Planning on the ground? Join the Navy

In 1939 the call went out to join the Navy—many responded

The right stuff (David Kendall on the application form) a tremendous form with a narrow little band about an inch wide in which to write up one’s academic career, and huge boxes for sporting achievements in which I could write absolutely nothing! Duties (as explained to Barnard)  officially to teach the junior officers basic mathematics  really to answer questions about bets. “You’re in the Officers’ Mess and people will ask you about poker. How are you at it?”

None were chosen

21 Planning? Join the Army

Undergraduate (John Hammersley) I have just started to read mathematics here in Cambridge. Is there any use for mathematics in the army?

Don/Sergeant There is no use for mathematics in this war and in any case you are only an undergraduate. The services have taken just three professional mathematicians from Cambridge, one for the navy to tell them about underwater explosions, one for the air force to explain stellar navigation My mathematical job is to add up the daily totals of recruits for the army, navy and air force respectively.

22 UCL Statistics volunteers for war

Like his father, Egon Pearson wanted to contribute + keep his department together

BUT “I would rather look after an anti-aircraft gun than have to compute range tables” SO  The whole Department moved to the Ordnance Board  People in the department include D. J. Bishop, Norman Johnson (1917-2004), B. L. Welch (1911-89) and F. N. David (1909-1993)  No new statisticians trained: the teaching department closed and the Ordnance team recruited nobody

23 Cambridge statisticians volunteer

 Wishart (infantryman in First War) works for Military Intelligence and Admiralty—doesn’t contribute to math stats

 Bartlett joins the Projectile Development Establishment of the Ministry of Supply (M of M reborn)

 Anscombe his research student goes too

 Bartlett does contribute to math stats (and to stochastic processes) with research and by training David Kendall

24 1940-5: rockets and probability

Initially the work was on anti- Bartlett became interested in aircraft rockets and then on stochastic processes— air-borne ground attack largely unconnected with war weapons. work and under the influence Lots of design and analysis of of Jo Moyal a refugee from . Continuation of France and familiar with pre-war research international probability.

25 Bartlett’s apprentice

 Oxford First in 1939  Career in astronomy or analysis?  March 1940 joins PDE and begins works as a “computer”  Becomes a statistician David Kendall (1918-2007)  Replaces Anscombe as Bartlett’s assistant *Kendall’s boss tells him:  After war follows Bartlett into “I’ll give you a week to learn applied stochastic processes the subject. Go up to London, and stay in Anscombe’s  In 1953+ works with Harry Reuter lodgings. You’ll help him on stochastic processes a la Doob . during the day with whatever he’s been doing.”

26 Kendall’s (later) co-author

 Graduates in 1941

 War-service for Admiralty— don’t know its nature but seems to have had no influence on post-war career

from 1946 working on differential equations

 Starts in probability in 1951 Harry Reuter  Ties up with Kendall 1953 (1921-92)  Professor of Pure Mathematics in 1963 at Durham 1959-65

27 The students

 Planned careers diverted—examples  C A B Smith  Oscar Kempthorne 

 Unplanned/unwanted careers  national need for statisticians—stats teaching for all  Statistical war work

 A major destination—SR17

28 Cedric Smith (1917-2002)

 Part III distinction in 1938.

 research in statistics under Bartlett, Wishart and Irwin: PhD in 1942

 hospital porter for rest of war (Quaker and conscientious objector)

 Other Quaker 20/60 Ken Tweedie (1919-96) Manchester + Liverpool

 CAB to UCL at end of war

29 Frank Anscombe (1918-2001)

 Part III distinction 1939

 Research student of Bartlett

 Goes with Bartlett to PDE (see above)

 SR 17 (see below) 1943

 Rothamsted 1946.

30 Oscar Kempthorne (1919-2002)

 Entered in 1937

 Part III distinction 1940

 Department of Tank Production, Ministry of Supply

 Rothamsted 1941

31 Cambridge mathematics teaching at War numbers of male undergraduates in 2 wars year total year total 1914 150 1939 140 1915 86 1940 140 1916 43 1941 101 1917 25 1942 72 1918 16 1943 89 In Second (shorter degrees)  Part I numbers held up  Part II shrank from 60 in ’39 to 21 in ’43  Part III virtually disappeared

32 Wartime lecturers

Gone  Wishart  Bartlett

Remained  Jeffreys theory of probability  Eddington theory of errors

Came  J. Oscar Irwin (part of the University of London was evacuated to Cambridge)

33 Student reviews of Irwin’s lectures  “moments, cumulants, and descriptive measures of frequency distributions which did not seem to me to be intellectually very exciting” Durbin

 “wasn’t terribly inspiring” Cox of Jeffreys’s lectures  “intriguing but almost totally incomprehensible” Cox

