View source for Biography:Henry Mann

{{Short description|Mathematician and statistician (1905–2000)}}
{{other people}}
'''Henry Berthold Mann''' (27 October 1905, [[Place:Vienna|Vienna]] – 1 February 2000, Tucson)<ref>{{citation|url=http://www.math.ohio-state.edu/history/biographies/mann/|archive-url=https://web.archive.org/web/20110102153248/http://www.math.ohio-state.edu/history/biographies/mann/|archive-date=2011-01-02|publisher=Ohio&nbsp;State University, Department of Mathematics|title=Henry Berthold Mann: 1905-2000}}</ref> was a professor of [[Mathematics|mathematics]] and [[Statistics|statistics]] at the [[Organization:Ohio State University|Ohio State University]]. Mann proved the [[Mann's theorem|Schnirelmann-Landau conjecture]] in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the ("Mann-Whitney") ''U''-statistic of [[Nonparametric statistics|nonparametric statistics]].<ref name="Olson" >{{cite book|last=Olson|first=John|chapter=Henry&nbsp;B. Mann (with photograph)|title=Number&nbsp;theory and algebra: Collected papers dedicated to Henry&nbsp;B. Mann, Arnold&nbsp;E. Ross, and Olga Taussky-Todd|pages=xx-xxv|publisher=Academic Press [Harcourt Brace Jovanovich, Publishers]|year=1977|mr=469653|url=http://www.math.ohio-state.edu/history/biographies/mann|isbn=0-12-776350-3|editor-first=Hans|editor-last=Zassenhaus|location=New York-London}} (The web-link is to a slightly updated edition of the biography.)</ref> Mann published the first mathematical book on the [[Design of experiments|design of experiments]]: {{harvtxt|Mann|1949}}.<ref name="Johnson"/>

==Early life of a number theorist==
Born in [[Place:Vienna|Vienna]], [[Place:Austria-Hungary|Austria-Hungary]], to a Jewish family, Mann earned his Ph.D. degree in mathematics in 1935 from the [[Organization:University of Vienna|University of Vienna]] under the supervision of [[Biography:Philipp Furtwängler|Philipp Furtwängler]].<ref name="Olson"/><ref>{{MathGenealogy|id=9142}}</ref> Mann immigrated to the United States in 1938, and lived in New York, supporting himself by tutoring students.<ref name="Olson"/>

In [[Additive number theory|additive number theory]], Mann proved the [[Mann's theorem|Schnirelmann–Landau conjecture]] on the asymptotic density of sumsets in 1942.<ref>{{Cite book
  | last1 = Khinchin   | first1 = A. Ya.
  | title = Three Pearls of Number Theory
  | publisher = Dover
  | location = Mineola, NY
  | year = 1998
  | isbn = 978-0-486-40026-6
  | pages=27–28}}</ref> By doing so he established [[Mann's theorem]] and earned the 1946 Cole Prize.<ref name="Olson"/><ref>[https://www.ams.org/profession/prizes-awards/ams-prizes/cole-prize-number-theory Frank Nelson Cole Prize in Number Theory], American Mathematical Society, retrieved 2011-01-24.</ref>

==Statistics==
In 1942 the Carnegie Foundation awarded Mann a fellowship to learn statistics while assisting the [[Operations research|operations research]] group of [[Biography:Harold Hotelling|Harold Hotelling]] at [[Organization:Columbia University|Columbia University]]. His group also supported [[Biography:Abraham Wald|Abraham Wald]], and Wald and Mann collaborated on several papers. In statistics, Mann is known for the [[Mann–Whitney U test|("Mann–Whitney") ''U''-statistic]] and its associated hypothesis test for [[Nonparametric statistics|nonparametric statistics]]. Collaborating with Wald, Mann developed the Mann–Wald theorem of [[Asymptotic theory (statistics)|asymptotic statistics]] and [[Econometrics|econometrics]].<ref name="Olson"/>

