JulianaThurston at 13:52, 25 January 2026

2026-01-25T13:52:22Z

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{{Short description|Hungarian mathematician}}
{{Infobox scientist
| name = Abraham Wald
| image = Abraham Wald in his youth.jpg
| caption = A young Wald
| birth_date = {{birth date|1902|10|31}}
| birth_place = [[Cluj-Napoca|Kolozsvár]], [[Kingdom of Hungary]], [[Austria-Hungary]]
| death_date = {{death date and age|1950|12|13|1902|10|31}}
| death_place = [[Nilgiri Mountains]], [[India]]
| field = [[Mathematics]] [[Statistics]] [[Mathematical economics|Economics]]
| work_institutions = [[Columbia University]] [[Cowles Commission for Research in Economics]]
| alma_mater = [[Babeș-Bolyai University|King Ferdinand I University]] [[University of Vienna]]
| doctoral_advisor = [[Karl Menger]]
| doctoral_students = [[Herman Chernoff]] [[Meyer Abraham Girshick]] [[Milton Sobel]] [[Charles Stein (statistician)|Charles Stein]]
| known_for = [[Wald's equation]] [[Wald test]] [[Wald distribution]] [[Wald–Wolfowitz runs test]] [[Wald's martingale]] [[Wald's maximin model]] [[Mann–Wald theorem]] [[Decision theory]] [[Sequential analysis]] [[Sequential probability ratio test]]
| author_abbrev_bot =
| author_abbrev_zoo =
| prizes =
| footnotes =
| children = [[Robert Wald]]
| signature =
}}

'''Abraham Wald''' ({{IPAc-en|w|ɔː|l|d}}; {{IPA|de|valt|lang}}; {{langx|hu|Wald Ábrahám}}, {{langx|yi|אברהם וואַלד}}; {{birth date|1902|10|31|df=y}} – {{death date|1950|12|13|df=y}}) was a Hungarian and American mathematician and statistician who contributed to [[decision theory]],<ref name=DuppeWeintraub2015>{{cite journal
| author = Duppe, Till
| author-link = Till Duppe
| author2= Weintraub, E. Roy
| author2-link = E. Roy Weintraub
| journal = History of Political Economy
| volume = 48
| issue = 191
| pages = 635–655
| year = 2015
| title = Losing Equilibrium: On the Existence of Abraham Wald's Fixed-Point Proof of 1935
| publisher = Econometrica, Vol. 19, No. 4
| doi = 10.1215/00182702-3687283
| hdl = 10419/149731
| hdl-access = free
}}</ref> [[geometry]] and [[econometrics]], and founded the field of [[sequential analysis]].<ref name=Morgenstern1951>{{cite journal
| doi = 10.2307/1907462
| author = Morgenstern, Oskar
| author-link = Oskar Morgenstern
| journal = Econometrica
| volume = 19
| issue = 4
| pages = 361–367
| year = 1951
| title = Abraham Wald, 1902–1950
| publisher = Econometrica, Vol. 19, No. 4
| jstor = 1907462
}}</ref> One of his well-known statistical works was written during [[World War II]] on how to minimize the damage to bomber aircraft and took into account the [[survivorship bias]] in his calculations.<ref name="Mangel1984">{{cite journal |last1=Mangel |first1=Marc |last2=Samaniego |first2=Francisco J. |title=Abraham Wald's Work on Aircraft Survivability |journal=Journal of the American Statistical Association |date=June 1984 |volume=79 |issue=386 |pages=259–267 |doi=10.1080/01621459.1984.10478038 |publisher=[[American Statistical Association]] |url=http://people.ucsc.edu/~msmangel/Wald.pdf |jstor=2288257}}</ref> He spent his research career at [[Columbia University]]. He was the grandson of Rabbi [[Moshe Shmuel Glasner]].