34 The Committee: choice or no choice

: I didn’t want to go into statistical work, which I thought would be rather unexciting … they put me into a unit called the Army Operational Research Group.  Dennis Lindley: I much preferred the Civil Service to the armed forces  Statistics or electronics? Norman Bailey chose electronics and went to Admiralty signals department. (The work involved statistics so it was stats anyway)

35 Other destinations of 20/60s

 Armed forces  (1924-2010), air force navigator  John Hammersley (1920-2004), army ballistics

 Scientific Civil Service but not stats  Michael Healy (1923-2016), Admiralty  Reuter, Admiralty

 Other  Maurice Quenouille (1924-73) interested in stats to Rothamsted—just like peacetime

36 Sent to be a statistician  Going alone e.g.  Cox to Department of Structural and Mechanical Engineering at RAE Farnborough  “attached to the air force and concerned with the interpretation of tests of new weapons”

 Going to a group—SR17  1942: from 18 wranglers (firsts): Baines Plackett Redfern  1943: from 16 wranglers: Godwin Lindley Walker; from 5 senior optimes Burman and Winsten 37 SR 17 = Ministry of Supply’s Advisory Service on Quality Control

 Need not foreseen

 Improvised in 1942

 Set up by a civil servant and an analyst (Frank Smithies)

 Responding to American example

 The British expert on quality control—Egon Pearson— not involved

38 Statistical knowledge + connections

Seniors

 Edward van Rest (born 1901) worked on forestry statistics pre-war

Barnard with . A. Fisher around 1957  Anscombe was young George Barnard (1915-2002) but already experienced graduated from Cambridge and went  Barnard, the main source to Princeton to do mathematical logic. Frank Smithies was a friend there. of ideas, was self-taught Connection with Smithies got him into SR 17.

39 SR 17: the work I

Geoff Jowett  we were sent round ordinance factories to install quality control charts and inspection schemes …

 In convincing others that we had a good product to sell we convinced ourselves

40 SR 17: the work II

Dennis Lindley  We attended the National Gallery concerts at midday and we did the Times crossword. Seriously it was like being a group of Ph.D. students without a supervisor  Much practical work was done  but in our section, under George Barnard, we were just learning statistics. We read all the “big papers” and slowly began to understand what the subject was about

41 Not just learning—publications

A string of technical reports (some became journal articles  No. Q.C/S/7 The Choice of Control Limits and Sample Sizes for Control Charts. 1944  No. Q.C./R/28 On some Properties of Binomial Sequences. 1944  No. Q.C./R/27 A Contribution to the Theory of Maximum Precision in Industrial Experimentation 1944  etc

42 SR 17 in retrospect

 In its short life SR 17 produced more statisticians than any of the regular peace- time establishments  Unlike its US counterparts which involved established statisticians SR 17 had no big guns to support it  It realised the First War dream of KP—useful war work that drew talent to statistics

43 What then for the wartime recruits?  Finishing degree

 Most return to being students. Delicious anomalies: Artillery Major Hammersley JRSS author back as an undergraduate.  Academic posts  Plackett spends year at NPL then to Liverpool as Lecturer  Barnard becomes Senior Lecturer at Imperial  Leaving statisics  Ralph Henstock of integral fame

44 Not quite the new dawn so recalled

 “as late as 1955, certainly as late as 1950, I would have still seriously considered giving up statistics. Partly because the career opportunities in statistics at that time seemed terrible.  There was this burst of activity during the war and immediately following,  but … the possibility of ever becoming a full professor in the university system seemed very remote indeed.”

45 END

46 Literature

Papers in preparation (basis for the present talk)

 John Aldrich (2018) “The immense demands of war”—British Mathematical Statisticians in two World Wars  John Aldrich (2018) “It took a global conflict”— the Second World War and Probability in British Mathematics

WW I

 June Barrow-Green (2014) Cambridge Mathematicians’ Responses to the First World War  June Barrow-Green (2015) “Anti-aircraft guns all day long”: Karl Pearson and Computing for the Ministry of Munitions  Anna Carlsson-Hyslop (2015) Human Computing Practices and Patronage: Antiaircraft Ballistics and Tidal Calculations in First World War Britain  William Van der Kloot (2011) Mirrors and smoke: A. V. Hill, his Brigands, and the science of anti-aircraft gunnery in World War I

47 Inter-war period

 John Aldrich (2009) and Continental Probability in the Inter-War Years  John Aldrich (2010) Mathematics in the London/Royal Statistical Society 1834- 1934

WWII Surveys

 George Barnard and Robin Plackett (1985) Statistics in the United Kingdom,1939-45  Helen Joyce (2014) They also served: How statisticians changed the War and how the War changed statistics, Economist, December 20th.  David Edgerton (2012) Britain’s War Machine

Individual experiences

 Interviews in Statistical Science and Econometric Theory  Obituaries in Biographical Memoirs of Fellows of the Royal Society and JRSS

48