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“I didn’t want to be a statistician”Making mathematical statisticians in the

Second World War

John Aldrich University of Southampton

Seminar Durham January 2018

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The individual before the event

“I was interested in mathematics. I wanted to be either ananalyst or possibly a mathematical physicist—I didn't wantto be a statistician.”

David Cox Interview 1994

A generation after the event

“There was a large increase in the number of people whoknew that statistics was an interesting subject. They hadbeen given an excellent training free of charge.”

George Barnard & Robin Plackett (1985) Statistics in the United Kingdom,1939-45

Cox, Barnard and Plackett were among the people who became mathematical statisticians

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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

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Some 20/60s (in 1968)

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“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 Dennis Lindley Aberystwyth 1960 Peter Armitage School of Hygiene 1961 Robin Plackett Durham/Newcastle 1962 H. J. Godwin Royal Holloway 1968 Maurice Walker Sheffield 1972

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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 Hermann Bondi.

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

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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

Afterwards7

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A glance at the Great WarInteresting 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

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In 1914 mathematical statistics had one centre in UK: Karl Pearson at UCLOver 20 years KP had built up a team researching and teaching biometry/statisticsHe and his team of computers could produce tables like

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‘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 connections10

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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

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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

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Pearson’s old students— Greenwood & Yule, good war, bad war

Udny Yule (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. He “never spoke to me of these years with any affection” recalled Maurice KendallDid some joint work with Greenwood on accident proneness

Major Greenwood (1880-1949At Ministry of Munitions whichran the factories supplying thearmy. Work played to hisstrengths: studied sickness infactories

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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.

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The late 30s: math stats had spread

UCL still dominant. After KP’s retirement: Ronald Fisher at the Galton Lab, Egon Pearson 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 (Frank Yates), Shirley

Institute (L H C Tippett), Wool Industries Research Institute (Henry Daniels)

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

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

Karl Pearson graduated in 1879 Ronald Fisher graduated in 1912 Harold Jeffreys 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

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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 probability

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Wishart’s pre-war course: leading somewhere or nowhereKempthorne “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 statisticsB and more like him had unplanned careers

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Planning the scientific war—A V Hill

As Secretary of Royal Societyinitiates Register of ScientificPersonnel

Besides efficiency a personaldimension reflecting his ownexperience in Great War:

“I was aware that there wereother tasks I could undertakewhich were really more essential,but that was not the sort of thingone talked about when otherchaps were being killed.”

Nobel Prize for physiology

From 20s UCL professor In 30s advises

government on air defence

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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

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Planning on the ground? Join the NavyIn 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?”

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Planning? Join the ArmyUndergraduate (John Hammersley)

I have just started to read mathematics here in Cambridge. Is there any use for mathematics in the army?

Don/SergeantThere 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.

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UCL Statistics volunteers for warLike 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

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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

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1940-5: rockets and probability

Initially the work was on anti-aircraft rockets and then on air-borne ground attack weapons.Lots of design and analysis of experiments. Continuation of pre-war research

Bartlett became interested in stochastic processes—largely unconnected with war work and under the influence of Jo Moyal a refugee from France and familiar with international probability.

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Bartlett’s apprentice

David Kendall (1918-2007)*Kendall’s boss tells him:“I’ll give you a week to learnthe subject. Go up to London,and stay in Anscombe’slodgings. You’ll help himduring the day with whateverhe’s been doing.”

Oxford First in 1939 Career in astronomy or analysis? March 1940 joins PDE andbegins works as a “computer” Becomes a statistician Replaces Anscombe as Bartlett’s assistant After war follows Bartlett into applied stochastic processes In 1953+ works with Harry Reuter on stochastic processes a la Doob .

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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

Manchester from 1946 working on differential equations

Starts in probability in 1951

Ties up with Kendall 1953

Professor of Pure Mathematics at Durham 1959-65

Harry Reuter(1921-92) in 1963

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The students Planned careers diverted—examples C A B Smith Oscar Kempthorne Frank Anscombe

Unplanned/unwanted careers national need for statisticians—stats teaching for

all Statistical war work A major destination—SR17

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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

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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.

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Oscar Kempthorne (1919-2002)

Entered in 1937

Part III distinction 1940

Department of Tank Production, Ministry of Supply

Rothamsted 1941

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Cambridge mathematics teaching at Warnumbers of male undergraduates in 2 wars year total year total1914 150 1939 1401915 86 1940 1401916 43 1941 1011917 25 1942 721918 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

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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)

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Student reviewsof 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

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The Committee: choice or no choice

James Durbin: 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)

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Other destinations of 20/60s Armed forces John Nelder (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

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Sent to be a statistician Going alone e.g. Cox to Department of Structural and Mechanical

Engineering at RAE Farnborough Denis Sargan “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 Winsten37

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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

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Statistical knowledge + connections

Seniors Edward van Rest (born 1901) worked on forestry statistics pre-war Anscombe was young but already experienced Barnard, the main source of ideas, was self-taught

Barnard with R. A. Fisher around 1957George Barnard (1915-2002)graduated from Cambridge and wentto Princeton to do mathematical logic.Frank Smithies was a friend there.Connection with Smithies got himinto SR 17.

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SR 17: the work I

Geoff Jowett we were sent round ordinance factories to install

quality control charts and sampling inspection schemes …

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

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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

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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

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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

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What then for the wartime recruits? Finishing degree Most return to being students. Delicious

anomalies: Artillery Major Hammersley JRSSauthor 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

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Not quite the new dawnso recalled David Cox

“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.”

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LiteraturePapers 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

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Inter-war period

John Aldrich (2009) England 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