== Life and career ==
[[File:Abraham Wald.jpg|thumb|left|upright|Photograph of Abraham Wald from the [[Oberwolfach Research Institute for Mathematics]]]]
Wald was born on 31 October 1902 in [[Cluj-Napoca|Kolozsvár]], [[Transylvania]], in the [[Kingdom of Hungary]]. A religious [[Jew]], he did not attend school on Saturdays, as was then required by the Hungarian school system, and so he was [[homeschooled]] by his parents until college.<ref name=Morgenstern1951/> His parents were quite knowledgeable and competent as teachers.<ref>{{MacTutor Biography|id=Wald}}</ref>

In 1928, he graduated in mathematics from the [[Babeș-Bolyai University|King Ferdinand I University]].<ref>Anuarul Universității Regele Ferdinand I pe anul școlar 1927/28. p. 187. [http://documente.bcucluj.ro/web/bibdigit/periodice/anuaruluniversitatiidincluj/1927-1928/BCUCLUJ_FP_452283_1_1927_1928_007_0001.pdf Online access], University Library in Cluj, Romania.</ref> In 1927, he had entered [[Postgraduate education|graduate school]] at the [[University of Vienna]], from which he graduated in 1931 with a Ph.D. in mathematics. His advisor there was [[Karl Menger]].<ref name=Morgenstern1951/><ref name=DuppeWeintraub2015/>

Despite Wald's brilliance, he could not obtain a university position because of Austrian discrimination against Jews. However, [[Oskar Morgenstern]] created a position for Wald in economics. When [[Nazi Germany]] [[Anschluss|annexed Austria]] in 1938, the discrimination against Jews intensified. In particular, Wald and his family were persecuted as Jews. Wald emigrated to the [[United States]] at the invitation of the [[Cowles Commission for Research in Economics]], to work on econometrics research.<ref name=Morgenstern1951/> By September 1938 Wald was a Fellow of the Carnegie Corporation at Columbia University learning about modern English language statistics from [[Harold Hotelling]]. He was appointed to the Columbia Faculty in 1941 and remained there until his death.

[[File:Survivorship-bias.svg|thumb|left|The damaged portions of returning planes show locations where they can sustain damage and still return home; those hit in other places presumedly do not survive. (Image shows hypothetical data.)]]
During [[World War II]], Wald was a member of the [[The Statistical Research Group of World War II|Statistical Research Group]] (SRG) at [[Columbia University]], where he applied his statistical skills to various wartime problems.<ref name="Wallis1980">{{cite journal|doi=10.1080/01621459.1980.10477469 | volume=75 | issue=370 | title=The Statistical Research Group, 1942–1945 | journal=Journal of the American Statistical Association | pages=320–330| year=1980 | last1=Wallis | first1=W. Allen |jstor=2287451}}</ref> There was a difficulty: the work was secret and Wald was officially an enemy alien and, as such, barred from access to restricted matter. Hotelling recounts, “This impasse led to a facetious suggestion that each page he wrote should immediately be snatched away and never shown to him again, but was resolved when a federal court granted him a hearing long before his turn on the docket and promptly naturalized him.” <ref>{{cite journal |last=Hotelling|first= Harold|title= Abraham Wald |journal= American Statistician|date=1951|volume=5 |issue=1 |pages=18–19|doi= 10.1080/00031305.1951.10481914}}</ref>

The problems that the SRG worked on included methods of sequential analysis and sampling inspection.<ref name="Wallis1980" /> Another was to examine the distribution of [[Survivorship bias#Military|damage to aircraft returning after flying missions]] to provide advice on how to minimize bomber losses to enemy fire. Wald derived a useful means of estimating the damage distribution for all aircraft that flew from the data on the damage distribution of all aircraft that returned.<ref name="Mangel1984" /><ref name=Wald1943>{{cite tech report |first=Wald |last=Abraham |title=A Reprint of 'A Method of Estimating Plane Vulnerability Based on Damage of Survivors' |number=ADA091073 |institution=Center for Naval Analyses; [[Statistical Research Group]], [[National Defense Research Committee]] |via=[[Defense Technical Information Center]] |date=1980 |orig-date=1943 |url=https://apps.dtic.mil/sti/pdfs/ADA091073.pdf|archive-url=https://web.archive.org/web/20210512125414/https://apps.dtic.mil/sti/pdfs/ADA091073.pdf|url-status=live|archive-date=May 12, 2021}}</ref> His work is considered seminal in the discipline of [[operational research]], which was then fledgling.