Mann wrote the first mathematical book on the [[Design of experiments|design of experiments]] {{harvtxt|Mann|1949}}, whose principles allowed later statisticians to design and to analyze customized experiments. Like contemporary "self-help" and "how to"  books, the earlier books gave easy-to-follow examples but little theory beyond exhortations to follow three principles of Ronald A. Fisher—to "[[Replication (statistics)|replicate]]", to "establish control" (for example with [[Block design|blocking]]), and to "[[Randomization|randomize]]" ([[Random assignment|assignment of treatments to units]]). Earlier books provided useful examples of designed experiments along with the design's [[Analysis of variance|analysis of variance]], but no basis for constructing new designs for new problems, according to {{harvtxt|Johnson|1951}}.<ref name="Johnson">{{cite news|first=N.&nbsp;L.|last=Johnson|title=Review (of ''Analysis and Design of Experiments'' by H.&nbsp;B. Mann)|journal=Biometrika|volume=38|number=1–2| date=June 1951 |pages=260–261|jstor=2332334}}</ref>

According to Denis Conniffe: 
{{blockquote|
Ronald A. Fisher was "interested in application and in the popularization
of statistical methods and his early book ''[[Statistical Methods for Research Workers]]'', published in 1925, went through many editions and
motivated and influenced the practical use of statistics in many fields of
study. His ''Design of Experiments'' (1935) <!-- was also crucially fundamental
in the promotion of--> [promoted] statistical technique and application. In that book he
emphasized examples and how&nbsp;to&nbsp;design experiments systematically from
a statistical point of view. The mathematical justification of the methods
described was not stressed and, indeed, proofs were often barely sketched
or omitted altogether ..., a fact which led H.&nbsp;B.&nbsp;Mann to fill the gaps with a rigorous mathematical treatment in his well known treatise, {{harvtxt|Mann|1949}}."<ref name="Conniffe" >{{cite news|title=R.&nbsp;A. Fisher and the development of statistics—a view in his centenary year|last=Conniffe|first=Denis| publisher=Statistical and Social Inquiry Society of Ireland |location=Dublin|journal=Journal of the Statistical and Social Inquiry Society of Ireland| volume=XXVI|number=3|year=1990–1991|page=87 |hdl = 2262/2764|issn=0081-4776 |url=http://www.tara.tcd.ie/jspui/handle/2262/2764 }}</ref>
}}

==Later life==
In 1946 Mann returned to Ohio State University, where he served as a professor mathematics until his retirement in 1964. Mann then became a professor at the U.S. Army's Mathematics Research Center at the [[Organization:University of Wisconsin–Madison|University of Wisconsin–Madison]] 1964–1971. Mann was professor at the University of Arizona from 1971 to 1975.<ref name="Olson"/> His doctoral students include [[Biography:George Marsaglia|George Marsaglia]] and William Yslas Vélez. <!-- Continuing research during these years, Mann reported results of his own and his doctoral students in the second edition of his book on additive number&nbsp;theory ({{harvtxt|Mann|1976}}). -->

==Publications==
* {{Cite journal |last=Mann|first=Henry B. <!--  title=A proof of the fundamental theorem on the density of sums of sets of positive integers | doi=10.2307/1968807 | mr=0006748 | year=1942 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=43 | pages=523–527 | jstor=1968807 | issue=3 | publisher=Annals of Mathematics }}
* {{cite journal
 |first2=D. R. |last2=Whitney
 |title=On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other
 |journal=[[Annals of Mathematical Statistics]]
 |volume=18 |issue=1 |year=1947 |pages=50–60
 |doi=10.1214/aoms/1177730491
 |mr=22058 | zbl = 0041.26103
|doi-access=free}}
* {{cite book|last=Mann|first=H.&nbsp;B. <!-- title=Analysis and design of experiments: Analysis of variance and analysis&nbsp;of&nbsp;variance designs|publisher=Dover Publications,&nbsp;Inc|location=New&nbsp;York,&nbsp;N.&nbsp;Y.|year=1949|pages=x+195|mr=32177}}
* {{cite book|last=Mann|first=Henry B <!-- title=Introduction to algebraic number theory (With a chapter by Marshall&nbsp;Hall,&nbsp;Jr.)|publisher=The Ohio State University Press|location=Columbus, Ohio|year=1955|pages=vii+168|mr=72174}}
*{{cite book
|publisher=Robert&nbsp;E. Krieger Publishing Company
|location=Huntington, New York
|year=1976
|edition=Corrected reprint of&nbsp;1965 Wiley
|isbn=0-88275-418-1|mr=424744
}}

==References==
{{reflist|colwidth=30em}}


{{DEFAULTSORT:Mann, Henry Berthold}}
[[Category:American statisticians]]
[[Category:Number theorists]]
[[Category:Group theorists]]
[[Category:Econometricians]]

{{Sourceattribution|Henry Mann}}