Wald and his wife died in 1950 when the [[Air India]] plane (VT-CFK, a DC-3 aircraft<ref>{{cite web |title=Aircraft accident Douglas C-47B-5-DK (DC-3) VT-CFK Kotagiri |url=https://aviation-safety.net/database/record.php?id=19501213-1 |website=[[Aviation Safety Network]] |publisher=[[Flight Safety Foundation]] |date=26 September 2021}}</ref>) in which they were travelling crashed near the [[Rangaswamy Peak and Pillar|Rangaswamy Pillar]] in the northern part of the [[Nilgiri Mountains]], in southern [[India]], on an extensive lecture tour at the invitation of the Indian government.<ref name=Morgenstern1951/> He had visited the [[Indian Statistical Institute]] at Calcutta and was to attend the Indian Science Congress at Bangalore in January. Their two children were back at home in the United States.<ref>{{cite news|url=http://spectatorarchive.library.columbia.edu/cgi-bin/columbia?a=d&d=cs19501215-01|title=Prof. Wald Reported Among Victims of India Plane Crash|date=15 December 1950|newspaper=Columbia Daily Spectator|access-date=2018-02-08|issue=52|volume=XCV|page=1}}</ref>

After his death, Wald was criticized by Sir [[Ronald A. Fisher]] [[Fellow of the Royal Society|FRS]]. Fisher attacked Wald for being a mathematician without scientific experience who had written an incompetent book on statistics. Fisher particularly criticized Wald's work on the design of experiments and alleged ignorance of the basic ideas of the subject, as set out by Fisher and [[Frank Yates]].<ref name=Fisher1955>{{cite journal
|title=Statistical methods and scientific induction
|author-link=Ronald A. Fisher |first=Ronald |last=Fisher
|journal=Journal of the Royal Statistical Society, Series B
|volume=17
|year=1955
|pages=69–78
|jstor=2983785
|issue=1
|doi=10.1111/j.2517-6161.1955.tb00180.x }} (criticism of statistical theories of [[Jerzy Neyman]] and Abraham Wald)</ref> Wald's work was defended by [[Jerzy Neyman]] the next year. Neyman explained Wald's work, particularly with respect to the design of experiments.<ref name=Neyman1956>{{cite journal
|title=Note on an Article by Sir Ronald Fisher
|author-link=Jerzy Neyman |first=Jerzy |last=Neyman
|journal=Journal of the Royal Statistical Society, Series B
|volume=18
|year=1956
|pages=288–294
|jstor=2983716
|issue=2
|doi=10.1111/j.2517-6161.1956.tb00236.x }} (reply to Fisher 1955)</ref> [[Lucien Le Cam]] credits him in his own book, ''Asymptotic Methods in Statistical Decision Theory'': "The ideas and techniques used reflect first and foremost the influence of Abraham Wald's writings."<ref name=LeCam1986>{{cite book
|title=Asymptotic Methods in Statistical Decision Theory
|author-link=Lucien Le Cam |first=Lucien |last=Le Cam
|year=1986
|pages=xiii
}}</ref>

He is the father of the noted American physicist [[Robert Wald]].

== Notable publications ==
For a complete list, see {{citation
| year = 1952
| title = The Publications of Abraham Wald
| journal = Annals of Mathematical Statistics
| volume = 23
| issue = 1
| pages = 29–33
| doi = 10.1214/aoms/1177729483
| doi-access = free
}}
* {{citation
| doi = 10.2307/1906982
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| journal = Econometrica
| volume = 7
| issue = 4
| pages = 319–331
| year = 1939
| title = A New Formula for the Index of Cost of Living
| publisher = Econometrica, Vol. 7, No. 4
| jstor = 1906982
}}
* {{citation
| doi=10.1214/aoms/1177732144
| first=Abraham
| last=Wald
| author-mask = 1
| ref = none|journal=Annals of Mathematical Statistics
| volume=10
| issue=4
| pages=299–326
| year=1939
| title=Contributions to the Theory of Statistical Estimation and Testing Hypotheses
| url=https://projecteuclid.org/download/pdf_1/euclid.aoms/1177732144
| doi-access=free
| bibcode=1939AnnMS..10..299W
}}
* {{citation
| doi = 10.1214/aoms/1177731868
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| journal = Annals of Mathematical Statistics
| volume = 11
| issue = 3
| pages = 284–300
| year = 1940
| title = The Fitting of Straight Lines if Both Variables Are Subject to Error
| doi-access = free
| bibcode = 1940AnnMS..11..284W
}}
* {{citation
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| title = Sequential Tests of Statistical Hypotheses
| journal = The Annals of Mathematical Statistics
| volume = 16
| issue = 2
| date=June 1945
| pages = 117–186
| doi = 10.1214/aoms/1177731118
| doi-access = free
}}
* {{Cite book
| first = Abraham
| last = Wald
| author-mask = 1
| ref = none
| title = Sequential Analysis
| year = 1947
| publisher = [[John Wiley and Sons]]
| location = [[New York City|New York]]
}} Reprinted, Dover publications, 1973, {{isbn|0-486-43912-7}}.
* {{cite book
| first=Abraham
| last=Wald
| author-mask = 1
| ref = none
| title=Statistical Decision Functions
| year=1950
| publisher=[[John Wiley and Sons]], New York; [[Chapman and Hall]], London
| page=ix+179
}}<ref>{{citation|author=Robbins, Herbert|author-link=Herbert Robbins|title=Review: A. Wald, ''Statistical decision functions''|journal=Bull. Amer. Math. Soc.|year=1951|volume=57|issue=5|pages=383–384|url=http://projecteuclid.org/euclid.bams/1183516235|doi=10.1090/S0002-9904-1951-09520-8|doi-access=free}}</ref>

== References ==
{{Reflist}}

== Further reading ==
* {{cite journal
| author = Wolfowitz, Jacob
| author-link = Jacob Wolfowitz
| year = 1952
| title = Abraham Wald, 1902–1950
| journal = Annals of Mathematical Statistics
| volume = 23
| issue = 1
| pages = 1–13
| doi = 10.1214/aoms/1177729480
| doi-access = free
}}
* {{cite web |last1=Casselman |first1=Bill |author-link=Bill Casselman |title=The Legend of Abraham Wald |url=http://www.ams.org/publicoutreach/feature-column/fc-2016-06 |website=Feature Column |publisher=[[American Mathematical Society]] |date=June 2016 |access-date=29 May 2020}}

== External links ==
* {{MathGenealogy|id=36887}}
*[https://apps.dtic.mil/sti/citations/ADA091073 ''A Method of Estimating Plane Vulnerability Based on Damage of Survivors'' by Abraham Wald, Defense Technical Information Center 1943]

{{Authority control}}

{{DEFAULTSORT:Wald, Abraham}}
[[Category:1902 births]]
[[Category:1950 deaths]]
[[Category:Scientists from Cluj-Napoca]]
[[Category:Jews from Austria-Hungary]]
[[Category:Jewish emigrants from Austria after the Anschluss to the United States]]
[[Category:Emigrants from Austria after the Anschluss to the United States]]
[[Category:Presidents of the Institute of Mathematical Statistics]]
[[Category:Fellows of the American Statistical Association]]
[[Category:Hungarian statisticians]]
[[Category:Econometricians]]

[[Category:Columbia University faculty]]
[[Category:Jewish American scientists]]
[[Category:Victims of aviation accidents or incidents in India]]
[[Category:20th-century Hungarian mathematicians]]
[[Category:Babeș-Bolyai University alumni]]
[[Category:University of Vienna alumni]]
[[Category:Mathematical economists]]
[[Category:Hungarian operations researchers]]
[[Category:Functional analysts]]
[[Category:American operations researchers]]
[[Category:20th-century Hungarian economists]]
[[Category:Fellows of the Econometric Society]]
[[Category:Mathematical statisticians]]
[[Category:Victims of aviation accidents or incidents in 1950]]
[[Category:20th-century American statisticians]]

Abraham Wald - Revision history

JulianaThurston at 13:52, 25 January 2026